Contingent laws about local regularities. Though certain kinds of events are ruled out as ontologically impossible by the necessary principles about local regularities, that leaves open many ways for bits of matter to behave. Indeed, it leaves open the possibility that no change actually takes place at all. But if bits of matter in space do change as time passes, they must change in determinate ways, and how they move and interact is what is described by the basic laws of physics. Since that is something that can be known only by observing what happens in nature, those regularities are not ontologically necessary. Assuming that they have ontological causes, they depend on the specific kind of matter and specific kind of space that constitute the actual world. Thus, although spatiomaterialism explains the basic nature of what exists, ontological philosophy needs to make additional assumptions about the specific essential natures of the matter and space it postulates in order to explain the truth of the basic laws of physics.

The properties mentioned in basic laws of physics are called “physical properties,” and as noted in Properties, ontological philosophy takes physical properties to characterize the extrinsic essential aspects of the nature of matter and space. (Intrinsic essential natures, by contrast, are what explain phenomenal properties.) And in the same way that physical properties (and spatial relations) are explained as aspects of the basic substances constituting the world, basic physical laws describing how they change can be explained as aspects of those substances as they endure through time.

If the matter postulated by an ontology were simply assumed to have whatever essential nature is required to make the basic laws of physics true, there would be no genuine ontological explanation of why the basic physical laws are true. That is what materialism does (hence, its other name, “physicalism”). Indeed, that is the only way that physical properties can be introduced by materialism, because when space is reduced to spatial relations among bits of matter (as materialism does, being implicitly committed to spatial relationism), matter is the only possible ontological cause of physical properties and regularities about how they change over time. But a spatiomaterialist ontology recognizes two basically different ontological causes, and so space can work together with matter to constitute properties, relations, and how they change over time. When it comes to explaining the truth of physics, therefore, what ontological philosophy is looking for is a description of a more specific essential nature of matter and space such that, when space contains all the bits of matter, objects have physical properties and spatial relations which change in the ways described by the basic laws of physics.

It may not be surprising that spatiomaterialism can explain the truth of the physics that prevailed at about the end of the 19^th Century, because classical physics afforded an intuitive understanding of the laws of physics, as descriptions of how material substances move and interact in space as time passes and it assumed that space and time are absolute. What cast doubt on the possibility of a spatiomaterialist explanation were the revolutions that spawned contemporary physics. In particular, relativity theory seems to deny that space and time are absolute, as spatiomaterialism requires. Thus, instead of looking for a spatiomaterialist ontology that would make relativity theory (and the other laws of physics) true, contemporary physicists see the “holy grail of physics” as merely discovering a “Theory of Everything,” that is, a single law from which all the other laws can be derived.

At present, there are four basic laws of physics, each describing one of the four basic forces that are now thought to be at work in nature (electromagnetism, the strong force, the weak force, and gravitation), and the task that physics has set itself is to discover a single law that entails (together with suitable initial and boundary conditions) all four of those laws. (That seems possible in the case of the first three, because they can all be formulated as gauge field theories, but attempts to formulate Einstein’s general theory of relativity in a compatible way have been forced to assume that there are as many ten or eleven dimensions to space )

To take the goal to be the discover of a single, basic law is to assume that efficient-cause explanations are the most basic explanations that physics can give. And since ontology itself is not assumed to be explanatory, the only entities that contemporary physics takes to be real are those referred to by the basic law of physics, that is, scientific realism.

Ontological philosophy, on the other hand, assumes that ontology itself is explanatory. That is what led us to recognize that the world is constituted by space as well as matter. Thus, we now expect space and matter to work together is some way to explain the truth of the basic laws of physics and, thereby, the truth of its efficient-cause explanations. Indeed, one of the mortgages we took out in order to use spatiomaterialism as our ontological foundation in proving necessary truths was the promise to give such an explanation of Einstein’s two relativity theories. We promised to show that even though we must take space and time to be absolute, it is possible to describe more specific essential natures of matter and space that would entail the truth of the special and general theories of relativity. But in order to lay the foundation for such a theory, we must first describe more specific essential natures of matter and space that would entail the truth of the laws of classical physics.

The attempt to discover the specific essential natures of matter and space in the actual world is, however, a project resembling empirical science, for it would have to discover which essential nature(s) of matter and space afford the best ontological explanation of the truths of the basic laws of physics in a spatiomaterial world. That is a project of empirical ontology, but nothing so definitive is claimed for what is sketched here. All that is required here is proof that it is possible to give such an ontological explanation of the truth of physical laws, for that will show that spatiomaterialism is not falsified by what is found empirical in nature by physics and, thus, that ontology affords a new approach to philosophy. Thus, though this sketch of how more specific essential natures of matter and space explain their truth will show that a deeper explanation is possible, it may not be the best ontological explanation of physics. That job can be left to ontology as branch of empirical, natural science that is more basic than physics.

Once it is recognized that ontological-cause explanation are prior to efficient-cause explanations, finding the best ontological explanation will become the “holy grail” of the most basic branch of natural science. Unlikely as it may seem now, physicists will eventually welcome substantivalism about space, because it opens up the possibility of a deeper explanation of the world and what physicists really want is the deepest possible explanation that can be supported by the empirical method. As we shall see, for example, it solves the current puzzle about the relationship between gravitation and the other three basic forces of nature.

Contingent laws: Classical physics. We begin with the spatiomaterialist ontological explanation of the truth of the basic laws of classical physics, including Newton’s laws of motion and gravitation and Maxwell’s laws of electromagnetism. If they can be explained ontologically, we can be confident that the rest of classical physics can also be explained ontologically, for the basic physical laws are like the axioms of a formal system and the rest of physics are like theorems that follow from them. That is basically the strategy we used for mathematics, ontologically explaining the truth of the axioms of set theory from which the rest of mathematics follows.

Though classical physicists assumed that space is absolute, they did not try to give an ontological explanation of the truth of the basic physical laws based on space being a substance. They did not recognize the validity of ontological explanations, and so they did not think of space as a substance that works together with matter to make the regularities being described true. Indeed, the action at a distance implied by Newton’s law of gravitation must have made any such project seem hopeless. Instead, their aim was to formulate physical laws mathematically so that they could make quantitatively precise predictions of the measurements that would be made in experimental situations. That method turned out to be a powerful means of seeing into the nature of the world, most spectacularly by revealing the nature of micro-processes, though by leaving out the deeper ontological explanation, it also made the Einsteinian revolution inevitable, as we shall see.

The simplest way to describe the specific natures of matter and space that would explain the truth of classical physics is to start by cataloging all the different entities mentioned by the laws of physics and showing how the forms of matter required to account for them all would, by being contained by space and enduring through time, make the regularities described by the basic laws of classical physics true. That method will leave some aspects of those regularities built into the natures that the kinds of matter and space that are assumed to constitute a spatiomaterial world like ours. But enough of those regularities will be given a genuine explanation to show that an ontological explanation of classical physics is possible -- and to lay the foundation for explaining how the basic laws of contemporary physics could be true in a spatiomaterial world.

Forms of matter. Though we cannot assume anything about the nature of matter or space that contradicts spatiomaterialism, there are many different possible spatiomaterial worlds. It is mainly the more specific nature of matter that we will be concerned with in explaining the truth of classical physics, and in any given spatiomaterial world, bits of matter may come in various forms, each with different ways of moving, interacting and being related to bits of matter in other forms.

Indeed, we will have to assume that matter takes qualitatively different forms, because the basic laws of classical physics mention entities that are as different from one another as material objects and light. Every basic entity mentioned by physics as having a location in space and time must be explained as matter contained by space.

A promising way to inventory all the basic forms of matter required to explain the laws of classical physic ontologically is to take as our working hypothesis that what is conserved according to the principles of the conservation of mass and energy is the quantity of the matter contained by space. Conservation of mass and energy is one of the most basic principles of contemporary physics, and this ontological thesis is a plausible interpretation of it. Indeed, when the principle was first recognized by physics, it was heralded as empirical confirmation of the traditional materialist view that physical processes are made up of substances that endure through time. Let us, therefore, take it as our working hypothesis.

The principle of the conservation of mass and energy holds that in any closed or isolated region of space, there is a certain quantity of mass and energy that never changes, regardless what happens there. That quantity could be the total quantity of matter, for that hypothesis would explain two aspects of the principle.

First, since matter is a substance, it neither comes into existence nor goes out of existence as time passes, and thus, it is conserved. Hence, the quantity of mass and energy could be the quantity of matter.

Second, the principles of local motion and local action explain why the quantity of matter does not change under the conditions described by the principle of conservation of mass and energy. If the only way that bits of matter can change location is by motion, they cannot change their location from inside the closed or isolated region to outside, or vice versa, unless they cross the boundary, and that is excluded. Nor can bits of matter outside the closed region affect what happens to the bits of matter inside, since that would involve action at a distance, contrary to the principle of local action (unless something moved across the boundary between inside and outside to mediate the force, which is excluded).

Let us set aside the peculiar effects that bits of matter may have on one another that are mediated by space itself, since they are not relevant to classical physics. As we shall see, there are always such effects crossing the boundaries, but they do not violate this conservation principle, because, as it turns out, they carry neither energy nor mass.

Thus, it is plausible that the quantity to which classical physics is referring in the principle of the conservation of mass and energy is the total quantity of matter in closed or isolated regions of space.

There is, however, one aspect of contemporary physics that is relevant at this point in our argument. Though mass and energy were thought to be conserved separately in classical physics, Einstein discovered, as a consequence of his special theory of relativity, the famous equation connecting them (E=mc²). That is further evidence that mass and energy are just different forms of the same basic material substance, because if they were different forms of matter, we would expect them to be commensurable.

Indeed, the suggestion that they are basically the same stuff has turned out to be true, for there are actual physical processes in which they are converted into one another, most spectacularly in the nuclear reactions used in nuclear weapons (fission and fusion).

The conservation of mass and energy is now seen as a consequence (or presupposition) of the basic laws of contemporary physics. It is a way of formulating what is called a “symmetry” about those laws, that is, something that is invariant as other things change. But that it to treat it formally, as a basic symmetry principle of contemporary physics, and here, it will be interpreted ontologically, as describing an aspect of the world that is caused by the permanence of the matter that coincides with space.

Furthermore, the conversion between mass and energy will be assumed here in order to explain the various forms of matter ontologically, quite apart from explaining any of the phenomena covered by Einstein’s special theory of relativity.

The assumption that all the forms of mass and energy described by physics are various forms of matter that coincide with space is just a working hypothesis. It will serve my purposes, because it is a simple and plausible way of laying out an ontological explanation of the laws of physics (classical and contemporary) and, as we shall see, it does show that there is at least one way that spatiomaterialism can explain them all ontologically. Though it may not be the best spatiomaterialist explanation of them, it will suffice to provide an ontological foundation for explaining the global regularities, because it will show that, for all that physics knows empirically, spatiomaterialism could be true.

This ontological explanation of the truth of the principle of conservation of mass and energy implies that there are as many different forms of matter as there are kinds of mass and energy recognized by physics in confirming this principle empirically. And in order to explain the truth of the laws of classical physics, we must recognize four (or, perhaps, six) qualitatively different forms of matter (with varieties of each). They are (1) material objects with rest mass, (2) the kinetic energy involved in the motion of rest masses, (3) the energy due to gravitation, and (4) the energy due to electromagnetism. (Since the latter two each involve two basically different forms of energy, as potential energy and as actual waves, they might better be counted as two forms of matter each, yielding a total of six.) Let us consider briefly how each kind of energy can be explained as a form of matter and then we will see how these forms of matter would explain ontologically the truth of the laws of classical physics.

Matter as material objects with (rest) mass. Material objects with rest mass are the form of matter that is usually intended when people think of matter. Ordinary material objects have definite locations in space and can be at rest. The quantity of rest mass in any such object (at rest) would be the quantity of matter constituting its existence. The endurance of matter through time would then explain the principle of the conservation of mass in classical physics.

Even at the altitude of classical physics, however, material objects have further properties. Since different material objects cannot occupy the same places at the same times, some sort of interaction keeps them from doing so, when their motion would otherwise bring them to the same location. Such interactions are explained in physics by forces that the objects exert one another.

Thus, we will assume that some material objects have electric charges by which they can interact with other charged objects. And we will assume that every material object exerts a gravitational force by which it attracts every other material object. Such forces are, as we shall see, aspects of the matter that exists in the form of rest mass, and since these aspects involve regularities about change, they are dispositional properties.

However, since the forces are spread out in the space surrounding where the material object with rest mass is located, we must assume that some of the matter constituting its existence is somehow spread out in space, for otherwise the matter would not be able to explain the forces that the material objects exert. But as we shall see, all the matter constituting the material object is counted in its rest mass, and the object interacts as if all its (rest) mass were concentrated at its center, where the material object itself is said to be located.

We will also assume, as classical physics did, that ordinary material objects, such a billiard balls and cream puffs, are composed of simpler material objects, such as “atoms,” the parts of atoms (protons, neutrons and electrons), and the parts of parts of atoms (such as quarks), though we will also leave the natures of these particles and the forces binding them together unexplained until we take up contemporary physics.

The simplest parts of material objects are now known to be particles that are quite unlike material objects in various ways, but I will just assume that they can also be explained ontologically by spatiomaterialism until I show that the truth of quantum mechanics can be explained ontologically by spatiomaterialism. (The nature of the basic particles of physics is explained ontologically in Change: Cosmology: Basic objects.)

Kinetic matter. All the other forms of matter recognized by classical physics are classified as energy by physics, and the most surprising implication of this ontological explanation of classical physics is probably that kinetic energy is a form of matter, for it means that the motion of objects with rest mass is itself a form of matter. There is no way to avoid this implication, given our working hypothesis, because even in classical physics, kinetic energy can be converted into other forms of energy (such a light and potential energy), and other forms of energy can be converted into kinetic energy.

To hold that kinetic energy is a form of matter is to hold that the motion of a material object is constituted by a bit of matter that exists in addition to the matter counted in the (rest) mass of the material object. This bit of matter must somehow be attached to (and, therefore, located with) the matter that makes up the rest mass of the material object, and as a result, both must coincide with space in a way that carries it and the material object across space as time passes. Let us call it “kinetic matter.” More will be said about the essential nature of matter in this form when we take up quantum mechanics, but for now we need only recognize that quantitatively different varieties of kinetic matter would propel objects at different speeds or in different directions. Kinetic matter would be like a motor, except that instead of consuming energy, it is just a bit of matter that endures through time as a substance, and thus, as long as it continues to exist in that form, the material object continues to move. There are, however, interactions by which kinetic matter can be transferred to other material objects, supplemented with kinetic matter transferred from other material objects to join it, and converted into other forms of matter.

To treat kinetic energy as a form of matter is to depart from the received understanding of physics. Kinetic energy is usually treated abstractly as just another quantity that is mentioned in the laws of physics and must be taken into account in order to predict or control what happens in particular situations. When we think of kinetic energy as a form of matter, however, we expect to find other properties that it must have, and that is what leads to a deeper ontological explanation. Kinetic matter must be located, as we have assumed, with the rest mass that it is moving, and as we shall see in explaining quantum mechanics ontologically, kinetic matter has other properties that explain the quantitative relationship between kinetic energy and momentum.

The other forms of matter into which kinetic matter can be converted are those postulated in order to explain gravitation and electromagnetism. Gravitation and electromagnetism are forces that material objects exert on one another, and in order to explain the distinctive kind of energy involved in each, we will assume that the forces themselves are a form of matter. That is, the energy (or matter) associated with these forces can exist in two different forms, potential or actual (that is, as forces being exerted by material objects or as waves of forces that exist independently of material objects).

Potential energy. Potential energy is the energy that material objects have when they exert forces on one another. Such forces must be a form of energy, because they can change how the objects involved are moving.

The amount of potential energy that exists in any situation depends on the distance across which the forces can continue to accelerate the objects involved. When the distance is maximum, the potential energy is maximum. But physics sets the maximum quantity at zero. Thus, any subsequent state in which some potential energy has been converted into kinetic energy (or into some other form of energy) is counted as negative potential energy. This is sometimes said to be just a mathematical convention, but according to this ontological explanation of potential energy, it represents the fact that the kinetic energy acquired by objects being accelerated is another form of the same matter that previously existed in the form of potential energy, that is, as forces being exerted by the material objects.

As suggested above, some of the matter making up a material object that exerts a force must be conceived as being spread out in the space around it as a force field, and that matter is counted as part of its rest mass. When potential energy is consumed, objects accelerate, changing the positions of the objects that were exerting the forces. That alters the force field they jointly impose on space, and the result is a reduction in the quantity of matter constituting those forces and, thus, the material objects themselves. That is, the material objects lose rest mass as their potential energy is consumed as kinetic energy, because some of the matter counted in the rest mass is converted from constituting a force field to constituting the motion of objects with rest mass.

On this ontological theory, therefore, the reason that the potential energy that is consumed as kinetic energy is negative (rather than just a smaller positive quantity) is that the kinetic energy must be subtracted from the rest masses of the material objects that were exerting the forces in order to balance the account. The kinetic energy is a different form of the same bits of matter that previously existed as forces being exerted by the objects. Thus, at the end of such a process, when as much kinetic (or other) energy has been actualized as possible in the situation, the material objects are in a position where their forces cannot accelerate one another and more, and the potential energy is some negative quantity. And since the total quantity of energy (or matter) involved in the process does not change as time passes, the principle of the conservation of mass and energy is true.

Though the equivalence of mass and energy is entailed by Einstein’s special theory of relativity, it is assumed here, as I warned earlier, in order to explain ontologically the conversion of energy between kinetic and potential forms.

The matter that explains potential energy is, therefore, included as part of the matter that explains the (rest) masses of material objects, and as we shall assume, it is the matter that constitutes the forces exerted by the object. Since those forces are spread out in space like a field, this is to take the force field to be a form of matter that coincides with all those parts of space. Likewise, the strength of the force at any point in space will be taken as a measure of the “thickness” of the matter coinciding with space at that point. And the total potential energy that can be converted to kinetic energy (or other forms of energy) depends on the total amount of matter in this form that exists along the pathway of the object being accelerated (which depends on the length of the path and the “thickness” of the matter at each point along the path)

To be sure, this ontological assumption will seem empirically unwarranted from the point of view of inferring to the best efficient-cause explanation. What happens in the relevant situations can be predicted with laws describing the forces and descriptions of the locations of the kinds of objects involved, without any need to refer to matter making up the forces involved. In the received formulations of physics, force fields are usually explained as spatially variable dispositions, that is, in terms of regularities about how material objects of certain kinds would be accelerated, if they were located there. But ontologically speaking, there must be a substance located there to accelerate the body, and though this description of matter in the form of potential energy does not tell us much more about it than is described by the relevant laws of physics, it does make us look for further properties of such force-field matter. Such properties will be described in the ontological explanations of Einstein's general theory of relativity and quantum mechanics.

More generally, furthermore, remember that we already have empirical reasons for believing that space and matter are substances, and what is at issue is whether the laws of physics can be descriptions of regular changes in the aspects the basic substances we have postulated. This is not an attempt to show that physics must recognize matter in these forms in order to predict what will happen, but only that it can and, thus, that physics provides no reason do doubt that spatiomaterialism is true.

Energy as waves of forces. If forces are a part of the matter constituting the rest mass of a material object that is spread out in space around it, then references to that matter by way of rest masses and as negative energy are indirect, and they obscure its real nature. Moreover, there is other evidence that forces are a form of matter, for such forces can also exist independently of material objects (that is, when they are not counted as part of their rest masses). They exist as light waves, in the case of electromagnetism, and as gravitational waves, though the latter were not recognized until Einstein’s discovery of the general theory of relativity. In both cases, the waves propagate across space on their own, and since they act on objects that they encounter in their paths like forces of the appropriate kind, those waves are best explained as matter existing in much same form that helps constitute the rest masses of material objects, except that it now exist independently of material objects. But given the difference between its form as part of the rest mass of material object and its form as an independently existing wave, we should probably postulate two different forms of matter for each kind of energy, gravitational and electromagnetic (yielding six forms of matter in all).

Gravitational matter. The nature of the force of gravity was problematic in classical physics, because it was supposed to enable material objects to act on one another at a distance, and an adequate ontological explanation of it cannot be given here until we take up the spatiomaterialist interpretation of Einstein’s general theory of relativity. According to Newton, gravity is a universal force of attraction among material objects whose strength is in proportion to the products of their masses and inversely proportional the square of the distance separating them. When material objects (and energy) have accumulated at a certain location in space, as in planets and stars, the gravitational force is strong enough to make an enormous difference in what happens in the surrounding space.

According to contemporary physics, the mass that is responsible for gravitation is not just the rest masses of the material objects, but also includes the mass equivalent of their kinetic energy and electromagnetic energy. That is readily explained by this ontological theory, if matter in all forms exerts gravitational forces, and it will be assumed here.

Without giving a deeper explanation of its nature, we can think of the gravitational force field as a form of matter that is spread out in the space around the center of gravity and has the power where it is located to accelerate towards itself other material objects that coincide with the same part of space. The strength of the force at any location as described by Newton’s law can be thought of as varying with the amount (or “thickness”) of matter in this form spread out in that part of space. But since the quantity of gravitational matter is already counted in the rest mass of the matter accumulated at that location, the force field is just an aspect of the accumulated matter (or an extrinsic property of the matter located there).

Though we are assuming that the gravitational force field is a form of matter in order to explain how classical physics is true, I promise to give a deeper ontological explanation of gravitational matter and how it is related to other forms of matter in making up the rest mass of a material object when we take up contemporary physics. But for now, spatiomaterialism leaves us no option but to recognize the gravitational force itself as a form of matter in some sense, for otherwise there would be nothing to exert the forces involved. Space by itself cannot exert gravitational forces, because they vary with location, whereas space is uniform throughout. But as we shall see, gravitational matter can be a condition of space that is imposed on it by the accumulation of matter at a nearby location.

Gravitational potential energy is the matter that can be extracted from material objects because they are so located relative to one another in space that the gravitational forces that they exert on one another can accelerate them toward one another. When gravitation accelerates material objects to the some location, they acquire kinetic energy, and when they collide, some of it may be turned into other forms of energy. Though that means, on this ontological explanation, that the material objects involved have less rest mass than they did when they were still attracting one another across the distance separating them, there is no violation of the principle of the conservation of mass and energy, because the missing rest mass is now counted as the kinetic (and other forms) of energy of the objects at the center. The reason that classical physics does not recognize that the rest masses of the material objects at the center of gravitation have become less than they were before they accumulated there is that it assumes that any potential energy that is less than the maximum possible is a negative quantity.

In particular, it is possible to hold that the kinetic (and other forms of) energy that material objects acquire as they accelerate toward one another comes from the gravitational matter that was spread out in the space between them, because the motions of the objects so alters the force field between them that less gravitational matter is required for them to exert a gravitational force on one another.

The total matter, both rest mass and forms of energy, accumulated at the center of gravitation determines the strength of the gravitational field around that center, and the field is stronger than it was when the material objects were still separated, even though some gravitational matter has been converted to kinetic (and other forms of) energy, because the accumulation of bits of matter at the same location makes their gravitational fields coincide more completely with the same parts of space, so that the gravitational matter at any location in the field they jointly impose on space is spread more thickly.

Though gravitational matter is just part of matter counted in the rest mass of a material object, gravitational matter can also exist independently, as gravitational waves. But we can leave that until we take up the ontological explanation of Einstein’s general theory of relativity.

Electromagnetic matter. The electric force is another kind of force that we will assume that material objects can exert. It has a more complicated structure than gravity, because material objects can exert two opposite electric forces, positive and negative, and in either case, the electric force interacts with another force, the magnetic force. How material objects interact by these forces is what is described by Maxwell’s laws, and they will be explained in more detail later. For now, let me merely suggest how electric forces can be explained as a form of matter, by analogy with gravitational matter.

Material objects that exert an electric force are said to have an electric charge, either positive or negative. In order to explain ontologically how Maxwell’s laws are true, we will assume that the matter making up such a material object coincides with space in a way that makes its total rest mass seem to have a determinate location at the center even though some of its constituent matter is spread out around it like a force field. Since the strength of the forces in this field fall off in proportion to the square of the distance from the center, their strength at any point can also be explained as the “thickness” of the electromagnetic matter spread out in that part of space, though it must have a more complex structure to explain the direction of the force, because it depends on the sign of the charge and its motion.

The electromagnetic matter making up the electric field is already counted as part of the rest mass of the material object in balancing the mass and energy books. Thus, the electric field is actually an aspect of the material object, that is, an extrinsic property of the material substance that has the electric charge.

Electromagnetic matter in this form is electrical potential energy, because the force field can accelerate material objects affected by it, namely, other material objects with electric charges. Like gravitational potential energy, electromagnetic matter is converted to kinetic (or other forms of) energy, and such conversions change the rest masses of the objects exerting the electric forces appropriately, because material objects are actually either acquiring or losing matter. But once again, the changes in rest mass may not be recognized as such, because any amount of potential energy less than the maximum possible is counted as a negative quantity.

In the case of electromagnetism, the interaction of electric forces with magnetic forces makes it necessary to recognize that matter of basically the same kind can also exist independently of material objects as waves, such as ordinary light.

When these two forces are coupled, as described below, they propagate across space as a wave of electric and magnetic forces. Since those forces interact with charged objects in much the same way as the electric (or magnetic) forces exerted by material objects directly, electromagnetic waves are basically another form of electromagnetic matter. But since the electric (and magnetic) forces exerted by charged material objects directly are so different from electromagnetic waves, it is probably best to think of electromagnetic matter as existing in two different forms. In one form, its quantity is included in the rest masses of the objects (and the negative potential energy of the situation), and in the other form it is added to the rest of the mass and energy in calculating the total quantity that does not change over time in a closed or isolated system.

Electromagnetic energy is not portrayed as mere waves in contemporary physics. There are two reasons, one that we will accept in the end and one that we won’t.

The first reason is that electromagnetic waves are now known to have a particle-like nature, which has given them the name “photons.” The discovery of their particle-like nature is at the very foundation of quantum mechanics, and it will not be disputed here. We shall see how spatiomaterialism can explain their particle-like when we take up the ontological explanation of quantum mechanics.

The second reason for avoiding the notion of electromagnetic waves is that the notion of waves requires a substratum or medium in which the waves occur, such as the water in which ocean waves occur and the air in which sound waves occur. In classical physics, electromagnetic waves were thought to occur in the “luminiferous ether,” which was assumed to be at rest in absolute space. But when absolute space was rejected with the rise of relativity theory, the notion that light propagates in such a medium was rejected with it. Spatiomaterialism entails, however, that space and time are absolute, and so we do not have that reason for denying the reality of the ether. And since our reason for accepting absolute space and time is that space is a substance (not merely a way of thinking about references to locations and times in the equations of physics, as classical physics did), we have the option of explaining the ether ontologically, that is, as an aspect of space itself.

In other words, we will take the motion of electromagnetic waves to exhibit an aspect of the nature of space. Much the same is true of any form of matter, because the properties of any bit of matter are an aspect of something constituted jointly by the bit of matter and the part of space with which it coincides. But in the case of electromagnetic waves, we will hold that their velocity, that is, the velocity of light, manifests a basic aspect of the nature of space (what will be called the “inherent motion” of space or the “ether”).

It may seem that there are other kinds of energy, besides kinetic energy and the energy that is due to electromagnetism and gravitation, recognized in classical physics, but they all turn out in the end to be reducible to these basic forms.

Chemical energy, for example, is a form of potential electromagnetic energy that depends on how charged particles are configured in atoms and molecules. Heat turns out to be the kinetic energy in the random motion of the smallest material objects. Kinetic energy can also be stored internally in molecules as vibrations of parts of atoms.

There are, of course, other forms of energy associated with the short range forces that are involved in the constitution of more basic material objects, such as the strong forces exerted by protons and neutrons (or the color forces exerted by quarks) and the weak forces that are apparently involved in the constitution of quarks and electrons (and show up observationally in radioactive decay). But we are leaving them aside until we take up contemporary physics, taking the internal structure of material objects with rest mass for granted.

The reason we are taking all these kinds of mass and energy to be forms of matter is that they can be converted into one another without changing the total mass and energy in the region, that is, because the total mass and energy is conserved. Electromagnetic waves interacting with charged particles can convert them into kinetic energy. But this ontological explanation of classical physics takes the conversion between potential and kinetic energy to be an instance of the convertibility of mass and energy into one another. How these forms of mass and energy are converted into one another is described by the basic laws of physics.

To hold that these kinds of mass and energy are basically different forms of matter which move and interact in the ways described by the laws of physics is to hold that matter has a temporally complex nature. What is assumed about the essential nature of matter must include how each kind moves and interacts, including how they change from one form of matter to another.

However, spatiomaterialism opens up the possibility of a deeper ontological explanation of how these forms of matter are related to one another, which might explain how they can be converted into one another. Since ontological philosophy takes space to be a substance, it may be possible to describe the essential nature of matter in a way that makes it possible to explain ontologically why it takes these different forms by how generic matter coincides with space and other bits of matter. That is to suppose that the same material substance could have the properties defining any special form depending on its current relationship to space (and, perhaps, other bits of matter at its location).

For example, if there were a geometrical aspect to generic matter, differences in the forms mentioned above (or some of them) might have an intelligible ontological explanation as different ways in which generic matter engages with the geometrical structure of space. An explanation of the nature of some forms of matter along these lines will be suggested by a theory about the nature of matter that will be offered as an ontological explanation of the truth of quantum mechanics, and it will explain the simplest particles recognized by physics (in Basic Objects under Cosmology under Change.) It illustrates a research project that would be promising, if ontological philosophy is on the right track.

To explain the truth of the laws of physics by postulating a kind of material substance that can change from one form to another with different essential properties is to make the forms of matter similar to Aristotle’s basic substances. Aristotle believed that the simplest kinds of substances (earth, air, fire and water) could be converted into one another, for example, as fire gives its form to other substances, such as wood, changing its essential form to fire. As the essential properties (or essential form) of the substances change, the substratum (or material cause) was supposed to endure unchanged. There is, however, a difference. Spatiomaterialism does not assume, as Aristotle did, that (essential) forms of matter and their substratum are basic principles. Spatiomaterialism is a variety of materialism, in Aristotle’s sense, because it denies that individual substances necessarily involve his two principles (or ontological causes), substratum (material cause) and essential form. Bits of matter are independent substances, and their capacity to change from one form of matter to another is just part of the essential nature of material substance. However, since spatiomaterialism does recognize another basic kind of substance, besides matter, with which it coincides, it is possible that those regularities have a deeper ontological explanation.

Leaving aside for now deeper ontological explanations of these forms of matter, our project here is to show that classical physics can be explained ontologically by spatiomaterialism. That is to explain the truth of the laws of classical physics by their correspondence to aspects of a spatiomaterialism world, and it will be accomplished here by assuming that the bits of matter that coincide with space have these basic forms: material objects with rest mass, kinetic matter, gravitational matter (as part of the matter making up objects with rest mass) and electromagnetic matter (both as part of the matter making up material objects with electric charges and as electromagnetic waves).

The laws to be explained are Newton’s laws of motion and gravitation as well as Maxwell’s laws of electromagnetism. That will suffice to show how the physical properties mentioned by the basic laws of classical physics can be aspects of these forms of matter, and it will explain the regularities among them as temporal aspects of a world constituted by such substances enduring through time.

Since what is at issue is the correspondence between these laws and aspects of substances, what is crucial is not the quantitative aspects of those laws, which are generally the focus of attention in physics, but how those quantities can be explained ontologically by substances of the kind postulated by spatiomaterialism. I will describe how aspects of these forms of matter would explain the properties mentioned by the laws of physics, and I will show that they can explain the quantitative relationships among them and how they change over time. But I will merely show that the quantities can all have the right signs, change in the right directions and have the right orders of magnitude. It is not a matter of making any new, quantitatively precise predictions of what will happen, because any more precise quantitative correspondence can be made to come out right simply by making the right assumption about the essential nature of matter. It is enough to explain them ontologically.

Not every aspect of those physical laws will be given a genuine ontological explanation. But enough will be explained to show that it is possible for spatiomaterialism to explain the truth of classical physics. That will put us in a position to show how spatiomaterialism can also explain the truth of contemporary physics, both relativity theory and quantum mechanics. We begin by sketching an ontological explanation of Newton’s laws of motion and gravitation and then take up Maxwell’s laws of electromagnetism.

Newton’s laws of motion. Newton’s laws of motion are remarkably simple.

First law of motion: “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it.”

Second law of motion: “The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

Third law of motion: “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Law of gravitation: material objects always attract one another in proportion to the product of their masses and inversely as the square of the distance separating them.

Newton’s laws describe how material objects move and interact, and since we postulate matter in the form of material objects with rest mass, we need only see how the regularities described by Newton’s laws of motion would be explained on the assumption that kinetic energy and potential energy are forms of matter as well. That requires making further assumptions about the specific essential natures of these forms of matter and about space, but as we shall see, it affords genuine, even illuminating, ontological explanations of some aspects of classical physics.

According to our working hypothesis, the motion of a material object with rest mass is due to the kinetic matter attached to it. The kinetic matter must coincide with the same part of space as the material object itself, but in a way that that moves the material object across space as time passes. Each speed and direction of motion for any given material objects would involve a (quantitatively) different variety of kinetic matter (which could be explained ontologically by aspects of how kinetic matter coincides with space, such as its direction and quantity).

Newton’s first law of motion. Newton’s first law is an immediate consequence of this ontological assumption about kinetic matter. Since the kinetic matter that makes the material object move is itself a substance that endures through time with the same essential nature, the object in motion will continue moving at the same speed and in the same direction (unless it interacts with another bit of matter).

What does not change according to the first law of motion is called “velocity,” because it includes two aspects of the object’s motion, its speed and its direction. That is why we assume that, for any given material object, each different speed and each different direction requires a different variety of kinetic matter. The velocity is not the kinetic matter, but just a property of the material object with the kinetic matter, that is, an aspect of the substances constituting the object with rest mass together with its kinetic matter and how both are contained by space. (The three dimensional structure of space makes it possible to represent any velocity mathematically as a certain speed in each of any three mutually perpendicular directions. Quantities that depend on direction in this way are called “vectors.”)

Newton’s first law must be true, if the motion of objects is due to kinetic matter, because all the ways that an object might be thought to change its speed or direction on its own are ontologically impossible. A change in its motion would require kinetic matter of one variety to come into existence and another variety would have to go out of existence as time passes, which substances cannot do. Or it would require the variety of kinetic matter to change its essential nature, which no form of matter can do on its own. Or it would require space to contain kinetic matter in a different way at different locations, which is not compatible with the uniformity of space.

To be sure, in order to explain motion as a form of matter that connects material objects to space in a certain way, the objects must have an absolute velocity, that is, a certain velocity in absolute space. That may seem doubtful in contemporary physics, but it is just what spatiomaterialism entails about the nature of space and that is what is at issue in this ontological explanation of physics.

Notice that the assumption that an object’s velocity is due to its kinetic matter solves a problem that motion otherwise poses for any ontology that that postulates only substances enduring through time. The problem was first posed by Zeno as a paradox about motion. He pointed out that, at each moment, an object must be at rest (as we assume by holding that nothing exists but the present), and he asked, How is motion even possible in that case? If motion is simply how location changes as time passes, motion does not really exist, because the object always has only one location at each moment as it is present. This is not just a puzzle about the continuousness of time and space, because holding that to move is just to have a location that varies continuously with time leaves a problem about why the moving object has a different location the next moment, whereas the object at rest does not. What makes the object in motion different from the object at rest at each moment? To be sure, it is possible to simply assume that the essential nature of all material objects includes the temporally complex property of changing locations again, if it did so the last moment. That is what materialism does in this case (as in the case of every other basic law of physics), and it is not very satisfying, because there is nothing to distinguish the moving object from the one at rest at any moment except where each was the previous moment (which is not something that exists at that moment). If, however, motion is constituted by a bit of kinetic matter that exists in addition to the object with rest mass, then motion is actually a substance that endures through time, and thus, what makes the moving object at any moment different from an object at rest is something that exists at that moment (not just the fact that it has a different position the previous moment).

The first law of motion allows for velocity to change when the material object interacts with another object, and given the forms of matter we are postulating, the only way that a material object can change velocity is for kinetic matter to be transferred to it or from it or both. Somehow the object must come to have a different variety of kinetic matter attached to it. That is basically what interactions do to objects with rest mass. In such an interaction, Newton’s laws say that the object is subject to a force, and our working hypothesis implies that the exertion of a force on the object somehow transfers kinetic matter to and/or from it.

Interactions are something that we expect, given our assumption that material objects are a form of matter that cannot occupy the same place at the same time, because if they can move, they can move to the same location at the same time and something must keep them from being contained by the same part of space. The simplest kind of interaction is a collision of material objects that is elastic, that is, in which nothing changes but the velocities of the material objects that collide. Though collisions of ordinary material objects are mediated by electromagnetic interactions, we can, for present purposes, abstract from the nature of the forces and consider only what happens when material objects collide. We know that they exchange kinetic matter. But we do not know how much is transferred or what effect it has on their velocities. The regularities about such transfers of kinetic matter are what is described by Newton’s second and third laws of motion.

Newton’s second law of motion. Newton’s second law holds that the exertion of a force is what changes the velocity of a material object. Since forces are exerted by other objects, the force on any object has some direction or other, which determines in some way the direction in which the object’s speed changes. It also has a determinate strength and its action on the object has a certain quantity. But how much an object’s speed changes in the direction of any given force depends on another factor, its rest mass, or the quantity of matter embodied in it. That is, what changes when a material object is subject to a force is its momentum, or the product of its velocity and its rest mass.

In the case of material objects composed of many parts with the same rest mass, our working ontological hypothesis offers an explanation of the relevance of rest mass in determining the change of velocity. In order for the composite object to move in a certain way, each of objects of which it is composed (each “atom,” if you will) must move in the same way (assuming that the parts have unchanging spatial relations to one another). Since each part must be moved across space by its own bit of kinetic matter, a force can change the velocity of the whole only by changing the velocity of each part in the same way. Thus, the change in velocity caused by a force varies inversely with the total rest mass of the material object. It must be spread out among all the parts, so to speak. For example, an object with twice as much rest mass has half as much change in velocity, if subjected to the same force. In other words, what changes is not merely its velocity, but its momentum, the product of its velocity and its rest mass.

The second law of motion also holds in the case of elementary material objects with different rest masses. But without a deeper ontological explanation of the nature of kinetic matter and material objects with rest mass, that regularity can only be assumed as part of the essential natures of those forms of matter.

Velocity is not a measure of the amount of kinetic matter, because the change caused by the transfer of kinetic matter to or from an object depends on its rest mass. But it might seem that momentum is the measure of kinetic matter, since it is what changes when kinetic matter is transferred. However, momentum, like velocity, is just a property of the material object with kinetic matter, and we can begin to see why by considering the third law of motion.

Newton’s third law of motion. Newton’s third law describes a more inclusive regularity than the second, for it includes the object that is the source of the force, describing how it is affected as well. This law holds that the action of one object on another is opposed by an equal and opposite action of the other object back on the first. That is, every action of one object on another is actually a symmetrical interaction of the two objects involved. And since what the action changes is momentum, this law says that the change in the momentum of one object is equal and opposite to the change in momentum of the other object. Thus, Newton’s third law of motion entails the conservation of momentum. That is, in any interaction, the sum of the products of the velocity and mass of all the objects involved in the interaction does not change in any direction regardless how the objects may interact.

The conservation of momentum may make it seem that momentum must be the measure of the total quantity of kinetic matter involved. Suppose, for example, that two equally massive objects moving toward one another at the same speed were to collide. Given our working ontological hypothesis, we might try to understand why the two objects rebound from one another by thinking of the interaction as each object transferring its kinetic matter to the other, for that would also explain why both objects come out with velocities in the opposite direction. Each acquires the other object’s kinetic matter. And if the objects had different rest masses and different velocities, this would even explain how much the velocity of each changes.

Momentum cannot, however, be the measure of the amount of kinetic matter, because it is a quantity that depends on the direction of the motion, whereas the quantity of kinetic matter does not. (In other words, momentum is a “vector quantity,” whereas kinetic energy, as a substance, must be a “scalar quantity,” which does not depend on the direction of motion.) To illustrate the problem, suppose that two objects colliding with equal and opposite momentums do not rebound from one another, but simply come to a stop. The latter is compatible with Newton’s third law of motion, because the change in the momentum of one is still equal and opposite to the change in momentum of the other. Each loses an equal and opposite momentum. Action and reaction are symmetrical. But if momentum were the measure of kinetic matter, it would mean that their kinetic matter simply goes out of existence, for their momentums cancel out. And since that is impossible for a substance, momentum cannot be the measure of kinetic matter.

It is no great surprise, of course, that momentum is not the measure of the quantity of kinetic matter on this ontological explanation, for we postulated the existence of kinetic matter in the first place in order to account for kinetic energy. But the foregoing example does bring out the difference between momentum and kinetic energy. It is currently explained only mathematically: in Newtonian physics, momentum is the product of an object’s rest mass and its velocity (mv), whereas its kinetic energy is one-half the product of its rest mass and the square of its velocity (1/2 mv²).

It is a subtle difference, which was not obvious even to classical physicists at first. The difference was not recognized by Cartesians, and Leibniz was so struck by kinetic energy being different from momentum, or mere motion, that he took the existence kinetic energy as evidence of a vis viva, a “force of life” in the object, which helped inspire his belief that atoms are really “monads,” or minds.

The ontological difference between kinetic energy and momentum is that the former is the quantity of a form of matter that can be attached to objects with rest mass and the latter is a quantitative property that material objects have when kinetic matter is attached. Momentum is just an aspect of those two kinds of material substances as they are contained by space, an aspect that depends on the direction of the motion in space. Newton’s second and third laws of motion describe the regularity about how that property changes when material objects interact, including the conservation of momentum. The kinetic energy is, however, part of the substance constituting the object in motion, and so it is conserved because it is a substance.

This is just the beginning of an ontological explanation of the difference between kinetic energy and momentum. Though we can see that they are different, it does not explain the quantitative relationship between them, that is, why kinetic energy varies with the square of velocity, while momentum varies with velocity. That can be explained only later, when we take up a deeper ontological explanation, the quantum theory of matter. There is a more specific nature of kinetic matter that entails momentum being related to kinetic energy as the velocity to the square of velocity.

In the foregoing case, where colliding objects with equal and opposite momentums simply stop, the collision is not elastic, that is, something changes besides the motion of those objects. Instead of dropping out of existence, the kinetic energy is converted into another form of matter (such as potential energy in new forces being exerted among its parts) or transferred to other objects (such as the kinetic energy of the parts of the objects, that is, becoming heat).

Newton’s law of gravitation. Newton’s law of gravitation holds that material objects exert an attractive force on one another that is proportional to the product of their (rest) masses and inversely proportional to the distance between them. But since each object exerts such a force on the other, an object must have a gravitational field around it even when there are no other objects in its neighborhood. There is, in other words, a gravitational force at every location in the space around the material object. Those forces are radially symmetric around the object itself, and their strength declines with the square of the distance from the object.

The gravitational field is explained ontologically by postulating matter in the form of gravitational matter, which is spread out in space around the material object exerting the gravitational force, though its quantity is included, along with matter is some other (yet to be described) forms, as the rest mass of the material object. This affords an obvious ontological explanation of many of the aspects described by Newton’s law of gravitation. Gravitational forces are directed toward the object, since that is the center of the rest mass of the material object that spreads gravitational matter out in space. The forces are radically symmetric, because the object is located in three dimensional space. And the strength to the force falls off with the square of the distance, because that is how fast space spreads out sideways as you move away from the source of the force.

The force of gravity is not given an ontological explanation in classical physics. Instead, it is usually described as just a disposition at each point in space to exert a precise, mathematically described force on any material object (with a certain mass), if it were located at that point. Talk of “dispositions” is a way of predicating regularities of objects as if regularities were just properties of the objects. But that is to leave those regularities unexplained. There is no alternative in classical physics, because it assumed that gravity involves action at a distance (which is implicitly to deny the reality of the space across which it is supposed to act). Talk of gravitation as a disposition is a way of being skeptical about the reality of such forces as anything beyond their effects. This ontological problem was eliminated by Einstein’s general theory of relativity, and that discovery is what we are anticipating by including gravitational energy as a form of matter in this explanation of the truth of classical physics.

Gravitational matter helps explain the truth of the principle of the conservation of mass and energy, however, only by being counted as a negative quantity, that is, as potential energy. The maximum quantity of potential energy is zero, because according to our our ontological explanation of that accounting practice, potential energy is actually part of the matter that is already counted in the rest mass of the material object whose forces are a potential source of kinetic energy.

This theory calls for a deeper explanation of how the matter appears both as a material object, with a definite location and rest mass, and at the same time as force field spread out in the space around that center of mass. We will consider such a theory later, but for now, we must simply recognize that the rest mass includes both forms of matter. And we can use the notion of gravitational potential energy to illustrate further the puzzling relationship between momentum and kinetic energy.

Gravitational forces exist as fields in which forces are exerted continuously over time and material objects change momentum continuously as they move through them. The way in which material objects interact by gravitational forces can be described as a conversion between potential and kinetic energy, and since such conversions are also a way of explaining the interaction of material objects by electric and magnetic forces, I will describe some of its features by considering what happens to a ball thrown upwards in a (nearly) constant gravitational field, such as near the surface of the earth.

The ball has an initial momentum when it leaves the hand that is proportional to its upward velocity. But since its momentum is constantly decreasing as the result of the constant downward gravitational force on it, there is a point at which the ball comes to a stop and starts falling again, after which its downward velocity increases until we catch it. The ball had kinetic energy when it left our hand, but at the top of its trajectory, it has lost all its kinetic energy. And by the time we catch it, the ball has regained kinetic energy. Since kinetic energy is a form of matter, it never simply goes out of existence or comes into existence, but merely changes form. It is converted into potential energy, which the ball has because it is located in a way that enables the gravitational force to accelerate it over some distance, that is, can acquire kinetic energy from those forces as the object moves through the gravitational force field. If we think of it ontologically, we see the ball losing kinetic matter as it rises, but since the distance across which the gravitational force can accelerate the ball increases, it gains potential energy (which increases the rest masses of both ball and earth). And when it falls, it loses potential energy (decreasing rest masses) and acquires kinetic energy. Since the ball has lost all its kinetic energy at the top of its trajectory, when it is at rest, its potential energy at that point must be equal to its kinetic energy at the beginning and end of its trip. The potential energy depends on two factors, the force exerted by the earth on the ball and the ball’s location in that force field. Both are needed to accelerate the ball and give it kinetic energy, and since the force is nearly the same at every location, the potential energy turns out to be proportional to the height to which it rises, that is, to the distance it can fall in the (constant) gravitational field.

This allows us to see, once again, the difference between momentum and kinetic energy. How much faster would we have to throw the ball upward in order for the point at which its stops and starts falling again to be twice as high? It is not necessary to double its velocity, as we would find if we tried. Instead, the initial velocity needs to be increased only by the square root of two (or about 1.4). The reason is that the ball consumes kinetic energy in rising to a certain height in the gravitational field, not momentum, and since kinetic energy varies with the square of the velocity, it is not necessary to double the initial velocity to double kinetic energy). (Likewise the time it takes will also increase only by a factor of the square root of two, since gravity changes its momentum at the same amount each unit of time and the amount of momentum to be changed is only increased by the square root of two.)

The conversion between kinetic and potential energy is basic to classical physics, though the quantities become more complex when we take into account that gravitational forces are not constant, but have a strength that varies inversely with the distance from the center of gravity. But we need not consider all the complexities of the quantitative relations (though these ontological causes must be able to explain them in the end), because we are merely trying to see what is involved in an ontological explanation of the basic laws of classical physics. We have seen how such ontological causes would make Newton’s laws of motion true, and spatiomaterialism is not trivial, like materialism, considering that it implies the existence of kinetic matter (and begins, at least, an explanation of the relationship between momentum and kinetic energy). The one form of matter that has not been described is electromagnetic waves, and that brings us to the explanation of Maxwell’s laws of electromagnetism.

Maxwell’s laws of electromagnetism. The other basic set of laws making up classical physics at the end of the 19^th Century were Maxwell’s four laws of electromagnetism. They describe the electric and magnetic forces and how they interact, and these forces can be explained in much the same way as gravitation, that is, as a form of matter that coincides with space by being spread out spread out in space like a field, and yet contained in the rest mass of material objects with electric charges.

Electromagnetism is more complex than the gravitational force, because there are two forces, electric and magnetic, which interact with one another, and there are two opposite electric forces that material objects can have, positive and negative.

Maxwell’s great triumph was to show how the interaction of the electric and magnetic forces can couple them in a way that propagates both across space at a fixed velocity, that is as electromagnetic waves propagating at the velocity of light. Since electromagnetic waves exist independently of all the other forms of mass and energy (and, thus, the other three forms of matter, on this ontological account), there is less room for doubt about these forces being a form of matter.

It is now known that electromagnetic interactions mediate all the non-gravitational interactions among molecules, among atoms in molecules, and even between electrons and protons in atoms. Even the elastic collisions that we took for granted in discussing Newton’s laws of motion are mediated on the micro level by interactions involving both electric and magnetic forces among objects with electric charges. But all these interactions involve events with a unit-like nature which was unexplained until the discovery of quantum mechanics, and we will take them up later (in Change: Quantum mechanics.)

At this point, I will discuss aspects of the regularities described by Maxwell’s laws in an order that adds up to an explanation of electromagnetic waves, and then I will discuss how spatiomaterialism can explain such waves ontologically.

Electric charge. One of Maxwell’s laws describes the electric forces that can be exerted by material objects. When a material object has an electric charge, it exerts a radial force surrounding the center of rest mass whose strength declines with the square of the distance. This is like the force of gravity, except that the electric force acts on other objects because of their electric charges, rather than their mass. And unlike the gravitational force, the electric force can be either attractive or repulsive, depending on whether the other object has an opposite or same electric charge, respectively. The electric force can give such objects kinetic energy (or become another form of energy, such as an electromagnetic wave), and so it is counted as potential energy. But once again, the maximum potential energy is zero, making it a negative quantity when some of it has been consumed.

Spatiomaterialism can explain potential electrical energy ontologically as some of the matter that is counted in the rest masses of the material objects exerting the electric forces. Thus, when potential energy is consumed, the rest masses of the charged objects are less. If we think of the potential energy as a form of electromagnetic matter that is spread out in space around the objects with the electric charges, we can see why the quantity of potential energy varies with the matter.

Objects with opposite charges attract, and their potential energy is maximum when they are far apart from one another, because their electric fields more nearly approximate a spheres (of forces declining with the square of radius), which requires the maximum quantity of electromagnetic matter to constitute them. But when opposite charges are next to one another, their electric fields are mostly neutralized, and the electric field they jointly set up is deformed in a way that requires less electromagnetic matter. In this case, their total rest mass is less than if they were independent of one another.

Objects with like charges repel, and their potential energy is maximum when they are close to one another, because instead of neutralizing one another, their electric fields oppose one another. Though holding them together yields an electric force that is twice as strong as the radial force field they jointly set up, additional electromagnetic matter is required for the two charged particles to have a force repelling them from one another. In this case, their rest masses are greater than they would be if the objects were at a distance from one another.

In either case, in the equations describing these situations, the potential energy is represented as zero when it is maximum, and thus, what is actually a loss of rest mass, which comes from consuming potential energy and converting electromagnetic matter into other forms of matter, is counted as negative potential energy.

The electric field is also more complex than gravitation in another way because of its interaction with the magnetic force. It affects the motion of a charged object in an electric field. For example, in an electric field is set up by a material object too massive to move much, a charged object that is accelerated by it will increase its velocity not only in the direction of the force, but also in a direction perpendicular to both the electric force and the direction of its own motion in the electric field. That is the work of the magnetic force. The magnetic force on the charged object is a function of its velocity through the electric field as well as the strength of the electric field. This effect of electric forces is not mentioned in this first law, but is a consequence of another of Maxwell’s laws.

No magnetic charges. The second law holds that there is no material object with a magnetic charge, even though there are magnetic forces. A material object with a magnetic charge would have a radial force surrounding its center of rest mass which declines with the square of the distance. Instead, as it turns out, magnetic forces occur in fields in which they are all directed around a closed loop, such as a circle.

According to another law, as mentioned above, the magnetic force can arise because of the motion of a material object with an electric charge. For example, when electric charges are moving in a certain direction through space, they set up a magnetic field in which the magnetic forces are aligned in a circle around their direction of motion. (Such a circular field is set up even when the moving electric charges are neutralized locally by opposite charges, as in a wire in which a current is flowing, and the net strength of the electric force is not changing at any point in space in the surrounding space.)

Coupling of magnetic and electric forces. The two remaining aspects of the regularities described in Maxwell’s equations explain electromagnetic waves. One holds that a change in the magnetic field causes a circular electric force around the direction of the magnetic forces. The other holds that a change in the electric field causes a circular magnetic field around the direction of the electric forces. In both cases, the strength of the field being set up varies with how fast the first field changes (and thus indirectly on the strength of the forces). But the directions are reversed (so that an increasing electric force causes a magnetic force, while an increasing magnetic force causes a electric force in the opposite direction). Furthermore, the change in the strength of each force generates a force of the other kind that is related to it spatially in a certain direction, so that changes in the two forces are coupled as a wave that propagates across space at the velocity of light.

An impression of how electromagnetic waves propagate can be gathered by considering how the motion of electric charges generates them. Consider, for example, a current of electrically charged objects in a wire that is changing direction. The current sets up a magnetic force circling the wire, but as the electric charges slow down, the magnetic force declines (because the rate of change in location of the electric charges becomes lower). The decline in the magnetic force field causes an electric force that circles it. But the change in that electric force causes, in turn, a magnetic field around its direction, which is in the opposite direction of the first magnetic field. And the change in the second magnetic field then causes an electric field, this time in the opposite direction. And finally its change causes a magnetic field that is like the one caused by the electric charges in the wire, except that it is located a fixed distance away from the wire which depends on the velocity of light. Thus, the changes in the two forces are coupled in a way that propagates across space at the velocity of light as an electromagnetic wave. And a steady succession of such waves is generated as long as the current in the wire continues to oscillate. That is basically how antennas send electromagnetic waves.

Electromagnetic waves are a form of energy counted in the principle of the conservation of mass and energy, and though the quantitative details are not relevant here, we should consider what our working hypothesis implies about the nature of "electromagnetic matter." The matter involved in these waves is similar to the matter that makes up the electric field of a material object with an electric charge, except that in the electromagnetic wave, the electric force is changing and the changes couple it with a magnetic force that also changes. The forces interact in such a way that they go through complete cycles, putting them in a position to do the same thing over and over again. But the forces they generate are so related to one another in space that the wave moves across space over time at certain fixed velocity, that is, the velocity of light.

The matter constituting electromagnetic waves may not be as different from the electromagnetic matter constituting electric charges as this contrast makes them appear. According to current quantum theory, material objects with electric charges also have a spin angular momentum. Since that is a magnetic force, it suggests that the electric charge may actually be an electric force that is changing cyclically by somehow spinning around an axis. That possibility will lead us to speculate (when discussing quantum mechanics and the basic particles) that the opposite electric charges (positive and negative) differ from one another by being in opposite phases of their cycles wherever they are located in space.

Inherent motion in space. Maxwell deduced the velocity of light in a vacuum from measurable constants mentioned in his laws, and since classical physics assumed that space is absolute, it could hope to explain this implication as the result of electric and magnetic forces being exerted on an extremely elastic substance that was assumed to be at rest in absolute space. They called it the “luminiferous ether” (or “ether,” for short). Since the ether was supposed to be a kind of matter, it seemed plausible to explain the propagation of electric and magnetic forces mechanically, as an interaction between charged particles and the ether, on the model of waves of forces in ordinary material objects. That project did not work out, but that does not mean that space cannot be playing a similar role in the motion of electromagnetic waves.

In recognizing that space is a substance, spatiomaterialism departs from classical physics as well as from materialism. Though classical physics assumed that space is absolute, it did not take space to be a substance that could interact with bits of matter in any way other than providing all the locations where they are could move or be located. In particular, space was not supposed to affect the motion of bits of matter, at least, not in the way other bits of matter can. But since spatiomaterialism has independent reasons for believing in the existence of space as a substance enduring through time (that is, in addition to presentism, reasons deriving from the recognition of the validity of ontological-cause explanations and inferring to the best ontological-cause explanation of the natural world), it has no reason to doubt that space can interact with bits of matter in ways that are quite comparable to the interactions of bits of matter in space. Thus, spatiomaterialism can use space to explain the velocity of light without having to postulate the existence of the ether as an additional kind of matter that coincides with space. We can take talk about the ether to be referring to an aspect of space as a substance. That is what we will do by taking space itself to be the medium of light transmission.

To be the medium of light transmission, space must have an aspect by which it interacts with electric and magnetic forces and carries them across space as electromagnetic waves at a certain velocity. In order to explain how space does so, I will assume that there is an “inherent motion in space.” By “inherent motion,” I mean a further relationship among the parts of space, beyond the geometrical relations we have already assumed, which involves their endurance through time. We have assumed that the parts of space are particular substances, that is, so that each point has an existence that is distinct from all the others and each point endures, like any substance, through time, never coming into existence nor going out of existence. But since only the present moment exists, only one moment in the history of each part of space exists, and that moment in the history of all the parts of space always occurs at the same time. That is how these substances exist together as a world, and it is the wholeness of space that relates the bits of matter it contains as parts of the same world. This temporal aspect of the nature of the parts of space is the ontological foundation for a further relationship among the parts of space. What I am calling the "inherent motion of space" (as our substitute for the "luminiferous ether") is a spatio-temporal relationship among the parts of space.

Such a temporal aspect to space is not only plausible, but also required by the role of space in constituting what happens. If the parts of space did not have a spatio-temporal relationship to one another, they could not affect one another as time passes. Nor could they enable bits of matter to affect one another.

The geometrical relations among the parts of space explains which parts of space can be affected by any other given part, namely, those nearby, then those next to it, and so on. But in order for a change occurring at any one part of space to affect another part of space, the other part of space must change at a later moment. If the effect were immediate, the effect would not be distinct from the cause, and they could not act on one another like particular substances enduring through time. Space would interact with bits of matter as a whole. Thus, let us assume that the rate at which one part of space can affect another part of space as time passes is finite. That would be a maximum velocity by which one part of space can affect other parts of space. I call it the “inherent motion” in space in order to make clear that it is a temporal aspect of the nature of space as a substance.

I think of the "inherent motion" as a motion sweeping through every part of space at the same velocity, both ways in every direction possible in three dimensional space, at every moment. This is how space is an ontological cause, along with the nature of electromagnetic matter, of the velocity of light. That is, we can explain the motion of electromagnetic waves as bits of matter (or so-called “photons’) being carried along by the inherent motion. But there is an inherent motion, even when there are no photons. Indeed, it would be happening, even if there were no matter in the world. In other words, the inherent motion is an aspect of space as a substance.

The postulation of an inherent motion may seem ontologically excessive, since all we need to assume is that the parts of space are so related temporally, as well as geometrically, that there is a maximum rate at which it is possible for what happens to matter at one part of space to affect what happens to matter at another parts of space. Thus, it may be urged that the inherent motion is not real, but merely the velocity of possible effects across space. It is merely a spatio-temporal geometry about space, that is, a geometry describing how the present moment of any one part of space is related to the past or future moments of other parts of space because of the maximum velocity with which events can affect one another. Such an account, it could be argued, would be a better ontological explanation in the end.

Though a spatio-temporal geometry to space may be a sufficient ontological explanation, I will continue to speak of it as the "inherent motion in space." I can take this liberty, because I am not claiming that the more specific natures of matter and space that I am introducing in order to explain the truth of physics are the best possible spatiomaterialist ontological explanation of the basic laws of physics, only that they are a possible spatiomaterialist ontological explanation. That is all that is required for ontological philosophy to make the case for using spatiomaterialism as the foundation for its argument about necessary truths. And I allow myself the liberty of postulating an actual inherent motion in space, because that invokes an image (in rational imagination) that makes it easy to think about an aspect of the essential nature of space that will be central in the following explanation of the laws of contemporary physics. I find it preferable to “spatio-temporal geometry,” because talk of motion brings out vividly the temporal aspect of what might otherwise be seen as a static structure (such as spacetime in Einsteinian relativity). And it emphasizes that it is always happening everywhere in space, connecting the parts of space ontologically in a further way than merely having geometrical relations, a way that is central to the existence of causal connections among events in the world.

As it turns out, nothing turns on the difference between saying that space has a an inherent motion and saying that space has a spatio-temporal geometry, as long as we recognize that we are talking about an aspect of a substance that endures through time and has the opposite nature from matter. The motion of electromagnetic waves (or photons) is only one manifestation of this aspect of the essential nature of space. There will be several others as we proceed, and it will be a somewhat more complex aspect of space by the time we are through, variations in its velocity at different locations in space. It is easier to think about these ontological effects of space by thinking of space as having an inherent motion prior to the motion of photons, because the picture is spatial imagination is more concrete.

The the inherent motion in space is the medium of light transmission, and though it may also be called the "ether," as it was in Newtonian physics, it is ontologically important to keep in mind that it is an aspect of space. The ether was supposed to be an ethereal matter that is at rest everywhere in space, and no such thing is needed in a spatiomaterial world, because when space is a substance, it can interact with bits of matter in much the same way as other bits of matter.

It should be noted, however, that just as it made sense to speak of being at rest in the ether, it will make sense to speak of being at rest relative to the medium of light transmission. In either case, it is the reference frame in which the one-way velocity of light is exactly the same both ways in every direction in three dimensional space. It was assumed in Newtonian physics that being at rest in the ether would be at rest in absolute space, because they assumed that the ether was at rest in absolute space. Though we also assume that there is a reference frame that is at rest relative to the light medium, we will not assume that it is at rest in absolute space, because in order to explain ontologically the truth of the general theory of relativity, we will have to assume that the light medium itself can have a velocity in space. That will be to hold that that inherent motion in space can have a different velocity at different locations. But if you prefer, such talk can always be translated into talk about the spatio-temporal geometry of space as a substance enduring though time.

The basic laws of classical physics can, in sum, be explained ontologically by postulating various forms in which matter can coincide with space as a substance. Those forms of matter are material objects with rest mass, kinetic matter, gravitational matter, and electromagnetic matter (including both matter as electric and magnetic forces and as electromagnetic waves). And they explain the truth of the laws of classical physics in the sense that a world made of such substances enduring through time has aspects (properties, relations and regularities about change) that correspond to those laws.

That is, the laws of classical physics are true because they correspond to an aspect of the world that has been constructed from our assumptions about the basic nature of substances, about space and matter as the two opposite kind of basic substances that make up the world, and about the specific forms of matter that coincide with space. There is, therefore, one way, at least, that a spatiomaterialist ontology can make its basic laws true, which shows that spatiomaterialism is possible, as far as classical physics is concerned.

Thus, we have laid the foundation we will need in order to explain the truth of the basic laws of contemporary physics ontologically. The first step in that project has already been made by postulating an inherent motion in substantival space to explain the velocity of light ontologically. In assuming that light has a medium through which it is transmitted, it may seem that we are resurrecting the "luminiferous ether" of Newtonian physics. But if so, it is no longer a strange form of ethereal matter at rest in space, but an aspect of space itself. Space itself is the medium of light transmission.

Contingent laws: Contemporary physics. In the early 20th Century, revolutions in physics have made it seem impossible for spatiomaterialism to explain the basic laws of physics ontologically. There were two revolutions, Einstein’s two relativity theories and quantum mechanics. The first led to the belief in spacetime, and the second made it seem that processes at the micro-level are indeterministic. These new theories were irresistible in physics, because they were justified by the empirical method in the same way as Newtonian physics had been. They were inferences to the best efficient-cause explanations, where the best depends heavily on making surprising, quantitatively precise predictions that turn out to be true when measurements are made. And both revolutions have been extremely fruitful, leading to surprising predictions in new fields.

Two theories are involved in the Einsteinian revolution: the special theory of relativity, which covers phenomena that occur in material objects with velocities approaching that of light, and the general theory, which is a more accurate account of gravitational phenomena. Together with quantum mechanics, the special theory led to quantum field theory, a more accurate account of electromagnetism, which included the discovery of spin and positively charged electrons. As a gauge field theory, quantum electrodynamics became the model for theories about the two short range forces, the so-called weak and strong (or color) forces, which are responsible for the composition of particles in ordinary material objects, and that has exposed more basic particles of nature, such as quarks and neutrinos. Together with the observation that the universe seems to be expanding (Hubble's law), the general theory is now used to support the big bang theory about the origin and expansion of the universe. In sum, our understanding of every kind of physical phenomenon has been radically enriched by these two revolutions in physics.

There is one way, however, in which these two revolutions do not fit well together. It is often characterized as the main theoretical problem of contemporary physics. Einstein’s general theory of relativity explains gravitation, one of the four basic forces, but it is mathematically quite different from the theories describing the other three forces (electromagnetism, the color force and the weak force). The latter three are formulated as gauge field theories, making it possible to fit them together mathematically, but no one has found a simple way of connecting them with Einstein’s general theory of relativity. Attempts to connect them have led some physicists to believe that there are ten or more dimensions to space!

Notice that this theoretical problem in contemporary physics is basically a mathematical problem. It derives from the so called "holy grail" of physics, which is to discover a single law from which all the laws of physics, describing all the basic forces, can be derived. But the incompatibility between quantum theory and the theory of gravitation is very likely intractable as a mathematical problem.

Physics is crying out for a new approach. That is what ontological philosophy supplies. The solution to the main problem of contemporary physics is an extra benefit of its spatiomaterialist interpretation of contemporary physics.

Each of the basic revolutions of contemporary physics poses, however, a challenge to spatiomaterialism all by itself.

Einstein’s two relativity theories pose a challenge to ontological philosophy, as we have already seen, because they seem to describe a world in which space and time are not absolute. Realism about Einsteinian relativity entails the belief in spacetime, which puts time ontologically on a par with space: each moment in time is supposed to exist alongside every other moment in time, just as each point in space exists alongside every other point in space, as equal parts of an eternal four-dimensional world. But the belief in spacetime is incompatible with spatiomaterialism, because spatiomaterialism holds that only the present moment exists and takes space to be one of two opposite kinds of substances that endure through time. Thus, unless there is a way that Einstein’s special and general theories of relativity can be true in a world where space and time are absolute, ontological philosophy cannot use spatiomaterialism as the foundation for its arguments about what is necessary. Showing how the belief in spacetime could be replaced in a spatiomaterial world was one of the mortgages we took out in order to make this argument, and now the time has come to pay it off.

Quantum theory however, may also seem incompatible with spatiomaterialism. In addition to its apparent denial of determinism, it seems to deny that physical processes are constituted by material substances that coincide with space. Quantum mechanics is often interpreted, at least, as denying that the smallest entities have definite locations and as implying that they behave in ways that are incompatible with the principle of local motion and local action.

Quantum mechanics is less challenging than Einsteinian relativity, because the received interpretation of it (the so-called “Copenhagen interpretation, due mainly to Bohr) is more like skepticism about ever knowing the real nature of the smallest bits of matter than a generally accepted ontological belief about what exists on the micro-level that is incompatible with spatiomaterialism. The belief in spacetime is incompatible with the belief in absolute space and time.

It is possible, however, for spatiomaterialism to explain the truth of both theories. What is more, by explaining their truth ontologically, it solves the problem about how gravitation is related to the other three forces of nature. This ontological solution to the basic theoretical problem of contemporary physics will also provide the foundation for more speculative suggestions about cosmology, both the basic particles recognized by high energy physics and about the origin of the large scale structure of the universe.

Relativity theories. The two theories involved in Einsteinian revolution will be discussed in sequence. The notion of spacetime was introduced with the special theory of relativity as a way of explaining measurements made from objects with very high relative velocities, and Einstein used it as the basis for his explanation of gravitation. In a parallel way, the ontological explanation of spacetime in the special theory of relativity will be the foundation for the ontological explanation of the role of spacetime in the general theory of relativity.

In the case of Einstein’s special theory of relativity, it may not be surprising that it is possible for spatiomaterialism to explain its truth, for even Einsteinians admit that the empirical implications of Einstein’s theory could be explained on the assumption that space is absolute. It is just a matter of assuming that one of all possible inertial reference frames is at absolute rest and explaining the appearance that it is not different from the others on the assumption that absolute space causes certain distortions in material objects that move through it. Such a theory is possible, and it was begun, at least, by Newtonian physicists before Einstein first published his special theory of relativity.

The ontological explanation of Einstein’s general theory of relativity may be more surprising, because contemporary physicists apparently do not even suspect that it is possible to understand the gravitational phenomena discovered by Einstein on the assumption that space and time are absolute. The universal acceptance of the special theory of relativity and its notion of spacetime as a description of the nature of space and time has kept physicists from even considering a very simple, intuitively satisfying, ontological explanation of gravitation.

The spatiomaterialist special and general theories of relativity that result are not ontologically necessary truths, according to ontological philosophy, because they do not follow from spatiomaterialism, but rather depend on what has been discovered empirically about what happens in the world. All that needs to be shown is that it is possible for Einstein’s two theories to be true in a spatiomaterial world.

Once the laws of physics are explained ontologically, the additional assumptions that must be made about the nature of matter and space in order to explain them will be incorporated into the foundation of ontological philosophy as a way of explaining ontologically other aspects of the world, such as the global regularities. That is how we incorporate the laws of physics into spatiomaterialism. But since those further explanations will depend on the more specific natures of matter and space assumed here in order to explain the truth of classical and contemporary physics, their ontological necessity will be only conditional. They hold only of all possible spatiomaterial worlds like ours, that is, in which the laws of physics are true.

As it happens, however, the spatiomaterialist ontological explanation of the truth of classical physics together with its explanation of quantum mechanics seem to entail the ontological assumptions that have to be made in order to explain the truth of the special theory of relativity. If so, the regularities described by Einstein's special theory of relativity have a deeper ontological explanation, even if they are not unconditionally ontologically necessary.

It should be mentioned, however, that the explanation of the global regularities to be given under Change does not depend on this ontological explanation of the truth of contemporary physics. Given that space is a substance, they depend only on matter obeying the regularities described by the laws of contemporary (and classical) physics. Though we shall make further assumption about the nature of space and matter in order to explain ontologically the truth of quantum mechanics, the basic objects of physics, and the origin of the universe, they are required only to show the possibility of spatiomaterialism. They are not relevant in explaining the global regularities.

Einstein’s special theory of relativity. To explain how Einstein’s special theory of relativity can be true in a spatiomaterial world is to show that the regularities it describes can be constituted by substances of the kinds postulated by spatiomaterialism, that is, that it can correspond to aspects of space and matter as substances enduring through time.

In addition to the assumptions already made about the forms of matter and the inherent motion in space in order to explain the truth of classical physics ontologically, further assumptions about the nature of space and matter will be needed to explain special relativity. They are basically distortions of the kind that Lorentz described in fast moving material objects before Einstein’s first paper (time dilation and length contraction, though there must be compensating changes in masses and longitudinal forces as well), though something more must be said about the synchronization of clocks at a distance in order to explain the truth of all the predictions of the special theory.

In the first section, A Brief History of the Special Theory, I will give a brief history of how Einstein’s special theory of relativity was accepted in order to show that these distortions in fast-moving objects provide everything required to explain why Einstein’s theory is true.

Lorentz first described these distortions in order to explain the surprising results of the Michelson-Morley experiment, which established that it was not possible to measure the absolute rest and motion of a material object by measuring the velocity of light relative to it. But Lorentz’ theory was rejected in favor of Einstein’s special theory of relativity, which took a radically different approach. That was not a mistake within physics, because Einstein’s theory was superior according to the empirical method of science of physics (that is, inferring to the best efficient-cause explanation, or by the criteria of predicting and controlling what happens). But Einstein’s theory is not the best ontological-cause explanation of the phenomena. Indeed, as we shall see when Einstein’s premises and conclusions are explained ontologically, even its apparent superiority as an efficient-cause explanation rests on an illusion.

In the second section, The Lorentz Distortions, I show how Lorentz explained the undetectability of absolute motion or rest and the other distortions that are required for all the laws of physics to hold the same way on a moving inertial reference frame.

In the third section, The Symmetry of the Lorentz Distortions, I show how Einstein's definition of simultaneity at a distance combines with the Lorentz distortions to explain the puzzling symmetry about any pair of inertial reference frames that is emphasized by Einstein in calling his theory a theory of "relativity." This symmetry implies that inertial reference frames are empirically equivalent as far as experiments that observers on each frame can perform on one another are concerned, and as we shall see, it is just an appearance that depends on the mis-synchronization of clocks on inertial frames according to Einstein's definition and how that combines with the Lorentz distortions.

In the fourth section, The Ontological Necessity of the Lorentz Distortions, I will argue that although the Lorentz distortions are new laws of physics, they have a deeper explanation given our ontological explanation of the laws of classical physics and a plausible assumption about the nature of material objects (which will be justified later as a way of explaining the truth of quantum mechanics and what physics now knows about the microstructures of material objects). But given our assumption about space being the medium of light transmission (that space has an inherent motion), that conception of the nature of material objects will make it possible to show that the Lorentz distortions are not merely ad hoc assumptions made in order to retain the belief in absolute space, as is often charged, but rather have a necessity about them.

In the end, therefore, we will see that, in making the argument for his special theory of relativity, Einstein did not discover anything about the natural world that cannot be explained by an ontology, like spatiomaterialism, that implies that space and time are absolute. But what is more, spatiomaterialism explains special relativity in a way that removes all the mysteries about spacetime and makes it possible to explain ontologically, as well, why Einstein’s general theory of relativity is true. That will solve the main theoretical problem of contemporary physics, the relationship between gravitation and the other basic forces of nature, and it also has some surprising implications for cosmology.

A Brief history of Einstein’s special theory of relativity. The main conclusions of Einstein’s special theory of relativity are the Lorentz transformation equations. They are called the “Lorentz transformation equations,” because they had already been discovered, before Einstein’s first paper, by H. A. Lorentz, taking a Newtonian approach. That is where I will pick up the story about the Einsteinian revolution in physics, since spatiomaterialism is merely following in the footsteps of Lorentz. What I will call the four “Lorentz distortions”are sufficient to explain all the of the predictions by which Einstein’s special theory of relativity has been confirmed.

Lorentz. By 1887, some eighteen years before Einstein’s paper, Michelson and Morley had made experiments that showed that light has the same velocity relative to any object, regardless of its own motion. What made their result puzzling was the Newtonian assumption that the medium in which light propagates is a “luminiferous ether,” a very subtle kind of material substance that was supposed to be at rest in absolute space. Given that the velocity of light is everywhere the same relative to absolute space, they expected that the velocity of light, as measured from a material object, to vary with that object’s own velocity in absolute space—just as the velocity of ripples propagating in a pond arrive faster (or slower), when a boat is moving toward them (or away from them).

Michelson and Morley used an interferometer, which compares the two-way velocities of light in perpendicular directions; that is, light is reflected back from mirrors in perpendicular directions and the signals are compared to see if one is lagging behind the other. They made measurements at various points in the Earth’s orbit around the sun, where the Earth should have different velocities in absolute space. On a moving object, the time it takes for light to travel both to and from a distant mirror in the direction of absolute motion should be different from the time it takes to travel an equal distance in the transverse direction.ⁱ The margins of error were small enough, given the velocity of light and the velocity of the Earth in its orbit around the sun, that it should have been possible for their interferometer to detect absolute velocity. But Michelson and Morley failed to detect any difference at all in the time it took light to travel the same distance in perpendicular directions. Absolute motion could not be detected.

Length contraction. The Michelson-Morley result was surprising, but even before Einstein published his special theory in 1905, Lorentz had proposed a Newtonian explanation of it. Lorentz showed, in 1895, that their result could be explained physically, if the motion of such an apparatus in absolute space caused its length to shrink in the direction of motion as a function of its velocity by a factor of . Lorentz argued that this length contraction is a real physical change in the material object that depends on its motion relative to absolute space.

The equation was L=L_o, where L_o was the length at absolute rest. The shrinkage had been proposed independently by George F. Fitzgerald in 1889 and hence became known as the “Lorentz-Fitzgerald contraction”.ⁱⁱ

Lorentz tried to explain the length contraction physically, as an effect of motion through a stagnant ether on the electrostatic forces among its constituent, charged particles.ⁱⁱⁱ But he could just as well have taken it to be a law of physics, making the Lorentz-Fitzgerald contraction the discovery of a new, basic physical law. (An ontological explanation of it will be suggested in the last section of this discussion of the special theory of relativity.)

Lorentz also described the length contraction as a mathematical transformation between the coordinates of a reference frame based on the moving material object and the coordinates of a reference frame at absolute rest. Lorentz started with the Galilean transformation by which Newtonians would obtain the spatial coordinates used on an object in uniform motion in the x-direction, or x’ = x - vt, and combining that with the length contraction he had discovered, he came up with the transformation equation, for obtaining the spatial coordinates on the moving material object.^iv

Time dilation. There is, however, another distortion that material objects undergo as a function of their absolute motion. That is a slowing down of clocks (and physical processes generally) at the same rate as the length contractions, or the so-called "time dilation," which took somewhat longer for Lorentz to discover.

The Galilean transformation for time in Newtonian physics is simply t = t' , because Newtonian physics assumes that time is the same everywhere. But by using transformation equations to describe the distortions in material objects, Lorentz found that he had to introduce a special equation for transforming time: t’ = t - vx/c² (Goldberg, p. 94). The new factor in the transformation equation, vx/c², implied that time on the moving frame varies with location in that frame. Lorentz called it "local time," but he did not attribute any physical significance to it. "Local time" is not compatible with the belief in absolute space and time, and Lorentz described it as “no more than an auxiliary mathematical quantity” (Torretti, p. 45, 85), insisting that his transformation equations were merely “an aid to calculation” (Goldberg, p. 96).

The slowing down of physical processes is called “time dilation.” Lorentz discovered this distortion by tinkering with various ways of calculating the coordinates used on inertial reference frames in relative motion. Thus, it is natural to describe time dilation as the slowing down of clocks on the moving reference frame. It was included in the final version of Lorentz's explanation, now called the “Lorentz transformation equations.” (Lorentz 1904) Those equations contained not only the length contraction and transformation for “local time”, but also the implication that clocks on moving frames are slowed down at the same rate as lengths are contracted (that is, ). The final Lorentz equation for time transformation included both the variation in local time and time dilation: .

Though Lorentz took the distortions that he discovered in fast-moving material objects to be laws of nature, he did not think that they were basic. He thought they were effects of motion on the interactions between electrons and the ether which could be explained by his electronic theory of matter, and he saw explaining this effect as the the main challenge to Newtonian physics. The transformation equations themselves never seemed puzzling to Lorentz, because he never took them to more than just a mathematical aid to calculation.

Poincaré. H. Poincaré thought he saw more clearly what Lorentz had discovered than Lorentz himself. As early as 1895, Poincaré had expressed dissatisfaction with Lorentz’s piecemeal approach, introducing one modification of the laws of Newtonian physics after another in order to account for different aspects of the phenomenon discovered by Michelson and Morley. Instead of such ad hoc modifications, he urged the recognition of what he called a “principle of relativity” to cover all the phenomena involved in fast-moving objects. As Poincaré put it in 1904, the principle of relativity requires that “the laws of physical phenomena should be the same for an observer at rest or for an observer carried along in uniform movement of translation, so that we do not and cannot have any means of determining whether we actually undergo a motion of this kind” (from Torretti, 83).

A principle of relativity like this had, in effect, been affirmed by Newton himself, when he admitted that his laws of motion depend, not on the absolute velocities of material objects, but only on their relative velocities. That is, Newton had already denied that absolute rest could be detected by mechanical experiments. It seemed that absolute motion could be detected only when Maxwell had discovered that light could be explained as an electromagnetic wave. Thus, Poincaré saw Lorentz's discovery of distortions in fast-moving material objects as a way of extending Newton’s principle of relativity to cover electromagnetic phenomena.

Understanding how the undetectability of absolute motion could be a result of the distortions that Lorentz had discovered, he referred to Lorentz theory as “Lorentz’s principle of relativity” even after Einstein had published his special theory and Lorentz himself was attributing the principle of relativity to Einstein (Torretti 85, Goldberg 212, and Holton 178). Indeed, Poincaré joined Lorentz in the attempt to explain the Lorentz distortions by the motion of material objects through absolute space, also expecting to find their cause in the dynamics of electrons; he also thought that motion through the ether caused material objects to shrink in the direction of motion and natural clocks to slow down by the exact amount required to mask their motion, as implied by Lorentz’s transformation equations (Goldberg 94-102, Torretti 38-47). Furthermore, Poincaré apparently thought that what Lorentz said about those equations in his 1904 work answered his own demand that it be a “demonstration of the principle of relativity with a single thrust” (Goldberg 214-15).

Lorentz's explanation of the distortions was not, however, a complete explanation of the principle of relativity. There are really two quite different aspects of the phenomenon described by the principle of relativity, and Lorentz had explicitly explained only one of them.

What Lorentz’s electron theory of matter (and Poincaré’s own refinements of it) explained physically were the Lorentz distortions in material objects with absolute velocity. That explained the negative outcome of the Michelson-Morley experiment: the contraction of lengths in the direction of motion and the slowing down of clocks as a function of motion through absolute space does make it physically impossible to detect absolute motion on a moving object by measuring the velocity of light relative to it. And that is one way in which inertial reference frames are empirically equivalent, because it holds of measurements made using any material object in uniform motion as one's reference frame, regardless of its motion through absolute space.

But there is more to the principle of relativity than explaining the null result of the Michelson-Morley experiment. The transformation equations that Lorentz constructed to describe the effects of absolute motion on material objects predict the outcomes of other experiments, such as attempts to measure directly the lengths of high-velocity measuring rods and the rate at which high-velocity clocks are ticking away. Though such experiments are more difficult to perform, they are conceivable, and Lorentz's equations do make predictions about them: moving measuring rods will be shrunken in the direction of motion and moving clocks will be slowed down. That suggests another way of detecting absolute motion. One might compare measuring rods or clocks that are moving at a whole range different velocities with one another and take the one with the longest measuring rods and quickest clocks to be closest to absolute rest. Hence, the principle of relativity would be false.

It is not possible, however, to detect absolute rest in this way, and as it happens, its impossibility is also predicted by Lorentz's theory, because he formulated his description of the Lorentz distortions in terms of transformation equations. Transformation equations are equations for transforming the coordinates obtained by using one material objects as a frame of reference into the coordinates obtained by using another material object as a frame of reference, and to be consistent, they must work both ways. That is, it must be possible to obtain the original coordinates by applying the transformation equations to the transformed coordinates. Thus, whatever distortions observers at absolute rest may find in material objects with a high absolute velocity will also be found by observers in absolute motion in material objects that are at absolute rest.

The recognition that Lorentz's theory, being formulated in terms of transformation equations, implied that all such inertial reference frames are empirically equivalent is presumably what led Poincaré to proclaim that Lorentz had finally explained the truth of the principle of relativity. Absolute rest and motion cannot be detected from any inertial reference frame.

Lorentz's theory was not, however, an adequate explanation of the principle of relativity, for there is still something puzzling about the empirical equivalence entailed by the symmetry of the Lorentz transformation equations.

Lorentz meant his transformation equations to be a way of describing the length contraction and time dilation in material objects with absolute motion, for that would explain the Michelson-Morley experiment, that is, why absolute motion cannot be detected by measuring the velocity of light in different directions. But since the transformation equations describe a symmetry between the members of any pair of inertial reference frames, they imply that observers using a fast-moving material object as the basis of their reference frame would observe a length contraction in measuring rods that were at absolute rest and a time dilation in clocks at absolute rest. That makes it impossible to detect absolute rest or motion by comparing different inertial reference frames with one another. But it is puzzling, because it is hard to see how both views could be true at the same time, that is, how two measuring rods passing one another at high velocity could both be shorter than the other and how two clocks passing by one another could both be going slower than the other.

In other words, Lorentz's theory does not really give a physical explanation of what Poincaré called the "principle of relativity." What entails the truth of the principle of relativity is the description of the Lorentz distortions in terms of transformation equations; the inability to detect absolute rest and motion by comparing inertial frames with one another comes from the symmetrical relationship that transformation equations represent as holding between the members of any pair of inertial reference frames. That symmetry is not physically possible, at least, not in the sense of "physical" that Lorentz had in mind when he tried to explain the distortions as occurring to material objects because of their motion in absolute space. If inertial frames are material objects in absolute space, then their measuring rods cannot both be shorter than the other and their clocks cannot both be slower.

As we shall see, what enables Lorentz's transformation equations to predict the symmetry of distortions is the "local time" factor in the time equation, vx/c², which Lorentz insisted was just an "aid to calculation." It represents the readings that would be given by clocks on a moving reference frame that have been synchronized by using light signals between them as if they were all at absolute rest, that is, on the assumption that the one-way velocity of light is the same both ways along the pathway between any two clocks (as required by Einstein's definition of simultaneity at a distance). That assumption is false, as Lorentz understood these phenomena, and clocks on the moving inertial frame would be mis-synchronized. It can be shown, as we shall see, that this way of mis-synchronizing clocks on a moving frame combines with the Lorentz distortions that the moving frame is actually suffering to make it appear that its own Lorentz distortions are occurring in the reference frame at absolute rest (or moving more slowly). This is a physical explanation, given how the other frame's measuring rods and clocks are measured. But it is an explanation of the principle of relativity that reveals it to be the description of a mere appearance. Though there is an empirical equivalence among inertial frames, a physicist who accepted Lorentz's Newtonian assumptions would insist that it has a deeper physical explanation.

It was not Lorentz, however, but Poincaré who declared that Lorentz had explained the truth of the principle of relativity, and Poincaré's acceptance of Lorentz's explanation as adequate may have been colored by his own philosophical commitment to conventionalism. Poincaré viewed the choice between Euclidean or non-Euclidean geometry as conventional, and he argued that convention is also what raised inertia and the conservation of energy to the status of principles that could not be empirically falsified. Poincaré's acceptance of the principle of relativity should probably be understood in the context of this more or less Kantian skepticism about knowing the real nature of what exists. Considering how the standard of simultaneity at a distance varies from one inertial reference frame to another (depending on the "local time" factor in the Lorentz transformation equations), the principle of relativity could also be seen as a conventional truth.

Poincaré's pronouncement that Lorentz's theory had explained the principle of relativity could not have set well with Lorentz himself. Lorentz may have continued to call it "Einstein's principle of relativity" because he realized that it was not explained by his theory about how spatial and temporal distortions are caused in material objects by their absolute motion. What is responsible for the principle of relativity is the symmetry in pairs of inertial frames entailed by his equations being transformation equations. If the distortions didn’t hold symmetrically in any pair inertial frames, it would be possible to detect absolute rest and motion. But to my knowledge, Lorentz never argued explicitly that what he called "local time" on the moving material object (that is, vx/c² in the time equation) represents a mis-synchronization of clocks on the moving frame that causes the moving frame's own Lorentz distortions to appear to be occurring in the other inertial reference frame.

The Newtonian explanation of all the relevant phenomena did not, therefore, have an adequate defender. Lorentz was more concerned to find an adequate physical explanation of the distortions he had discovered in material objects, and Poincaré was more interested in defending conventionalism. That is the Newtonian context in which Einstein's special theory of relativity won the day.

Einstein. Einstein took a dramatically different approach from both Lorentz and Poincaré. Instead of taking the principle of relativity to be an empirical hypothesis that could be explained physically by deeper, Newtonian principles, or as a conventional truth, Einstein raised the principle of relativity to the status of a postulate, which was not to be explained at all, but rather accepted as basic and used to explain other phenomena (Zahar 90-2). The mathematical elegance of Einstein's explanation of these phenomena is stunning. From the premise that all inertial reference frames are empirically equivalent, he derived a description of how two different inertial reference frames would appear to each other; that is, he deduced the Lorentz transformation equations.

Einstein's new approach can be seen most clearly by considering the structure of his argument. It is represented below in a diagrammatic form.

The assumption that inertial frames are all empirically equivalent takes the form of three premises in Einstein’s argument: the Principle of Relativity, the Light Postulate, and Einstein's Definition of Simultaneity at a Distance (see table). Einstein's principle of relativity holds, with Poincaré, that the laws of nature hold in the same way on every inertial reference frame. That allowed Einstein to assume that Maxwell's laws of electromagnetism hold universally, and he considered what would be true of two different inertial frames in the same world. But in order to deduce the Lorentz transformation equations, Einstein also had to assume that that the velocity of light is the same relative to every inertial frame (the light postulate) and, accordingly, that simultaneity at a distance is defined on each reference frame as if the velocity of light is the same both to and back from a distance object.

What Einstein deduced from these premises are the “Lorentz transformation equations,” that is, equations for transforming the coordinates of any given inertial reference frame into those of any other.

The Lorentz transformation equations imply that any material object moving relative to any other inertial frame at a velocity approaching that of light will appear to suffer the Lorentz distortions: its clocks (and all physical processes) will be slowed down, and its measuring rods (and all material objects) will be shortened in the direction of its motion—both by the same amount, , which is a function of its velocity in the observer’s reference frame.

Einstein also inferred from these kinematic distortions and his principle of relativity that the mass of objects moving in an inertial frame increases at the same rate, making three distortions altogether. That dynamical implication is the source of Einstein's most famous equations, E = mc².

It should be emphasized that there are really two sets of transformation equations. It may not seem that way, because Einstein's conclusion is often stated as just one of the two sets of equations listed above, making it look mathematically simpler. But that formulation overlooks a mathematical detail and thereby obscures what Einstein's conclusion is about.

Though the Lorentz transformation is exactly the same both ways between the members of any pair of inertial reference frames, it requires two, non-identical sets of transformation equations, because their relative velocity has the opposite sign for each observer. That is, the two coordinate systems are set up so that their origins coincide when t = 0 and t' = 0, and since they are moving in opposite directions, the relative velocity is v for one of them and -v for the other. Thus, in order for the transformation to be symmetrical, one set of transformation equations has to have the opposite sign for the second factor in the numerator of the equations for space and time.

Since this seems to be a mere technicality, the conclusions of Einstein’s argument are usually represented as a single set of Lorentz transformation equations (the first set in the above table). Duplication is avoided by introducing a special mathematical symbol to make the single set of equations represent both transformations in any pair of inertial frames. Thus, Einstein's conclusion seems more like just another universal law of nature. But this is just homage to the Pythagorean ideal of mathematical simplicity, which obscures the fact that Einstein's theory is, in the first instance, about the symmetry that holds between the members of every pair of inertial frames.

It should also be emphasized that Einstein's theory is about how reference frames are related, and only indirectly about the material objects on which they are based. Though it does have implications concerning the relationship between material objects with a high relative velocity, that relationship is described by way of a mathematical transformation that holds between the reference frames based on them.

Inertial reference frames are based on material objects that are not being accelerated, and what makes the material object a reference frame is that it is used as the basis for a coordinate system by which the locations and times of events throughout the universe can be measured. (For this purpose, it is useful to think of an inertial reference frame as a grid of rigid bars extending wherever needed in space with synchronized clocks located everywhere.)

Notice that Einstein's three premises are all about reference frames based on material objects. Indeed, his definition of simultaneity prescribes how clocks must be synchronized to set up such a reference frame. The light postulate makes explicit the assumption about the velocity of light on which his definition of simultaneity is based. And the principle of relativity states that all the laws of physics will hold the same way within that reference frame as every other one, that is, will make correct predictions about what happens in that reference frame.

Einstein derives conclusions from his premises by assuming that there are two different inertial reference frames in the world and figuring out how they must appear to one another. Since his premises are about their reference frames, it is hardly surprising that his conclusion is about a mathematical transformation between their coordinates.

Indirectly, however, Einstein's conclusion is a description of how material objects with different constant velocities are related to one another as parts of the same world, since the reference frames in question are based on material objects. But to see Einstein's conclusion as a description of how material objects are related in space is to take Lorentz's approach. For Lorentz, these same transformation equations were just a mathematically convenient way of describing from the absolute frame the spatial and temporal distortions that occur in material objects with a high velocity in absolute space.

By calling his argument a theory of relativity, Einstein emphasized that his theory is about the empirical equivalence of all inertial reference frames, not the relationship between the material objects on which they are based. Observers on each inertial reference frame have their own view of the relationship between the material objects involved, but they are different views, and it is their views that are related by the Lorentz transformation equations. The symmetry of the relationship between their reference frames is what is crucial for Einstein, because that is what rules out any way of detecting absolute rest or motion by comparing inertial frames to one another and ensures that there is nothing to distinguish one inertial frame from another except their velocities relative to one another.

The Lorentz distortions in material objects are, however, a consequence of the Lorentz transformation equations that Einstein deduced. And if one does follow Lorentz, interpreting them as a way of describing the material objects on which the inertial reference frames are based, then the Lorentz transformation equations lead to paradoxes, as I have already suggested. Those equations imply that observers using any given inertial reference frame will find the Lorentz distortions occurring in the material objects on which the other inertial reference frame is based, and thus, the symmetry of the transformation for any pair of inertial frames leads to paradoxes.

Consider two inertial frames in motion relative to one another. From the first frame it appears that clocks on the second frame are slowed down. That would make sense, if from the second frame, it appeared that first-frame clocks were speeded up. But special relativity implies that it also appears from the second frame that clocks on the first frame are slowed down. That is, the distortions are symmetrical on Einstein’s theory, not the reverse of one another, as one might expect. And if the Lorentz distortions are really symmetrical, it is inconceivable that the two inertial frames are just material objects moving relative to one another in absolute space, because in absolute space, there can’t be two clocks next to one another both of which are actually going slower than the other. If one assumes that Einstein's theory is describing material objects, one must give up the assumption that those objects are located in absolute space. They are, of course, parts of the same world, but they must be related to one another in some other way.

The same problem arises from the symmetry of the length contraction and relativistic mass increase, for there cannot be two measuring rods passing one another in space that are both shorter than the other. Nor can there be two material objects both be more massive than the other. It is simply not possible for material objects located in absolute space.

None of this should be a surprise, however, because even the Light Postulate itself is incompatible with absolute space (or at least, with the assumption that light has a fixed velocity relative to absolute space). Though Newtonian physics had taken absolute space to contain the medium in which light propagates, Einstein assumed that the velocity of light relative to every object is the same, regardless of their own velocities relative to other objects in the world. Thus, Einstein held that the velocity of light would be the same in both members of any pair of inertial frames. This is not possible, if electromagnetic waves propagate through (an ether in) absolute space, like waves in water, for the motion of an object through waves propagating in space would change the velocity of those waves relative to the object—just as the motion of a row boat through ripples propagating in a pond changes the velocity of those ripples relative to the boat.

Taken as a description of the relationship between material objects in space, therefore, Einstein's special theory of relativity leads to paradoxes. But Einstein was not discouraged by these paradoxes. He was not thinking of inertial reference frames as material objects that are related in space, that is, in absolute space, or a space that is the same for both material objects. He was making a more abstract, mathematical argument and, in the process, giving physics a new standpoint from which to explain all physical processes.

That Einstein's basic approach is different from Lorentz's can be seen in what made Einstein curious about these phenomena in the first place. It was not the Michelson-Morley experiment, but rather something peculiar about the connection between classical mechanics and Maxwell’s theory of electromagnetism (Zahar 99-100). Einstein realized that even though Maxwell’s theory was standardly interpreted as referring to absolute space, absolute space was not needed in order to explain electromagnetic phenomena. For example, a conductor moving through a magnetic field at absolute rest moves electrons exactly the same way as if it were at absolute rest and the magnetic field were moving. That is what suggested the principle of relativity to Einstein, and though from it he derived the same transformation equations that Lorentz had proposed in 1904, Einstein claimed not to know about Lorentz's 1904 work.^v

By raising the principle of relativity to the status of a postulate, Einstein was assuming, in effect, that the deepest truth that can be known about the nature of space and time is that inertial frames are all empirically equivalent. And by relying on the predictions of measurements derived from that principle to justify his theory, Einstein had the support of the positivists, who dominated philosophy of science at that time. Indeed, Einstein admits to having been influenced by Ernst Mach at the time of his first paper on special relativity. To positivists, the paradoxes mentioned above about two clocks both going slower than the other and two measuring rods both shorter than the other are not real problems, but merely theoretical problems. Theoretical propositions that could not be spelled out in terms of observations were dismissed as "metaphysical," as if theories were mere instruments for making predictions. That attitude could be taken about the aforementioned paradoxes, because there is never any occasion in which two clocks can be directly observed both going slower than the other (or two measuring rods observed both shorter than the other). Observations are made from one inertial reference frame or another, and if both members of some pair of inertial frames are observed from a third reference frame, their clocks and measuring rods do not appear this way because of the Lorentz distortions that are introduced by its own velocity relative to them.

Though when taken as a description of material objects, the special theory of relativity is incompatible with the existence of absolute space, Einstein did not attempt to use its implications to show that absolute space does not exist. He was making a mathematical argument to show that accepted theories in Newtonian physics, which did assume the existence of absolute space, could all be replaced by theories that do not mention absolute rest or motion at all.^vi All he explicitly claimed was that physics does not require an “absolutely stationary space” and that the notion of a “‘luminiferous ether’ will prove to be superfluous” because the “phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the ideas of absolute rest” (Einstein, 1923 p. 37). It could be argued, therefore, that Einstein was merely imitating empiricist skepticism about theoretical entities generally by casting doubt on the reality of absolute space.

As it turned out, Einstein's theory proved to be remarkably successful in making surprising predictions of new experiments. For example, unstable particles have longer half-lives when moving at velocities approaching that of light. Clocks flown around the earth are indeed slowed down compared to clocks that stayed at home. The most famous new prediction of special relativity, E = mc², has been confirmed repeatedly. It is a consequence of the relativistic increase in mass, which Einstein first pointed out, and without it, high energy physics as we know it today would be inconceivable. Finally, the equations of special relativity have become (after Dirac) the foundation of quantum field theory as well as Einstein’s theory of gravitation. The Lorentz transformation is now so basic to physics that “covariance” (or “Lorentz covariance”) is taken as a constraint on all possible laws of physics.

To be sure, Newtonian physicists complained about the loss of intuitive understanding that came with the acceptance of Einstein's way of explaining these phenomena. It was no longer possible to construct in ordinary spatial imagination a picture of the nature of the world. But that objection did not detract from the predictive success of Einstein's theory, and the Einsteinian revolution made the capacity of mathematical arguments to make surprising predictions of precise measurements the establishment criterion for accepting theories in contemporary physics.

But physics is not just mathematics. A theory in physics is generally thought to be true when it corresponds to what exists, and if the special theory of relativity does not correspond to material objects in absolute space, we want to know what it does correspond to. The success in making surprising predictions of what happens by which Einstein's theory has been confirmed means that it corresponds to regularities that hold of change in the world, but it is natural to want to know the nature of what exists that makes those regularities true. The answer given by contemporary physics is spacetime, and it was Minkowski that has made that answer possible.

Minkowski. In 1908, Minkowski offered a mathematically elegant way of representing what is true from all inertial frames, according to Einstein’s special theory of relativity, using only the coordinates of any single inertial frame.^vii His was a “graphic method” which he said allows us to “visualize” what is going on. The key to his diagram was to represent time in the same way as space, and that is what has led to the belief that what exists is not space and time, but rather spacetime.

In Minkowski’s “spacetime diagrams”, time is represented as a fourth dimension perpendicular to the three dimensions of space (though when comparing two inertial frames, the spatial dimensions can be reduced to one by a suitable orientation of their coordinate frames). A material object at rest in space is represented, therefore, as a line running parallel to the time axis, and a material object with a constant, non-zero velocity is represented by a line inclined slightly in the direction of motion. Units for measuring time and space are usually chosen so that the path of light in spacetime (the “light-line”, t = x/c) bisects the time and space axes, making the “basic unit” of distance how far light travels in a unit of time.

Since the second frame of reference is based on a moving object, we can think of the tilted line representing its pathway as its time axis. From such a moving reference frame, the location of an object at rest in the first frame (such as one always located at its origin) would change relative to the moving frame. So far, this diagram of space and time would be acceptable in classical Newtonian physics, because it represents a so-called Galilean transformation for the coordinates of moving reference frames (in which distances in space would be related as x' = x – VT, where v is their relative velocity in the x-direction.)

What Minkowski discovered was that the Lorentz transformation for moving reference frames could be represented by tilting the space line of the moving frame equally in the opposite direction and lengthening the units of time and space. That is, the time-line and the space-line of the moving frame are inclined symmetrically around the pathway of light. (See the comparison of the Newtonian Diagram of Space and Time and Minkowski's Spacetime Diagra

In either the Newtonian or Minkowski's diagram, every point represents the location of a possible event in space and time (called a “world-point”), and superimposing a second reference frame makes it possible to give such coordinates in either reference frame. From the coordinates for any event in the first reference frame, we can simply read off the coordinates for the same event in the moving reference frame, and vice versa. In the case of event E, for example, the coordinates in the first frame are (2,1), and in Minkowski's diagram, they are (1.3,0.3). All possible reference frames can be represented in this way, each with a different tilt to its time-axis representing its velocity relative to the first.

The two reference frames in the Newtonian diagram have a very simple relationship, because time coordinates are the same for both reference frames and there is no change in the units of either time or space. But Minkowski's spacetime diagram represents the Lorentz transformation, and not only are the units of time and space different, but the space-line of the moving reference frame is inclined relative to the first reference frame.

Minkowski’s spacetime diagram yields the same coordinates for the second reference frame that are obtained from the Lorentz transformation equations deduced by Einstein. Thus, it predicts that measurements of the second inertial frame will reveal its clocks to be slowed down and its measuring rods to be contracted in the x-direction.

But since the Lorentz transformation works both ways, it is possible to start with the second (tilted) reference frame and obtain coordinates for events in the first reference frame. Thus, it predicts that the moving observers will detect Lorentz distortions occurring in the first frame. This symmetry about the relationship between inertial reference frames makes it impossible to single out any particular frame as being at absolute rest by comparing reference frames with one another.

Minkowski's spacetime diagram may seem to mitigate the paradoxes resulting from the symmetry of the relationship between members of any pair of inertial reference frames, because it enables us to "picture" two clocks both ticking away slower than the other and two measuring rods both shorter than the other. It is just a result of how the inertial reference frames are related to one another.

But this wonderful power of Minkowski's spacetime diagram to represent these puzzling phenomena would not be possible, if the space-lines of different reference frames had the same slope. The inclined orientation of the space-line of the second inertial frame relative to the first frame is crucial to representing the Lorentz transformation, and it represents a disagreement between inertial observers about simultaneity at a distance. That is, observers using different inertial reference frames will disagree about which events at a distance are simultaneous with the origins of their systems when they pass by one another. That is the source of all the ontological problems with the belief in spacetime.

Though it is possible to interpret Minkowski's spacetime diagram as just a useful mathematical device for predicting the measurements that would be made on different inertial frames, that is what the Lorentz transformation equations already do. The historical significance of Minkowski's diagram is that it enables us to "picture" what exists in a world where Einstein's special theory of relativity is the deepest truth about the world. Thus, it leads to the belief in spacetime (that is, "spatiotemporalism," as I called it in Spatiomaterialism, or "substantivalism about spacetime," as it is called in the literature.)

The belief in spacetime comes from realism about special relativity. Scientific realism holds that theories in physics are true in the sense of corresponding to what exists, and spacetime is what must exist, if Einstein's special theory of relativity is the deepest truth about the real nature of what exists as far as space and time are concerned.

With regard to space and time, Newtonian realists would say that what their theories correspond to is absolute space and absolute time, that is, to a three dimensional space all of whose parts exists at the present moment and endure simultaneously through time. But that is not what Einstein's special theory of relativity corresponds to, because it implies that observers on all possible inertial reference frames are equally correct about the times and places of the events that occur in the world, even though they disagree about the simultaneity of events at a distance. What all the different inertial observers say about the times and places of events can, however, be true at the same time, only if what exists is represented by Minkowski's spacetime diagram. Thus, spacetime is the natural answer to the question about what corresponds to Einstein's special theory of relativity. According to realists about special relativity, what exists is spacetime, a four-dimensional entity that contains time as a dimension and, thus, is not itself in time.

Though Einstein may merely have been arguing in the spirit of the empiricist skepticism that prevailed in philosophy at that time, Minkowski made it possible to give a realist interpretation of Einstein’s special theory. His spacetime diagram showed how Einstein's theory could be interpreted as a description of what really exists in the case of space and time. Minkowski must have realized that he was giving a realist interpretation of Einstein's special theory of relativity when he introduced his spacetime diagrams; he said (Minkowski 75) that “space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”. In any case, later in the twentieth century, when logical positivism gave way to scientific realism, Einstein’s skepticism about absolute space, if that is what it was, spawned the belief in the existence of spacetime. Indeed, regardless what Einstein may have believed in 1905, he apparently came to agree that what he had discovered was spacetime. (See Einstein 1966, pp. 205-8).

Scientific realism is, however, a way of letting science determine one's ontology. That is not the best way to decide which ontological theory to accept, because the empirical method that science follows is to infer to the best efficient-cause explanation, and that may not be the best ontological-cause explanation. But we can see how realism led to an ontology based on spacetime.

Einstein's special theory of relativity was a better efficient-cause explanation of the relevant phenomena than Lorentz's way of defending his transformation equations, because it made all the same precise predictions of measurements, but in a mathematically simpler way. As an efficient-cause explanation, however, all that Einstein's special theory requires is an empirical equivalence of inertial reference frames. It assumes that inertial frames are experimentally indistinguishable from one another, and it derives a description about how they must appear to one another as parts of the same world (where Maxwell's laws of electromagnetism hold). That relationship is described by the Lorentz equations for transforming their coordinates into one another, and it is represented by Minkowski's spacetime diagram. But Einstein's was a mathematical argument, and no mechanism or cause of the empirical equivalence was given.

A realist interpretation of special relativity goes beyond mere empirical equivalence and holds that inertial frames are all ontologically equivalent. If special relativity is the literal and deepest truth about the world, then what observers on all possible inertial reference frames believe must be true at the same time. That is to hold, not merely that no experiment can distinguish any one inertial frame from all the others as the absolute frame, but that there is nothing about the nature of any inertial frame that makes it stand out from all the others. That means, among other things, that no assertion made by observers on one inertial frame can be true unless the same kind of assertion made by observers on every other inertial frame is also true. (Nor can any assertion made on one inertial frame be false unless the same kind of assertion made on every other inertial frame is also false.)

The virtue of Minkowski's spacetime diagram is that it enables us to "picture" what exists in a world where inertial reference frames are all ontologically equivalent. Though it may still be unclear what spacetime is, Minkowski's diagram does allow us to believe that all possible reference frames are related to what exists in the same way, for it accommodates all possible standards of simultaneity at a distance. But they can all correspond to what exists only if the world is a four-dimensional entity all of whose parts in both space and time exist in the same way.

It is clear that this ontological equivalence of inertial frames is incompatible with absolute space and time, because if space and time were absolute, one inertial frame would be singled out ontologically from all possible inertial frames. Only one of all possible inertial frames would have the correct standard of simultaneity. Its location in space and time could be shared by observers on many other inertial frames, but none of their claims about which distant events are simultaneous with their shared here and how would correspond to what exists.

Einsteinians do not use the term "ontological equivalence" to describe the relationship between different inertial reference frames, but that is what the belief in spacetime comes to. Most philosophers of space and time simply take it for granted that they must accept "substantivalism" about spacetime in order to interpret the special theory as a description of the real nature of what exists. ^viii

To believe in spacetime is to accept an ontology that is fundamentally different from Lorentz's Newtonian view, and the difference can be seen in what each implies about the nature of material objects.

Newtonian physicists assumed that material objects are substances that endure through time. They had to believe in absolute time, because the endurance theory of substances presupposes that only the present exists, or "presentism." (If the world is everything that exists, then objects that exist at only one moment in their histories must exist at the same time, for otherwise they would not be parts of the same world.) And since Newtonian physicists believed that material objects are all related to one another by (consistent) spatial relations, they were also forced to believe in absolute space. In a natural world, absolute time entails absolute space. Hence, the Newtonian world was made up of material objects in three dimensional space that endured through time.

Spacetime, on the other hand, is a four-dimensional entity. What exists is spacetime and all the events that are located in spacetime. Since time is an aspect of its essential structure, a spacetime world cannot endure through time. Thus, spacetime points and spacetime events must all exist in the same way independently of one another, if they exist at all. There are no material objects in a spacetime world, at least, not in the way that Lorentz believed. There are only the spacetime events that seem to make up the histories of so-called material objects. Thus, what is ordinarily called a "material object" is just a continuous series of spacetime events in spacetime. Its real nature is represented accurately by a “world line” in a spacetime diagram, because each spacetime event making up the history of a "material object" has an existence that is distinct from all the others, just as one point on a line exists distinctly from every other point on the line.

In short, whereas a material object in a Newtonian world exists only at each moment as it is present, but is identical across time, a so-called material object in a spacetime world is a continuous series of spacetime events, each of which exists eternally as a distinct part of the world. This is the difference between the endurance and perdurance theory of substances, and between the presentist and eternalist theory about time and existence.

Scientific realists sometimes assume that they can believe that Einstein's special theory of relativity corresponds to what exists without denying that they are themselves substances that endure through time by holding that only objects at a distance from themselves must exist the same way at all different moments in their histories. But that is not possible, if they believe that the truth of Einstein's special theory means that it corresponds to what exists for every observer. If Einstein's theory is universally true, then it must be true for inertial observers located elsewhere in the universe, and the only way that different inertial observes at a distance from us can all be correct about which moment in our local history is simultaneous with their passing by one another is if the moments in our local history all exist in the same way. We must perdure, rather than endure, because we are material objects at a distance for inertial observers elsewhere in the universe.

What Minkowski's “union” of space and time means ontologically is, therefore, that presentism is false. The denial of presentism is such a serious obstacle to an ontological explanation of the world that, in Spatiomaterialism, we were led to reject spacetime substantivalism (or "spatiotemporalism"), promising to justify it later by showing how it is possible for space and time to be absolute, despite the Einsteinian revolution. That is the argument we take up in the next section. But first, let us consider briefly why physics has ignored the ontological problems with eternalism.

What explains the ascendancy of the belief in spacetime is, once again, the empirical method of science and the physicists' addiction to mathematics as a means of practicing it. Behind Minkowski's spacetime diagram lies an elegant equation that has proved to be irresistibly attractive.

Minkowski provided a method of constructing in our own spacetime coordinate frame the spacetime coordinate frame that would be used by observers on an object moving relative to us. We may call their world-line the “moving timeline” (t = x/v), because it will be the time axis that moving observers use for their spacetime coordinate frame.

Minkowski formulated the conclusion of Einstein’s special theory as an equation that describes a hyperboloid in four dimensional spacetime: 1²  = c²t² - x² - y² - z². (When we orient our x-axis in the direction of the others’ motion, we can ignore the other two dimensions and it reduces to 1² = c²t² - x².) (It is the red curve in the diagram depicting how Minkowski's spacetime diagram is constructed.) The intersection of Minkowski’s hyperboloid curve with our time-axis is the unit of time in our frame (t = 1), and the unit of distance (in “basic units”) is the distance in our frame that light travels during that period of time (x = 1). The moving timeline (the time-axis of the moving spacetime frame) also intersects the curve described by Minkowski’s equation, and the distance of that point along our time-axis is the length of a unit of time on the moving coordinate frame according to our clocks.

As the diagram shows, moving clocks are slowed down in our frame. The other axis of the moving spacetime frame, the “moving space-line”, is also deduced from Minkowski’s equation. Moving space-lines all have the same slope as the tangent to Minkowski’s curve at the point of the moving timeline’s intersection with his curve. (Its slope is v/c²; the points on any line with this slope are simultaneous in the moving spacetime frame.) Finally, the unit of distance on the moving space-line is how far light travels in the moving frame during a unit of time on the moving frame.

Inertial frames are all equivalent on Minkowski’s theory, as on Einstein’s, since Minkowski’s equation determines precisely the same hyperbola in every moving inertial frame constructed this way in our own spacetime coordinate frame. That is, their hyperbolas all coincide. In particular, the same procedure on the moving coordinate frame, using the same equation (and taking the velocity to be -v along the x'-axis), produces the original coordinate frame. Or more abstractly, Minkowski’s equation can be generalized as a measure, s, of the separation between any two events that is the same in every inertial frame, despite variations in their coordinates for particular events: s² = c²t² - x² - y² - z².

In Minkowski’s equation, the parallel between the representation of space and time is remarkable. Time would be just another spatial dimension, except that it lacks a minus sign (and needs the velocity of light, c, to make units of time commensurable with distance). Indeed, that is how Minkowski includes relativistic mass increase. His equations’s form can be used to state the laws of nature that hold true in every inertial frame. In “four vector physics”, or “covariant” formulations of laws of physics, the energy of an object, E, takes the place of time and the three dimensions of momentum, p, take the place of the three spatial dimensions, so that the objects’ rest mass, m₀, rather than the separation, is what is the same about the object in all inertial frames: m_o²c⁴ = E² - p_x²c² - p_y²c² - p_z²c². The mathematics of four vector physics is so elegant and suggestive about the relationship of energy and momentum that it is not surprising that physicists now find themselves committed to the belief in spacetime.

By comparison with Lorentz’s ad hoc attempts to patch up classical physics in the wake of the Michelson-Morley experiment, Einstein’s argument was astonishingly simple and elegant, making it seem that Einstein had a deeper insight into these phenomena. And since Minkowski provided a diagram that made it possible to represent what special relativity implies about the world independently of particular reference frames, it is hardly surprising that the belief in spacetime has become the orthodox ontology in physics and the philosophy of science.

The acceptance of Einstein’s special theory of relativity involved, however, a remarkable change in the empirical method of physics, for it involved the abandonment of the requirement that explanations in physics be intuitively intelligible.

To follow the empirical method is to infer to the best efficient-cause explanation. Even in classical physics, theories were highly mathematical and confirmation was most convincing when they predicted surprising, quantitatively precise measurements. But since classical physicists still believed in absolute space and time, they also expected the best scientific theories to be intuitively intelligible, in the sense that it was possible to think coherently about what was happening in spatial imagination. But intuitive intelligibility was no longer possible when the best scientific theory required giving up the belief in absolute space and time. That was undeniably a loss, but physicists felt that they had to grow up and recognize that their deepest commitment was to judging the best theory by which is the simplest and most complete prediction of measurements. Since this came from mathematical theories, abandoning the requirement that physical explanations be intuitively intelligible left them addicted to mathematics.

What forced us to promise to explain how Einstein's special and general theories of relativity could be true in a world where space and time are absolute was the commitment of contemporary physics to the belief in spacetime. We had to take out that "mortgage" on spatiomaterialism as the foundation for ontological philosophy, because spatiomaterialism is committed to absolute space and time. This section will pay it off by showing how how the special theory of relativity can be true in a spatiomaterial world.

Let us recall, first, our reason for believing that space and time are absolute. We were inferring to the best ontological explanation of the world. That is not the method of empirical science, because an ontological theory is a theory about the nature of what exists, not only about what happens to it. The first basic issue about the nature of what exists has to do with the nature of time, and we concluded that we had to prefer presentism to eternalism because it alone could explain our observations about how the present moment is different from the past and future. Presentism holds that only the present exists. The past and the future do not exist. To be is to be in time.

We know by reflecting on ourselves as agents that the future does not exist, because if it did, we would not be able to control what happens in the world. We act as we do in order to make the future different from what it would be otherwise, and that would simply not be possible, if the future already existed. Every event must aleady be determined, if eternalism is true,

Reflection should be considered relevant evidence about the nature of what exists in the world, since the beings who do the reflecting are clear;y parts of that world. But contemporary physicists cannot escape this empirical falisfication of the belief in spacetime. There is also plenty of evidence for those who insist that only peception can supply the empirical data for choosing among theories. It is found in our perception of change. To perceive change, for example, to see a book falling from a shelf, is the recognize that certain spatial relations are going out of existence and other spatial relations are comming into existence. Defined as properties coming into existence and going out of existence, change might be called "presentist change," in order to distinguish it from "eternalist change," or change defined merely as objects having different properties or relations at different times. Anyone who perceives presentist change has plenty of observational evidence that only the present exists because properties (and spatial relations) cannot go out of existence, if the past still exists. Nor can properties (or spatial relations) come into existence, if the future already exists.

If eternalism were true, the present would not be different from the past or the future in this basic way, and thus, eternalism cannot explain what we observe about the nature of existence in perceiving persentist change.

Presentism is an indispensible assumption for any ontology that hopes to be explanatory, for it allows one to hold that what exists are substances that endure through time and, thereby, to explain what is found in the world as being constituted by basic substances and the manner in which they exist together as a world. All truths about the world, including truths about the past and the future, are thereby reducible to facts about what exists now.

On the other hand, if eternalism were true, one would have to postulate many more basic entities in order to explain the world, because one would have to postulate distinct basic entities for every moment in the history of every material object found in the world. Though such basic entities would not be substances in our sense, they would serve as the basic ontological causes in an eternalist explanation of the world, because they would constitute substances in our sense. The spacetime events that make up the world-lines of ordinary objects in Minkowski spacetime diagrams would be basic entities in this sense.

Eternalism is what makes the belief in spacetime unacceptable to empirically minded thinkers who want to know the truth about the nature of what exists. Empirical ontology seeks to discover the theory that corresponds to the basic nature of what exists, and since we have observational evidence that existence is what makes present different from the past and the future, any ontological theory that denies that fact is not very likely to be true. Indeed, it is empirically falsified by our perception of presentist change and our reflection on ourselves as agents.

Though “change” may be defined in terms of the difference between events located earlier and those located later on a world line, that is not presentist change (since there is nothing coming into existence or going out of existence over time). It is eternalist change. Presentist change entials eternalist change (since propositions about the future and the past can be reduced to propositions about the substances that exist now), but eternalist change does not entail presentist change (since there is no way to distinguish the present from the past and the future). Thus, there are observational facts that a presentist ontology, like spatiomaterialism, can explan that cannot be explained by any eternalist ontology, such as the belief in spacetime.

It is not the case that this problem about the nature of time has gone entirely unnoticed in the literature. Putnam [1967] noticed that substantivalism about spacetime contradicts our ordinary assumption about time (that only the present exists). But he focused on the incompatibility between the future being already determined and our view of ourselves as agents. Since he does not recognize reflection as observational evidence about the nature of what exists, he simply accepts the belief in spaceime as another case of scientific discoveries correcting ordinary beliefs. Putnam's point was also made by Rietdijk [1966].

Worries about having to hold that we are suffering a massive delusion in believing that the present is radically different from all the other moments in time are expressed by John Post (1987, Chapter 3) and Roger Penrose (1989, pp. 442ff). But it does not lead them to doubt that spacetime corresponds to the real nature of what exists.

Maxwell [1985], pp. 23-43, stands out as the only philosopher who sees the incompatibility of substantivalism about spacetime with our observation of how the present is different from the past and the future as justifying our rejection of the belief in spacetime in favor of the belief in absolute time. His view has not gathered support in the literature.

Others, like Stein [1968, 1991], have tried to avoid having to choose between the belief in spacetime and the openness of the future by taking the truth of Einstein's special theory of relativity to be relative to the “here and now.” He uses the velocity-of-light limit on causal influences between distant events to distinguish between spacetime events with a time-like relationship to the here and now (with the past being those events that could affect us here and now and the future being those that we could affect) from spacetime events with as space-like relationship to the here and now (namely those spacetime events that we could not affect and that could not affect us without effects traveling faster than the velocity of light). That allows Stein to take spacetime events that are related in a space-like way to the here and now as neither determined nor undetermined, but “indeterminate.” However, if relativity to the here and now does abandon the requirement that theories in physics be true at the same time for observers located everywhere in the universe, it does give up ontology as a theory about the nature of the substances that constitute the existence of everything in the world, for there is no way to explain indeterminate spacetime events by taking spacetime events to be the basic entities that constitute the world (much less by taking substances enduring through time to constitute the world).

Similar objections hold for the attempt by Smith ([1993], p. 4) to solve these ontological issues by reducing existence to “being real to.” What exists cannot be relative to any particular subject without giving up naturalism and accepting an ontology that makes subjective minds basic and reduces objects in space to them in some way.

Mathematics also obscures this issue in the literature. A logical analysis of the difference between invariant and ontological temporal relations is offered by Rakic [1997], but he apparently does not recognize that in introducing the ontological relation R, he is, in effect, adding Newtonian absolute time to STR. He does not see the ontological significance of his mathematical arugment.

In the face of the prima facie difficulties with accepting the belief in spacetime, it is surprising that there has been so little interest in replacing Einstein's special theory of relativity with an explanation based on the belief in absolute space and time. And it is all the more surprising, because the possibility of a “Newtonian” theory the phenomena covered by special relativity is widely admitted.

For example, it is admitted by Zaher [1989], Sklar [1992], and Dorato [1996], and it is even defended by Maxwell [1985], though for different reasons than will be given here. The equivalence of such a “Newtonian” theory to Einstein’s special theory is recognized by Maxwell [1985] and Smith [1993], shown mathematically by Prokhovnik [1985] and Bell [1987], and explained in a more intuitive way by Scribner [1989].

But commentators on Einstein’s special theory (such as Sklar 1992, pp. 27-30) often dismiss this possibility as a mere “compensatory theory”, as if it were a crutch for those who feel somehow psychologically crippled by the loss of an intuitively intelligible explanation, whereas our reason for believing in absolute space is that it is required by empirical ontology, given the observational evidence for presentism.

Spacetime is not, however, the only possible ontological explanation of the phenomenon described by Einstein's special theory of relativity. It is also possible to explain all those phenomena on the assumption that space and matter are substances enduring through time, even though that entails that space and time are absolute. We need only assume that space and matter are so related as basic substances constituting the world that the velocity of material objects through substantival space causes distortions in them in which clocks are slowed down, lengths are contracted in the direction of absolute motion, masses increase and forcefields are flattend in the direction of motion (all at the usual rate). These are the distortions that are implicit in the conclusions of Einstein’s argument, but in the following argument the order is reversed. Instead of assuming the principle of relativity and deriving the distortions as consequences, we shall assume the Lorentz distortions as basic laws of physics and derive the principle of relativity—that is, explain all aspects of the empirical equivalence of inertial reference frames by the Lorentz distortions.

There is probably an interesting story to be told about why Newtonian physicists did not defend such a theory about the empirical equivalence of inertial frames when it was still a live issue. Lorentz did explain the negative result of the Michelson-Morley experiment by the distortions he discovered, but he did even try to explain the symmetry in the transformation equations he used to describe them, because he thought of them as merely a convenient mathematical device for describing the effects of absolute motion on material objects. The reason that other physicists did not extend Lorentz's basically physical approach to explain why comparisons between inertial reference frames could not detect absolute rest and motion may be the devastating effects of World War I on the talent of that generation. An entire generation of potential physicists was wiped out, and after the war, the relative ease of reaching intersubjective agreement about mathematical arguments may have driven out the more divisive Newtonian arguments. To explain special relativity in terms of absolute space and absolute time requires intutive understanding, and such physical explanations could not be constructed without solving paradoxes about pairs of clocks both going slower than the other and light having the same velocity in different inertial frames. It also seemed ad hoc to postulate Lorentz distortions, since their only role in physics seemed to be making it impossible to detect absolute rest and motion. Einstein's elegant mathematical argument may have seemed superior in the young, abstract minds that picked up the discipline after the war untutored by the lost generation of Newtonian physicists. Thus, most students may simply have been taught Einsteinian equations from the beginning of their graduate careers, and those who demanded a more intuitive understanding of what they meant were weeded out as not being intellectually fit to do physics.

In giving the spatiomaterialist explanation of the truth of the special theory of relativity, I will start by following in the footsteps of Lorentz. But the spatiomaterialist explanation disagrees with Lorentz about what is required to explain special relativity, because it recognizes that it is necessary to explain not only the negative result of the Michelson-Morley experiment, but also why absolute motion and rest cannot be detected by comparing inertial frames with one another.

The inability to determine the absolute velocity of a material object by measuring the velocity of light relative to it is what Lorentz explained by postulating the slowing down of clocks and the shrinking of measuring rods in the measuring apparatus. Lorentz and Poincaré attempted to explain these distortions by the interaction of material objects with an ether, and I will suggest in the final section how they might be explained ontologically (by the unit-like, or quantum, electromagnetic interactions that constitute material objects in a spatiomaterial world like ours). In order to explain not only the kinematic phenomena on which Lorentz focused, but also the dynamic phenomena that make the laws of physics apply the same way on all inertial frames, it is necessary to recognize two additional distortions: an increase in mass and a flattening of forcefields in the direction of motion. But to focus on explaining the Lorentz distortions, even including all four, is to fail to recognize that there is another, quite puzzling aspect of the phenomena described by Einstein’s special theory that needs to be explained.

The puzzling aspect is the symmetry that holds between members of each pair of inertial frames. It is implied by the Lorentz transformation equations, and it is an essential part of the principle of relativity as the empirical equivalence of all inertial reference frames, for it implies that absolute rest and motion cannot be detected by comparting inertial frames with one another. Explaining this symmetry will require a two-step argument. The first step is to show that the effect of following Einstein’s definition of simultaneity at a distance in absolute space is to mis-synchronize clocks on a moving inertial frame in a certain way. The resulting disagreement about the simultaneity of events at a distance is widely recognized, but its role in causing the symmetry between inertial frames is not. Hence, the second step is to show how the mis-synchronization combines with the Lorentz distortions themselves to make it appear that the Lorentz distortions are always occurring symmetrically in the other inertial frame.^ix

The Lorentz Distortions. To hold that space is a substance enduring though time is to hold that space is absolute, and we have assumed that space is the medium of light transmission. There is an inherent motion in space that gives light a constant velocity relative to absolute space. On that basis, the spatiomaterialist theory must explain why inertial frames all appear to be alike, that is, why the velocity of light seems to be the same and why the laws of physics all apply the same way in every inertial frame. This "local equivalence" among inertial frames must be explained as a mere appearance, because motion across absolute space must change the velocity of light relative to the moving object, as suggested by the analogy to the boat moving through ripples in a pond. And the laws of physics describing interactions among material objects (dynamic phenomena) make different predictions for material objects with different velocities. In order for it to be impossible to detect absolute motion, moving material objects (that is, objects with with rest mass) must be distorted in certain ways.

There are four kinds of distortions in material objects with high absolute velocity: a slowing down of clocks, a contraction of lengths in the direction of motion, an increase in the mass of moving objects, and an decrease in the strength of forces in the direction of motion. These are what I will call the "Lorentz distortions." Only the first two were actually discovered by Lorentz, but all of them are required for the same kinds of reasons. Though I will not give a formal mathematical argument, enough will be said about each to explain their quantitative aspects.

The rate involved in all these distortions is , where v is absolute velocity. This is the rate of distortion that is required to explain why Michelson and Morley were unable to detect absolute motion by using an interferometer to measure the velocity of light. This apparatus reflects light from two mirrors lying in mutually perpendicular directions, and the velocity of light in each direction is determined by measuring the period required for each two-way trip (by the interference of the waves coming from the two directions).

Time dilation. Assume that one mirror lies forward in the direction of absolute motion with the other transverse to it. The need for physical interactions to slow down on moving objects can be seen by considering what happens on the transverse pathway as the apparatus moves through absolute space.

The transverse pathway of the interferometer is, in effect, a “light clock”, using the velocity of light to measure time. Since the velocity of light in absolute space is fixed, the light in a light clock with absolute motion must travel farther than in a light clock at rest, and that means that the moving light clock is slowed down. It is slowed down at the same rate that all physical processes must be slowed down in order to keep this effect from being detectable. (See diagram of the path of light on the transverse light clock.)

Light traveling along the transverse pathway must go farther than it would, were the apparatus at absolute rest, because to return to its starting place, the light must also keep up with the apparatus, which is also moving through space all the time that the light is traveling. To observers on the moving object, light seems to travel directly to the mirror and back, but its path in absolute space is actually along the hypotenuse (ct) of the triangle formed by the transverse pathway (L) and the motion of the starting point in absolute space (vt). This increases the period required for the two-way trip.

The period is increased at the usual rate (except as a function of absolute, rather than relative, velocity). The rate is obtained by Pythagoras’ theorem for the right triangle depicted in the diagram (L² + v²t² = c²t²) and solving for t. Since L/c is the period it would take light to travel to the mirror at absolute rest, the period required for each leg on the moving apparatus is .

Length contraction. The need for a contraction of the size of material objects in the direction of motion can be seen by considering what must happen to light clocks oriented in the direction of motion in order for absolute motion to be undetectable. Unless their lengths were also to shrink, it would still be possible to detect absolute motion by comparing the longitudinal light clock with the transverse light clock, because the former would be even slower than the later.

In addition to the distance back and forth along the longitudinal pathway, the light on the longitudinal must also cover, as we have seen, all the space that the apparatus itself travels during the period of its two-way trip. But in the longitudinal direction, there is a new factor at work, because the two legs of its trip are unequal. Light must travel farther in absolute space on the outward leg in the direction of the apparatus’ motion than on the return leg, because of the motion of the apparatus in absolute space.

That means that, relative to the apparatus, the effective velocity of light toward the (forward) mirror is slower than when coming back. On the outward leg, the velocity of light relative to the apparatus is c - v, and on the return leg it is c + v. But light spends more time traveling slower in the outward direction than it does traveling faster on the return leg, and since the effect on the total time of travel depends on how long it travels at each velocity, it does not make up all the time lost during the outward leg on the return leg. The whole period required would be longer than the period required on the transverse pathway, because with equal distances to cover to the forward mirror and back, it spends a longer time going at the slower (at c-v) than it spends going faster (at c+v). That would make absolute motion detectable, unless the measuring rod were contracted.

If material objects also shrink (at the usual rate), the measurements made by the interferometer will be the same regardless of its absolute motion and the principle of relativity will seem to be true. The required rate is easy to calculate because the new length, L', must be such that the period for the two way trip, L'/(c - v) + L'(c + v), is equal to the period for a two-way transverse trip derived in the foregoing discussion of time dilation. Simply solve for L'.

The two remaining distortions follow from the temporal and spatial (or “kinematic”) distortions, for unless there were further distortions, Newton’s laws of motion, notably his second law (F = ma), would be false and the deviation from what it requires would be a measure of absolute velocity. Time dilation and length contraction are both relevant to dynamic phenomena, because both are involved in the acceleration of material objects, which Newton’s law says is proportional to the force exerted on them. Thus, there are two dynamic distortions, an increase in mass and a decrease of the force field in the direction of motion, corresponding to the kinematic distortions.

Mass increase. The necessity of an increase in mass follows from the temporal distortion, because unless the masses of material objects increase at the usual rate with absolute motion, Newton’s second law of motion (F = ma) will be false and physical processes will not take place the same way in absolute motion as at rest.

For example, dynamic clocks, such as pendulum clocks and wind-up alarm clocks, which depend on the acceleration of material objects to measure time, would disagree with light clocks, and the difference between the two kinds of clocks would be a measure of absolute motion.

Consider a dynamic clock oriented in the transverse direction of the inertial frame’s absolute motion. Since light clocks are slowed down, the dynamic clock would seem to be speeded up, since the pendulum (or whatever) would be accelerating over the whole distance just as quickly as it does at rest. The only way the dynamic clock can be slowed down to match the slowing down of the light clock is for the mass being accelerated to be increased at the same rate the light clock is slowed down. Thus, mass must increase at the rate as a function of absolute velocity as time is slowed down.

Longitudinal decrease in the force field. The necessity of a decrease in forces exerted in the direction of motion follows from the spatial distortion, the shrinkage of measuring rods in the direction of motion, for unless the longitudinal force field decreases with absolute motion at the usual rate, Newton’s second law of motion will still be false and deviations from its predictions will be a measure of absolute motion.

Consider a dynamic clock oriented in the direction of the inertial frame’s motion. Although the mass of the pendulum (or whatever) will be increased at the usual rate and, thus, slowed down, it will still be accelerating under the force at the same rate for the same period as the transverse dynamic clock. But since measuring rods are contracted in the direction of motion, the pendulum would still seem to be accelerating faster, because it would seem to be going farther in the same length of time. In order for absolute motion to be undetectable, the pendulum in the longitudinal direction must accelerate more slowly over space. But it is not possible for this acceleration to be slowed down by a further increase in mass, since mass is a scalar quantity, which does not depend on the direction of motion, and only acceleration in the direction of motion has to be slowed down. The only way the acceleration of the pendulum could be slowed down only in the longitudinal direction is for the size of the force field in that direction to be decreased at the usual rate as a function of absolute velocity.^x

Thus, in order to explain the "local equivalence" of inertial frames, that is, why absolute velocity cannot be detected by measuring the velocity of light relative to the moving object and why dynamic clocks do not disagree with light clocks, as if their reference frames were at absolute rest in space, we need only assume that the nature of matter is such that these four distortions occur when material objects are in motion across absolute space. There are two kinematic distortions and two dynamic distortions, all at the same rate as a function of absolute velocity. The first two are the distortions first described by Lorentz, and the latter two are distortions that Einstein showed were entailed by the Lorentz transformation equations when mass and force are also taken into consideration.

In order to show that spatiomaterialism can explain the truth of Einstein’s special theory of relativity, therefore, I will assume that matter has this nature.

I have shown the necessity of these distortions here by following Lorentz and arguing backwards from the Michelson-Morley experiment to what is required for absolute velocity to be undetectable by measurements of the velocity of light on any given inertial frame (or from comparisons of dynamic clocks and light clocks), they are not as ad hoc as that makes them seem. As I will argue in the final section, they are the same distortions that would be caused by the nature of ordinary material objects, if they were constituted by unit-like electromagnetic interactions among its parts (among molecules, among atoms within molecules, and between protons and electrons within atoms).

What made it possible for Einstein to infer the Lorentz distortions from his principle of relativity (and his assumptions that light has the same velocity relative to every inertial frame) is that these are the only distortions in material objects that would make absolute velocity undetectable by measurements of the velocity of light and comparisons between light clocks and dynamic clocks. But since they are merely implicit in the Lorentz transformation equations he derived, they appear in the paradoxical form of symmetrical distortions between any pair of inertial frames, and that is the other aspect of these phenomena that needs to be explained.

The Symmetry of the Lorentz Distortions in Pairs of Inertial Frames. The four Lorentz distortions make it impossible to detect absolute rest (or absolute motion) by any local experiment, that is, by ordinary interactions among material objects on moving inertial frames, such as interferometers and comparing light clocks with dynamic clocks. But as Einstein's argument emphasized, the empirical equivalence of inertial frames implies that they are equivalent globally as well as locally. It is also impossible to detect absolute motion by experiments involving the relationships between inertial frames with high relative velocity, for example by comparing how fast their clocks are ticking or how long their measuring rods are. And as the symmetry of the two sets of Lorentz transformation equations implies, what makes it impossible to detect absolute motion by such global experiments is that the Lorentz distortions always appear to be occurring in the other inertial frame as a function of the velocity of the two references relative to one another. Thus, in order to explain the empirical equivalence of inertial frames ontologically, we must explain this symmetry in the members of any pair of inertial frames as an appearance.

The first step in that explanation is to take note of how clocks on inertial frames are mis-synchronized by using Einstein’s definition of simultaneity at a distance, if the velocity of light is actually due to an inherent motion in space itself.

The second step is to show how that mis-synchronization of clocks on inertial frames moving rapidly across space combines with the Lorentz distortions that they are actually suffering as a result of their absolute motion to make it appear that Lorentz distortions are always in the other inertial frame (and that the rate seems to be a function of their relative velocity).

The mis-synchronization of moving clocks. The strategy of spatiomaterialism is to explain the truth of the principle of relativity on the assumption that all forms of matter, including light and material objects, coincide with parts of space. The assumption that both matter and space are substances enduring through time makes it possible to explain presentist change, but it also entails that space and time are absolute. Thus, it must reject Einstein’s definition of simultaneity at a distance.

Einstein stipulates that a local event is simultaneous with the moment of reflection of a light signal from a distant mirror when that local event occurs halfway through the total period required for the signal to travel there and back. That is to assume that the velocity of light is the same in both directions. This assumption is true on inertial frames at absolute rest, but it is not true on objects moving through absolute space. If light everywhere has a fixed velocity relative to absolute space, the velocity of light relative to a moving frame is slower traveling outward in the direction of forward motion and faster in the opposite direction. Thus, clocks on moving frames that are synchronized according to Einstein’s definition of simultaneity at a distance will be actually mis-synchronized. It is important to be clear about the nature and amount of the error introduced, because mis-synchronization plays a crucial role in causing the appearances that make absolute motion undetectable by comparing inertial frames with one another, or the symmetry of Lorentz distortions in pairs of inertial frames.

The most revealing way to show the mis-synchronization is to use a diagram to represent the spatial and temporal relations among the relevant events. This is to use the Newtonian diagram of space and time, which is the spatiomaterialist counterpart to Minkowski’s “graphical method” of using spacetime diagrams for “visualizing” what is going on, and it is both simpler and easier to understand. Since spatiomaterialism assumes that space is a substance and, thus, absolute, the argument may begin with the coordinate frame at rest in absolute space. Nothing precludes representing time as an axis perpendicular to spatial dimensions, as long as we do not assume that anything exists but what is located on lines parallel to our absolute space-axis (horizontal lines in the diagram) for each moment. We can refer to events in the past and future, even though they do not exist, because they can be interpreted as references to space and matter which have, as substances, an existential aspect that entails that they did exist and will exist. We can also represent the motion of the other inertial frame as a timeline whose slope depends on its velocity (t = x/v), as Minkowski did. Furthermore, we can take this timeline to be the time-axis of the moving inertial frame, because that involves only a simple Galilean coordinate transformation of the kind used in Newtonian physics. So far, this is equivalent to Minkowski’s spacetime diagram.

Spatiomaterialism cannot, however, go on to assume that the moving frame has a space-axis that is inclined relative to our absolute space-axis, as Minkowski's spacetime diagram does. We must assume that moving measuring rods always lie parallel to the absolute space-axis, since all parts of moving rods are particular substances and must exist at the same time. But spatiomaterialism does hold, following Lorentz, that moving measuring rods lying in the direction of motion are contracted, and so we must recognize that the moving measuring rod is shorter than it would be if it were at absolute rest. Now, to see the significance of Einstein’s definition of simultaneity at a distance, we need only consider the geometry of synchronizing clocks in absolute space and time, that is, from the point of view of the absolute frame depicted below. (See the diagram below comparing the synchronization of both forward and afterward clocks on the absolute and moving inertial reference frames.)

The foregoing diagram depicts the general nature of the mis-synchronization, but we will need to know just how much clocks are mis-synchronized. Thus, consider the following diagram in which the moving measuring rod is depicted as L'.

The length of the contracted moving measuring rod in absolute space is L'. It is depicted at four locations that it occupies at crucial moments during the process of synchronization. The thinner inclined lines trace the path of each end of the rod where clocks are located. The thin dotted-line represents the path of the light used to synchronize the clocks at each end. Following Einstein’s definition of simultaneity, (1) moving observers send a light signal forward from the origin of their frame, (2) the light is reflected from a mirror at the forward end of their measuring rod (and the clock there is set at 0), and (3) they record when it returns. Einstein’s definition requires moving observers to set their clocks on the assumption that the light was reflected halfway through the total period required for its round trip. Since the light signal reaches the mirror in the period T₁ and returns to the observers in the period T₂, they assume it was reflected at (T₁ + T₂)/2 after the light was sent. Thus, they set their nearest clock so that it would have read 0 at that moment. But since the measuring rod is actually in absolute motion, the light does not reach the mirror at the far end until it has passed both the length of the measuring rod and whatever distance the rod travels during the first leg (T₁). And on the return leg (T₂), light does not have to travel the whole distance of the measuring rod, since the other end is also moving toward the light. But since moving observers assume that the reflection occurs halfway through the period required for the round trip, they are, in effect, assuming that the set of simultaneous events lies on the line that runs through the halfway point on the timeline for the clock at the observers’ end of the measuring rod and the point of reflection at the mirror on the timeline for the clock at the forward end of the measuring rod. That is what moving observers take to be their space-line as seen by us from the frame at absolute rest.

The result of mis-synchronizing clocks is precisely the same diagram for the moving frame that Minkowski constructed from his hyperboloid curve, representing the conclusion of Einstein’s special theory. (The same results would also follow from the Lorentz transformation equations.) However, we have derived the moving observers’ apparent space-axis (or space-line), not from a mysterious equation, but in a perfectly intelligible way. The moving space-line is rotated upward in the diagram, because the moving clocks have been mis-synchronized. And they have been mis-synchronized because the moving observers have followed Einstein’s definition of simultaneity at a distance, which assumes that the velocity of light is the same both ways in every direction relative to any inertial frame.

The amount of the error introduced by mis-synchronization will be as important as its cause in the next step of this argument, so bear with me for one final point. The home clock reading 0 is one event in absolute space and time, and the forward clock reading 0 is another event. The separation between them in the absolute frame has a curious value, both in space and in time. The moving measuring rod has a length of L', but the distance in absolute space between these two events turns out to be L'/(1 - v²/c²), which means that the mis-synchronization makes it seem that the moving measuring rod is expanded at the square of the usual rate (see above diagram). The length of time between the two events can be derived from the slope of the moving space-line in the diagram for absolute space and time (that is, v/c²).^xi This is the slope of the tangent to Minkowski’s mysterious curve at the point of intersection with the timeline for the observers’ nearest clock,^xii and it occurs in the second expression in the numerator for the Lorentz transformation for time.^xiii But in this context, the slope means that the difference in time between the events is v/c²[L'/(1 - v²/c²)] (or the product of the slope of the moving space-line and the distance between the points on it in absolute space). We will use these values shortly.

The Cause of the Apparent symmetry of Lorentz distortions. Attempt to detect absolute motion by measuring the rate of clocks and the length of measuring rods on the other inertial frame are "global experiments," and the reason that absolute motion cannot be detected is that the Lorentz distortions appear to be symmetrical. Since transformation equations must work both ways between any two inertial reference frames, this symmetry is entailed by Einstein's argument for the Lorentz transformation equations in his special theory of relativity. And this symmetry is an essential part of the empirical equivalence of inertial frames that Poincaré called the "principle of relativity."

If the clocks and measuring rods were material objects in absolute space, this symmetry would imply that clocks on two inertial frames passing one another in space are both going slower than the other and that their longitudinally-oriented measuring rods are both shorter than one another. It is one of the reasons that Einsteinians must give up the belief in absolute space and time. By the same token, spatiomaterialism must explain this symmetry about pairs of inertial frames as a mere appearance of space and matter as substances enduring through time, just as the local equivalence was.

This is the part of the explanation of the empirical equivalence of inertial frames that Lorentz left out of his Newtonian theory. But it is readily supplied by the geometry of events in absolute space and time. The apparent symmetry of the distortions is a result of the actual Lorentz distortions suffered by the moving frame, together with the mis-synchronization of moving clocks, as we can see by considering how the measurements of the others’ clocks and rods are made.

Length contraction. Consider first the apparent symmetry of length contraction. The most direct way to measure the others’ standard of length is to make simultaneous marks from both ends of one’s own measuring rod onto the other inertial frame as it passes by and compare that distance with the others’ measuring rod. This works fine for absolute observers; they mark off a distance longer than moving measuring rods lying in the direction of motion, indicating that the moving measuring rods are contracted. But it also seems to moving observers that absolute rods are contracted in the direction of motion, and we can see why by considering what takes place in making the measurement.

It is because (1) clocks on the moving frame have been mis-synchronized and (2) moving measuring rods are contracted. We have just seen that moving observers mis-synchronize their clocks when they accept Einstein’s definition of simultaneity: the distance in absolute space between the events at which moving clocks at both end of a moving measuring rod read the same time is equal to an expansion of the actually contracted measuring rod at the square of the usual rate, that is, (1 - v²/c²). Thus, when moving observers make what they think are simultaneous marks on the absolute measuring rod that is passing by, they mark off a distance on the absolute frame that is longer than their actually contracted measuring rod by the square of the usual rate, and since that distance is longer than the absolute measuring rod by the usual rate, the absolute measuring rod seems to be contracted at the usual rate.^xiv

In other words, as the absolute inertial frame comes toward them, the mis-synchronization of their clocks leads moving observers to make a mark from the afterward end of their own measuring rod first and then, after the moving frame has traveled some distance, they make a second mark from the forward end, so that distance marked off on the absolute frame includes both the length of the contracted moving measuring rod and all the distance that the absolute frame travels between making the two marks. That virtual expansion of the moving measuring rod makes it appear that the absolute measuring rod is contracted.^xv

The error introduced by mis-synchronization is, in short, a virtual distortion at the square of the usual rate, but in the opposite direction, so that when the method of measuring combines it with the actual shrinkage of the moving measuring rod, the effect is to make absolute measuring rods seem distorted at the usual rate relative to the moving rod. This same “geometrical mechanism” is at work in the measurement of how fast the other’s clocks are ticking.

Time dilation. The most direct way for us to measure the speed of clocks on the other inertial frame is for us to move in our inertial frame along with one of the others’ clocks that is passing by and to compare it with the series of clocks on our own frame by which we will be passing. (Observers cannot take a clock with them as they move through their own frame, because that would make it a clock on the other frame. But nothing precludes observers from keeping up with the other inertial frame and using clocks already located at various points on their frame for the comparison.) When observers on the frame at absolute rest keep up with the moving clock and compare it with a series of their absolute clocks, they observe the real slowing down of the others’ clock caused by its absolute motion. The symmetry of the distortions means, however, that when observers on a frame in absolute motion keep up with an absolute clock and compare it with the series of their own moving clocks by which they pass, the absolute clock seems to be slowed down.

But in the latter case, it is because (1) clocks on the moving frame have been mis-synchronized, (2) the moving observers are moving backwards on their own moving frame (-v) to keep up with the absolute clock, and (3) clocks on the moving frame are slowed down. The amount of deviation of a distant moving clock from absolute simultaneity with a local moving clock is, as we saw, a function of the distance in absolute space between the events at which two moving clocks have the same readings, namely, v/c² times the absolute distance (the slope of the rotated space line). In this measurement, that distance depends on how long the moving observer has been traveling at -v, that is, the distance -vt'. Thus, the deviation of the next clock from absolute simultaneity will be VT times v/c², or -t'(v²/c²). That amount of time plus the time that elapses during the moving observers trip from one clock to the next (that is, t') yields a total apparent time period of t' - t'(v²/c²), or t'(1 - v²/c²), which is a virtual speeding up of moving clocks at the square of the usual rate of distortions. Thus, since (1), the mis-synchronization of moving clocks, combines with (2), the moving observers’ motion on the moving frame, to produce, in effect, a virtual speeding up of moving clocks at the square of the usual rate, the result, when combined with (3), the actual slowing down of moving clocks at the usual rate, is that the absolute clock being compared with them appears slowed down at the usual rate.^{xvi, xvii}

In sum, given how the measurements are made, the mis-synchronization of moving clocks introduces a virtual distortion through which the moving observers’ own distortions are projected onto the absolute inertial frame. This can be seen in our diagram of events happening to particular substances in absolute space and time, for as we found, the mis-synchronization shows up as a rotation of the moving space-line that involves both a virtual speeding up of moving clocks and a virtual lengthening of moving measuring rods. Thus, to see how it gives rise to the apparent symmetry of the distortions, consider how the measurement of the others’ clock is represented below.

When absolute observers keep up with the moving clock and compare it with a series of their own clocks, they follow the moving timeline. When the moving clock says t'=1, they compare it with an absolute clock (located on that absolute space-line) which reads t=1/(represented by the horizontal line labeled I in the diagram). And when moving observers travel backwards on their own frame to keep up with the absolute clock, they follow the absolute timeline (x=0). When they pass by their own moving clock reading t'=1, they compare it with the absolute clock which reads t= (represented by the rotated moving space-line labeled II in the diagram). The difference between these two measurements is obviously due to the rotation of the moving space-line, which, as we have seen, comes from mis-synchronizing moving clocks. Notice that the absolute clock’s reading of t=1 lies between these two comparisons. Therein lies the power of mis-synchronization to cause the appearance. Combining the slope induced in the moving space-line by mis-synchronization (v/c²) with the movement of the moving observers in making the measurement (x' = VT, that is, keeping up with the absolute clock) is equivalent to a temporal distortion on the moving frame at the square of the rate of the actual distortion (1-v²/c²), but in the opposite direction. So, it combines with the actual slowing down of moving clocks to make the absolute clock seem slowed down relative to moving clocks.

The diagram also shows how the mis-synchronization is responsible for the apparent symmetry of the contraction of measuring rods. But in this case, it is the virtual expansion of the moving measuring rods induced at the square of the usual rate by the mis-synchronization that is relevant. When absolute observers make simultaneous marks on the moving frame, they find that the moving measuring rod is contracted at the usual rate (labeled III in the diagram). But when moving observers make what they think are simultaneous marks on the absolute frame, they actually mark off a distance that is expanded at the square of the usual rate (labeled IV in the diagram). Once again, the power of mis-synchronization can be seen in how the actual moving measuring rod is contracted relative to the absolute measuring rod and the virtual moving measuring rod is expanded relative to the absolute rod, both at the usual rate.

The symmetry of Lorentz distortions is, therefore, a symmetry betwen real distortions in reference frames in absolute motion and apparent distortions in the reference frame at absolute rest, and it is a thoroughgoing symmetry, which holds for all the basic ways of measuring the other frame's clocks and measuring rods. Indeed, any of the standard measurements can made from either member of the pair of inertial frames, though when they are considered from the point of view of the other inertial observer, they reveal that the other's clocks are speeded up and the other's measuring rods are expanded in the direction of motion. This can be seen in the table of measurements.

This explanation of the apparent symmetry of the kinematic distortions also accounts for the apparent symmetry of the dynamic distortions (though the longitudinal distortion in the force field is not always recognized as such by Einsteinians), for the apparent increase in absolute masses is implied by the false belief that absolute clocks are slowed down and the assumption that Newton’s laws apply the same way on all inertial frames (Einstein’s principle of relativity). Likewise, the apparent decrease in longitudinal forces is implied by Einstein’s principle of relativity and the false belief that absolute measuring rods are contracted in the direction of motion.

The apparent symmetry of the four distortions has been explained for the special case in which one of the inertial frames is at absolute rest, but it can be generalized to explain the apparent symmetry between any two objects moving in absolute space. In the general case, the rate of the apparent distortions is a function of their (apparent) relative velocity, and what is detected on both sides is partly a result of real distortions and partly illusions caused in the way described above.^xviii

Though observers on any pair of inertial frames agree about their relative velocity, it is worth noting that, on the spatiomaterialist explanation of the empirical equivalence, their measurements of relative velocity do not coincide with their real velocity relative to one another in absolute space: the apparent relative velocity is never more than the velocity of light, but the real velocity of inertial frames relative to one another can approach twice the velocity of light, because light moves at that velocity in opposite directions from any given point in absolute space.

Conclusions. One part of the promise made in Spatiomaterialism in order to use this ontology as a foundation for demonstrating necessary truths has been kept. We have seen that spatiomaterialism can explain the truth of Einstein’s special theory of relativity, and means that nothing established empirically by Einstein’s theory forces us to give up spatiomaterialism. Thus, if spatiomaterialism can also explain the truth of Einstein’s general theory of relativity (and quantum mechanics), physics will provide no grounds for doubting that spatiomaterialism is the best ontological explanation of the world. But there are a few implications of this ontological explanation of special relativity that should be noted in conclusion.

First, though we have discovered the power of absolute velocity to cause changes in material objects by following in the footsteps of Lorentz, that does not mean that we must postulate an ether in addition to absolute space.

Lorentz and Poincaré both expected to explain time dilation and length contraction as the result of an interaction between material objects and an ether at rest in absolute space (as if material objects were made of nothing but electrons that interact with the electromagnetic ether as they move through it). Though material objects must also have something to interact with on our explanation of the Lorentz distortions, we can take it to be space itself. We have postulated space as a substance that contains matter, and having already used that relationship to explain the truth of the laws of classical physics, we now use it to explain the Lorentz distortions. Indeed, I have suggested reasons for expecting Lorentz distortions to occur apart from what is necessary to make absolute motion undetectable.

Though there is no luminiferous ether, there is still a medium of light propagation, and it still makes sense to hold that there is an inertial frame in which light has the same one-way velocities in every pair of opposite directions. That will be important in our explanation of the truth of Einstein's general theory of relativity, because we will not always assume that the light medium is at absolute rest in space. The aspect of space by which it serves as the medium of light propagation is more complex than it appears now, because we shall have to assume that the velocity of light varies with location in space in a way that can be seen as depending on the velocity of the light medium relative to space. It is as if the ether were being accelerated in space, but even though that may suggest that the light medium is an ether after all, we will still not postulate an ethereal substance coinciding with space to explain this phenomenon.

Second, the difference between the actual Lorentz distortions in material objects with absolute velocity and the apparent symmetry of Lorentz distortions in pairs of inertial frames revealed by this ontological explanation shows that the mathematical representation of special relativity is hiding an aspect of reality.

The mathematical way of saying that inertial frames are all equivalent is to say that the laws of physics are covariant, or Lorentz covariant. That means that laws of physics that apply in one frame take the same form in any other inertial frame, that is, when they are subjected to the Lorentz transformation. (This equivalence is what is represented by Minkowski’s equation for the absolute separation between any two events and is the foundation for the equations of four-vector physics, which do not mention any specific inertial frame.) Einstein’s original article showed that covariance holds in the case of electromagnetism, and imposing covariance as a requirement on other physical theories has generated predictions that turn out to be true.

Despite the obvious simplicity, comprehensiveness, elegance, and fruitfulness of this mathematical representation of special relativity, however, it is a mistake to take covariance to be the deepest and most complete truth about the real nature of the world. Our ontological explanation of the truth of special relativity reveals that covariance actually represents two different phenomena, with two different ontological causes. There is the local equivalence of inertial frames, which is caused by the actual Lorentz distortions, and there is the global equivalence, which is caused by the mis-synchronization of clocks and how that makes one’s own Lorentz distortions appear to be in the other inertial frame.

Third, this ontological interpretation of the mathematical representations used in special relativity confirms that the method of physics is implicitly skeptical about ontological causes that are not entailed by realism about its efficient cause explanations.

When physics infers to the best efficient-cause explanation, it looks for laws of nature that represent the quantitative aspects of the regularities involved, because such mathematical representations can often be used to predict surprising, precise measurements that confirm their truth. The empirical method of science is so dependent on mathematical representations that, once experiments have confirmed their predictions, physicists are realists about their efficient-cause explanations. They let scientific realism determine their ontology.

Accordingly, the belief in spacetime is simply realism about special relativity. That is, substantivalism about spacetime is the ontology that results from taking the simplest mathematical theory that can predict all the relevant phenomena to correspond to what exists. Since the special relativity holds that all inertial frames are empirically equivalent, scientific realism takes the empirical equivalence among inertial frames to be an ontological equivalence. That is to replace absolute space and time with spacetime. But it is also the leave out an aspect of reality, for it is to ignore the observable fact that only the present exists.

Finally, the principle of relativity itself turns out to be merely a practical principle, without ontological significance. Though as a practical matter, the assignment of coordinates to events can be made only relative to an inertial frame whose absolute motion cannot be known, that does not mean that they do not have actual locations in absolute space as time passes. There is an absolute truth about the dates and places of events. Even though we can never know what they are, we can know that there is a fact of the matter about when and where they occur. That is what is implied by this ontological reduction of special relativity. I have called it an explanation of empirical equivalence, because by explaining the apparent truth of the principle of relativity, it denies that this relativity is a basic principle of physics.^xix

The Ontological Causes of the Lorentz Distortions. Lorentz explained the negative result of the Michelson-Morley experiment by distortions in material objects caused by their motion through absolute space, and his own research focused on explaining those distortions as an interaction between material objects and the luminiferous ether according to his electron theory of matter, a theory that is now known to be false. He could have simply assumed the Lorentz distortions as basic laws of physics, as we have thus far, but we will travel once again in Lorentz's footsteps by considering a deeper explanation of his distortions, an ontological theory that makes use of our assumption that there is an inherent motion in space and which uses certain assumptions about the nature of material objects that will not be defended until we explain the truth of quantum mechanics ontologically.

By contrast to Einstein's elegant mathematical derivation of the Lorentz transformation equations from the assumption that inertial frames are all empirically equivalent, Lorentz's Newtonian theory seemed merely to be tinkering with classical physics in an ad hoc manner. First, he recognized the length contraction, and then a few years later, a time dilation. And to extend his argument to explain why dynamic phenomena do not reveal absolute rest or motion, two more distortions would need to be recognized (an increase in mass and a flattening of force fields).

The Lorentz distortions are, however, neither arbitrary nor contrived. In fact, there is a certain necessity about them, as I will try to demonstrate by showing how they follow from what is known about the nature of material objects (or rather from the spatiomaterialist ontological explanation of what is known about them) together with our assumption that space is the medium of light transmission (with the velocity of light manifesting an inherent motion in space).

It is now known that material objects are constituted by electromagnetic interactions among its constituent parts, and the assumption that is required in order to explain the truth of quantum mechanics ontologically is that those electromagnetic interactions have a unit-like nature (or a “quantum” nature, as it is called).

Atoms, for example, are made of a nucleus of protons and neutrons which interacts by electric and magnetic forces with a number of electrons that is normally equal to the number of protons. It is a stable configuration, because the nature of those electromagnetic interactions between the nucleus and the electrons is such that the potential energy cannot be lower (that is, no more of their rest masses can be converted to kinetic energy or other forms of matter). That is contrary to what is expected according to the laws of classical physics. They imply that electrons would quickly spiral into the nucleus, radiating all their energy away as electromagnetic waves. But that does not happen, and the attempt to explain why not led to the discovery of quantum mechanics. The structure of the atom was one of the first discoveries.

On the ontological explanation of quantum mechanics defended in Quantum Mechanics, there is a unit-like, or quantum, nature to electromagnetic interactions. Interactions cannot take place unless they involve a certain minimum quantity of action. Thus, the energy level of electrons bound to a nucleus in an atom can change only in a step-like way, each involving a whole quantum of action in which the energy is carried away by a photon, the units of which electromagnetic waves are composed , according to quantum mechanics. And there is a minimum energy level for electrons in atoms, because in that state, as we shall assume, such electrons are bound to the nucleus by the smallest electromagnetic interaction possible.

The details about the unit-like nature of these quantum electromagnetic interactions will be discussed later. (See Change: Quantum mechanics.) What is relevant here is that material objects generally are constituted by such unit-like electromagnetic interactions among simpler material objects with electric charges. Not only atoms, but also molecules, crystals, and other complex structures composed of atoms depend on electromagnetic bonds among electrically charged parts that exhibit this quantum nature.

Material objects are composed of many such quantum electromagnetic interactions. They give the material object its structure as a whole, because all these quantum events not only coincide with space in a consistent geometrical pattern, but also fit together in time. Any given material object can interact with more than one other material object at a time, and since the quantum interactions are synchronized, the effects of different interactions of the object can be repeated regularly in the same way, cycle after cycle, constituting a structure that does not change over time.

We are assuming that space is the medium of light transmission, and since light is constituted electric and magnetic forces coupled according to Maxwell's laws, space must also mediate the exertion of such forces. Our working hypothesis is that space has an inherent motion by which it mediates light transmission, and thus, if electric and magnetic forces are exerted across space as time passed by way of an inherent motion in space, the electromagnetic interactions involved in the constitution of material objects will inevitably be affected by the object's motion through space as a whole. And the way that they are affected, given this ontological explanation of their quantum nature, explains the Lorentz distortions.

Whatever is going on in the quantum interactions constituting material objects, it involves the exertion of electric and magnetic forces, and any such inter-action requires photons traveling both ways between them. But since we have assumed that the motion of photons depends on the inherent motion in space, the material object as a whole will inevitably be affected by its motion across space, because it will change the effective velocity at which those forces are exerted.

I will assume that in each unit-like electromagnetic interaction, say, between the nucleus of an atom and one of its electrons, a photon travels, first, one way between the objects and, then, back the other way between them before a single quantum interaction is completed. (Indeed, the interaction may involve symmetrical two-way trips of photons, one starting from both of the objects involved in the interaction.) Such two-way trips are necessary, because quantum interactions occur only as a whole, if they occur at all. Never is one of the objects changed while the other is not. Since the objects are separated from one another in space, the only way that one of the objects can change when, and only when, the other object also changes is by something traveling both ways across space between them in the period of time that it take to complete the unit-like action. Nothing less is ontologically possible, if there are such unit-like electromagnetic interactions.

The material object’s motion across space will not make much difference as long as its velocity is small compared to the velocity of light. In fact, the velocity of light (that is, the inherent motion in space) is so enormous that the effect on most ordinary material objects is undetectable. Nevertheless, since material objects subject to appropriate forces will continue to accelerate, they can acquire velocities approaching that of light, and the objects will be affected by the change in the one-way velocities of light. There are four effects, and I will describe them qualitatively here, since an ontological explanation is meant to identify the aspects of the substances to which physical laws correspond. Their quantitative aspects would clearly be the same as the Lorentz distortions.

Slowing down of quantum interactions. The first and most obvious effect of high absolute velocity in space is a slowing down of all the quantum electromagnetic interactions constituting the material object, so that all processes take place more slowly.

Slowing down is inevitable, because in each unit-like interaction, the photons being exchanged must travel not only the distance between the parts with electric changes, but also all the distance covered by the material object as a whole in the time it take to complete the unit-like interaction.

Suppose, for example, that one of the electromagnetic interactions constituting an atom is oriented perpendicularly to the direction of the atom's motion through space. In order to complete the interaction, a photon must travel from the nucleus to the electron and then back again in the period of a single unit of interaction. But all the time that the photon is traveling, the atom as a whole is also moving across space, and thus, in keeping up with the atom, the photon will have to travel farther that in it would at rest. Since its velocity is due to the inherent motion in space, the photon cannot speed up, and so it will take longer to complete the two-way trip between the nucleus and electron. Unit-like electromagnetic interactions will take longer to complete on a moving atom than they would at rest. And since this is true of all the unit-like electromagnetic interactions constituting material objects, all physical processes involved will be slowed down at the same rate as a function of their absolute motion. (The quantitative description of this effect of absolute velocity is given in the discussion of the Lorentz Distortions.)

Longitudinal shrinking of quantum interactions. A less obvious, but no less necessary, effect of high velocity motion across space is a shrinking of the size of quantum electromagnetic interactions in the direction of absolute motion.

The two-way trip of an electromagnetic interaction in the direction of motion will be slowed down just as much as such a unit like interaction in the direction transverse to motion described above, because once again, the photon will have to cover all the extra distance across space that the material object as a whole covers during the period required to go both ways. Thus, the longitudinal quantum interactions will be synchronized with the transverse quantum interactions. But a further distortion of the quantum interaction is required in the direction of motion, because in order to remain synchronized with the transverse quantum interaction, the photon must travel a shorter distance.

The additional effect comes from the asymmetry of the two-way trip of the photon in the longitudinal quantum interaction constituting a material object, such as an atom. Unlike the transverse quantum event, the motion of the material object as a whole makes the effective velocity of light different in each direction. When the photon is traveling from the nucleus to the electron in the same direction across space as the atom itself, it has a lower velocity relative to the atom than it would at rest, because the other object is moving away from it all the time it travels. And then, on the return leg of its two-way trip, the photon is traveling in the opposite direction, and that makes its velocity relative to the atom higher, because its destination is moving toward it. The problem is that, even though the distance between the nucleus and the electron is the same both ways, the velocity of the photon is different, and thus, it cannot complete the two way trip in time to be synchronized with transverse quantum events -- unless the distance is shortened. The effect on the total time of travel depends on how long the photon spends traveling at each velocity, and since it spends more time traveling slower than the velocity of light relative to the atom on the forward leg than it does traveling the same distance faster than the velocity of light on the return leg, its completion of the two way trip would be delayed -- unless the distance between the electron and the nucleus were less than it would be at absolute rest.

This effect can also be seen from the point of view of absolute space. The photon traveling in the direction of motion has farther to go to reach its destination than in the opposite direction, because in the forward direction, its destination is moving away from it and in the backward direction its destination is moving toward it. Though the effects of the two legs are in opposite directions, they do not cancel out, because the photon spends more time chasing destinations that are retreating than it does traveling toward destinations that are approaching it. It cannot make up on the return leg all the time it loses on the forward leg. (The quantitative description of this effect of absolute velocity is given in the Lorentz Distortions.)

The first two distortions in material objects with a high velocity are what must happen, if material objects are constituted by synchronized, unit-like electromagnetic interactions and the propagation of electric and magnetic forces is due to an inherent motion in space. But two further changes in material objects are required in order for them to interact in the ways described by the basic laws of physics, one affecting the masses of the objects involved and the other affecting the forces they exert. They too can be explained ontologically, given the the various forms of matter that we have already postulated in order to explain the laws of classical physics.

Increase in mass. Quantum electromagnetic interactions involve the exertion of forces, as if the objects involved were accelerating one another in some way, and in order for forces to have the same effects on material objects with high velocity as they do on material objects at absolute rest, a further change is necessary, because the same interaction takes longer to be completed when the material object is moving across space at a high velocity.

Consider a quantum interaction in the transverse direction constituting a material object, such as an atom. The transverse distance between the two objects is not changed, but the time required for the interaction to take place is longer. The only way that it is possible for an unchanged force to accelerate an object more slowly is when the mass of the object is greater. Newton’s second law holds that the force is equal to the mass times the acceleration, and since the acceleration is lower, the mass must be greater by at the same rate.

Thus, we assume that the increase in the period of the unit-like electromagnetic interactions is accompanied by a similar increase in the masses of the objects from what their masses are at rest. And since all the quantum interactions among all the parts of the material object in motion are slowed down, the (rest) masses of all the parts increase accordingly, and thus, the (rest) mass of the material object as a whole increases at the same rate.

The increase in the mass of the moving material object can be explained, on our ontological explanation of the basic laws of classical physics, as simply the kinetic energy it acquires by its motion. Kinetic energy is one of the forms of matter, and since the quantity of matter determines its mass, the kinetic matter required to have a high velocity in absolute space can explain the increase in its mass.

The quantitative aspects of this explanation depends on the theory of kinetic matter in Change: Quantum mechanics. But we can already see, in principle, how its mass could increase to infinity as the material object approaches the velocity of light. In order to increase the velocity of the material object, each bit of kinetic matter as well as each bit of rest mass must be accelerated, that is, given additional kinetic matter, and thus, the amount of kinetic matter required to increase it at higher velocities depends on how much kinetic matter it already has. The limit is the velocity of light because of how the units of kinetic matter involve the velocity of light.

Longitudinal decrease in electric field. Though all quantum interactions suffer a time dilation and increase in mass, quantum interactions in the direction of motion suffer an additional distortion, which shrinks the lengths of the material objects they constitute. What remains to be noticed here is that such a shrinkage in the length of the moving material object also involves a change in the shape of the electric force fields exerted by charged objects. Instead of being spherical, they are flattened out in the direction of motion.

The electric force field is, we are assuming, a form of electromagnetic matter that is spread out around the center of mass of the object with a electric charge. It is what is responsible for the electric force that the nucleus, say, exerts on its electrons. But as we have seen, the forces exerted by way of such an electric field can act only over a shorter distance, and that requires us to hold that the electric field itself is shorter in the direction of motion than it is in the transverse direction.

Though the electric field is a form of matter according to this ontological explanation, it is not just matter being dragged along by the center of mass with the charge. The electric field is shortened both in front of the electric charge and behind by the same amount (with the transverse distance unchanged). Since that shortening is the result of having to complete a two-way trip with different one-way velocities of light, that suggests that the matter making up the electric field itself must be explained as a cyclic, unit-like change when we take up the ontological explanation of the basic particles (the simplest bits of matter with rest mass).

Let us assume, therefore, that the essential nature of matter making up a spatiomaterial world like ours is such that material objects in motion suffer these four kinds of changes, or “distortions” from what they are like at absolute rest, as a result of motion through a substantival space in which an inherent motion is responsible for the exertion of electric and magnetic forces.

Let me emphasize that the foregoing explanation of the four distortions is intended only to show how the four Lorentz distortions in moving material objects are not mere ad hoc contrivances for patching up a hole in Newtonian physics, but fit comfortably into this ontological explanation of the truth of physics, including its explanation of quantum mechanics.

Such an explanation of the four distortions is not required, however, to meet the challenge of showing that it is possible for spatiomaterialism to explain the truth of Einstein’s special theory of relativity. It would be enough simply to assume the Lorentz distortions as part of the basic nature of matter, as if they were basic laws of physics. Hence, doubts about the ontological assumptions I have made about the nature of material objects to explain the Lorentz distortions should not cast doubt on the capacity of spatiomaterialism, in general, to explain the truth of Einstein’s special theory of relativity.

Einstein’s general theory of relativity. By showing that spatiomaterialism can explain the truth of Einstein’s special theory of relativity (STR), I have answered the first part of the Einsteinian reservation about using spatiomaterialism as the foundation for demonstrating ontologically necessary truths. In this section, I will answer the second part. Einstein’s general theory of relativity (GTR) also makes it appear that this is not a spatiomaterial world, and I will show how its truth can also be explained by spatiomaterialism.

The way Einstein’s general theory of relativity explains gravitation does not, at first, seem compatible with spatiomaterialism. The foundation of the general theory is spacetime, for gravitation is explained as a “curvature” in spacetime, and since substantivalism about spacetime is incompatible with substantivalism about space, it seems out of the question that what the general theory refers to as “curved spacetime” could turn out to be an aspect of space and matter as substances enduring through time. (For a very accessible account of Einstein's general theory of relativity, see Clifford M. Will's Was Einstein Right?)

It is, however, possible for spatiomaterialism to explain why Einstein’s general theory of relativity is true. The key is what spacetime turns out to be in the ontological explanation of the truth of the special theory of relativity, for that makes it possible to explain curved spacetime as well. Curved spacetime is also an aspect of space and matter, even though as substances that endure through time, space and matter exist only at the present moment.

Though I go on in the next section to suggest an ontological explanation of quantum mechanics and, in the following section, take up some basic issues in cosmology, this explanation of the Einstein’s general theory of relativity pays off the second mortgage that we took out in order to use spatiomaterialism as the foundation for our philosophical argument. (See Necessary Truths.) Quantum mechanics is not so crucial to this project, because there is continuing disagreement about its ontological implications and some of the possibilities are compatible with spatiomaterialism.

We have already seen how the existence of consciousness can be explained in a spatiomaterial world (though the unity of consciousness will not be explained until I take up the mammalian brain in the sixth stage of evolution), and I have yet to take up the nature of goodness and holiness. But one of those four mortgages will be repaid when we see that Einsteinian physics provides not reason for denying that this is a spatiomaterial world.

In fact, spatiomaterialism might welcome the challenge of explaining Einstein’s general theory of relativity, because that means it does not have to defend Newton’s theory of gravitation. Newton’s theory is prima facie less hospitable to spatiomaterialism than general relativity. If a force did act immediately at a distance, it would contradict the principle of local action, implying that spatiomaterialism is false.

Newton’s theory describes an attractive force by which every material object acts immediately on every other material object, including those at a distance. Newton introduced it, in effect, as the best efficient-cause explanation of Kepler’s laws of planetary orbits, and it was confirmed by the deduction of many surprising, quantitatively precise predictions of measurements, becoming the model for the empirical method in physics. Despite its predictive success, Newton’s law of gravitation had nothing to say about how such forces are exerted on objects at a distance, except that they act instantaneously at a distance.

Action at a distance was puzzling to classical physicists, since it did not fit well with their intuitive understanding of nature as composed of space and matter in time. Even Newton was uncomfortable with the notion, and he refused to make any hypotheses about how gravitation worked in his Principia.^xx But action at a distance could not be rejected for being incompatible with spatiomaterialism, for that would require using space as an ontological cause, and Newtonian physics did not recognize the validity of ontological arguments. Still, when Einstein proposed an explanation of gravitation that implied that gravitational forces propagate at a finite velocity, even physicists were relieved at not having to believe in action at a distance. And it did remove what would otherwise be an insuperable objection to spatiomaterialism.

Einstein’s general theory of relativity was, however, another highly mathematical hypothesis, which predicted many quantitatively precise measurements, and since it implies that gravitational acceleration is caused by a curvature of spacetime, a realist interpretation of Einstein’s theory seems to imply that spacetime is a substance. But if the real nature of what exists in addition to mass and energy is spacetime, that is, a four-dimensional entity in which time is one of the dimensions along with space, then existence is not in time and “real change” is not ontologically possible. Thus, general relativity solved one ontological problem, but only by introducing another. The challenge is, therefore, to explain how curved spacetime can be understood as an aspect of a world constituted by space and matter as substances that exist only at the present moment.

Curved spacetime. Having discovered STR by assuming the local equivalence of all inertial frames, Einstein sought to use the same approach in explaining acceleration due to gravity, that is, by including reference frames that were being accelerated by gravitation. Thus, the main assumption of his general theory of relativity is the equivalence of inertial frames to reference frames falling freely in gravitational fields.

What Einstein himself called the “principle of equivalence” assumes that nothing can be detected within any reference frame (that is, locally) that would distinguish a reference frame in inertial motion from one in free fall.

Or, to put Einstein’s equivalence principle the opposite way, a reference frame at rest in a gravitational field is indistinguishable from one being accelerated by a force; the push that we ordinarily call the “force” of gravity is actually the force of the earth accelerating us upward from what is equivalent to inertial motion.

This further equivalence can be only local, however, because free-falling frames are obviously different in how they are related to the rest of the world, or globally. Though inertial frames simply continue in motion indefinitely, free-falling reference frames eventually collide with the center of gravity, because gravitational fields are imposed by matter concentrated at certain locations. Thus, what makes the general theory of relativity general is that it includes both inertial and free-falling reference frames, and Einstein’s highly mathematical description of how they fit together as parts of a single world is a theory of acceleration due to gravity.

Einstein’s strategy in GTR paralleled that of his special theory. In STR, Einstein used his principle of relativity (implying the equivalence of all inertial frames) to derive a mathematical description of how they must be related globally (the Lorentz transformation equations). In his general theory, Einstein started with the assumption that reference frames in free fall are locally equivalent to inertial frames, and using the four-dimensional, spacetime mathematics from special relativity, he derived equations describing how all reference frames, inertial and free-falling frames, are related to one another. In both theories, the equivalence of reference frames means that the laws of physics hold the same way on each of them. That means that there is a mathematical transformation of explanations of events given on any one reference frame into explanations given on the other in which the laws of physics have the same form. In special relativity, only a Lorentz transformation was required, making them Lorentz covariant. But in general relativity, it is a more general transformation, which includes both inertial frames and free-fall frames, called “general covariance”. How objects change their motion depends on centers of mass in their neighborhoods, and using general covariance as a constraint, Einstein was able to deduce equations that describe what classical physics attributed to a force of gravity.

Einstein’s general theory of relativity describes a spacetime world in which the accumulation of matter (both mass and energy) causes a “curvature” in the surrounding spacetime. This curvature explains the acceleration that Newtonian physics attributed to a force of gravitation, because it determines, in turn, the inertial path for any matter located there. (Such an inertial path though curved spacetime is called a “geodesic”).

GTR also predicts various new phenomena, including the bending (and slowing down) of light rays passing through gravitational fields, the precession of the perihelion of Mercury, and a gravitational red shift. These predictions all differ from classical physics, and since GTR entails the possibility of black holes, including rotating black holes, it has become the foundation of cosmology. Except for the precession of Mercury’s perihelion, these phenomena were not even expected before Einstein’s argument, much less explained, and so the confirmation of these predictions justified accepting the general theory by the empirical method of physics.

Realism about the general theory of relativity, like realism about the special theory, makes it hard to avoid thinking of spacetime as a substance on a par with what it contains. The curvature of space­time is supposed to cause the acceleration of mater that is ordinarily attributed to gravity, and it would be hard to explain how a property of spacetime can have such an effect on what it contains, if spacetime did not exist independently of matter.

GTR is, like STR, a highly mathematical theory. Gravitation is described by the Einstein field equations, which relate the distribution of mass and non-gravitational energy to the curvature of spacetime. Currently, GTR is usually interpreted in terms of differential geometry. Spacetime is postulated as a four-dimensional continuous manifold of points (M), and there are two kinds of (tensor) equations defined everywhere on the manifold. The metric-field tensor (g) defines the metric (and geometric) relations among points in spacetime, and the stress-energy tensor (T) represents the distribution of matter (mass and energy) in spacetime (and its effects).

Jointly, M, g, and T are called a “model” of GTR, and even for a world with a particular distribution of mass and energy, there are infinitely many different, yet empirically equivalent models. They all predict the same gravitational phenomena, but each model involves a different coordinate system, for each is based on a different local inertial reference frames at its location in spacetime, that is, adapted to material objects with different free-fall trajectories.^xxi Their empirical equivalence is an assumption that Einstein used to derive his field equations, and it is one of the meanings sometimes given to “general relativity”. On this geometrical approach, GTR also seems to imply substantivalism about spacetime, because the four-dimensional manifold of points (M) must be postulated in order to define the metric-field tensor (g) and stress-energy tensor (T).^xxii

The challenge that GTR poses for spatiomaterialism is that it implies that what exists is spacetime, rather than space and matter existing as substances in time. In a spacetime ontology, time is another dimension of what exists on a par with the spatial dimensions (except for a change in sign and the velocity of light as a scaling factor). Its implications about time were used in Spatiomaterialism: Time to show that spatiomaterialism is a better ontological explanation of nature than spacetime ontology (or “spatiotemporalism”). Substantivalism about spacetime makes it impossible to explain “real change”, because if what exists is a four-dimensional entity, and time is part of its structure, then nothing can be coming into existence or going out of existence as time passes.

As we saw in Spatiomaterialism, there is no way for spacetime substantivalism to avoid refutation by the fact that our experience of change itself take place through time and we are parts of nature, except by postulating an additional, subjective substance, for whom spacetime and the events it contains have the appearance of real change. Not only does the addition of such a subjective substance make spacetime ontology more complex, but it also poses the problem of relating eternal and enduring substances as parts of the same world, a problem that Plato never solved. And even if it could be solved, this modification would be ad hoc, for it would explain nothing but the appearance that change takes place through time. There is, therefore, no question that spatiomaterialism is a better ontology, if it is possible.

In order to show that spatiomaterialism is possible is to show that it can explain why GTR appears to be true, and that means explaining all the relevant phenomena on the assumption that nothing exists but space and matter enduring through time. This is to describe a model or solution of the Einstein field equations that differs from the prevailing geometrical interpretation because, instead of postulating a four-dimensional manifold and defining geometrical objects on it, spatiomaterialism postulates space and matter as substances enduring through time. Nothing exists in a spatiomaterial world but what exists at present, and thus, the interaction of space and matter must somehow have an aspect that explains what Einsteinians are referring to when they talk about “curved spacetime” and that aspect must explain all the phenomena predicted by the general theory.

We can tell that not in principle impossible for a world of substances that exist only at the present moment to explain the truth of GTR, because even on the received geometrical interpretation, there is a standard of simultaneity implicit in each model’s assignment of space and time coordinates to every event in the universe. All the spacetime events with the same temporal coordinates that we now have in some model for our universe (a certain “simultaneity hypersurface” in curved spacetime) could be all that actually exists at the present moment, and their spatial coordinates could be referring to parts of a three dimensional Euclidean substance. Of course, this could be true of only one model, for although every model assigns some coordinates to us now, different models entail different standards of simultaneity, and if different models were ontologically equivalent, the substances constituting the world would have to include spacetime.

Moreover, in order to hold, in effect, that one of all possible models represents absolute space and time, spatiomaterialism would have to show that there is a law of gravitation that explains not only the approximate truth of the Newtonian theory in it, but also all the new phenomena predicted by GTR. We can also tell that such a law is not in principle impossible, because GTR itself implies that the relevant events in that model are all related in a regular way. Still, the regularity would have to be described without referring to space­time or spacetime curvature, that is, explained as constituted by (Euclidean) space and matter enduring through time. And there would be problem about the regularity, only if its description turned out to be very complex.

Finally, since spatiomaterialism would take reality to be equivalent to what exists in a single model of GTR according to the received geometrical approach, we should also expect the spatiomaterialist law of gravitation to explain why different models are observationally equivalent, that is, to explain “general relativity”, in the sense that enabled Einstein to derive his mathematical representation of gravitation.

This is a tall order, but it is possible, as I will show here by giving an ontological explanation of why Einstein’s GTR is true. It is an intuitively intelligible explanation, rather than a mathematical explanation, because what is required to explain the truth of any theory ontologically is showing that there are aspects of the substances postulated by the ontology that correspond to the theory. That requires a qualitative argument, which identifies the kinds of regularities and how they are related according to the theory, and then shows that they can all correspond to aspects of the same world. To be sure, the aspects of the substances pointed out must be quantitatively adequate as well. But that is rather trivial, once the qualitative argument has shown what the parameters are, how they are related to one another, and the signs and order of magnitude of their quantities, because substances can be postulated as having whatever quantitative aspects are required to make the measurements come out correctly. Thus, I will leave it as a challenge to those who would disprove spatiomaterialism to show that the aspects identified here cannot all be quantitatively accurate.

Acceleration of the inherent motion in space. How can gravitation be explained in a spatiomaterial world? To be adequate, it must explain not only the acceleration due to gravity that Newton recognized, but also all the new phenomena predicted by the general theory of relativity. That is a challenge, because it must do so without appealing to spacetime. How can gravitation be explained with nothing but two opposite substances that exist only at the present moment?

As in the reduction of special relativity, there is no need to reject the mathematical equations or the interpretations by which they are tested empirically. All that needs to change is what we take them to refer to. Since we shall be starting from the assumption that space is absolute, this is to take an approach opposite to Einstein, just as we did in explaining special relativity.

Einstein called his explanation of gravitation a general “theory of relativity” because he assumed that gravitational phenomena, like all other phenomena, must obey the same laws in every reference frame, and his strategy was to explain gravitation by describing a way of transforming coordinates assigned by observers on different reference frames into one another that leaves the laws of physics unchanged. He assumed that the velocity of light has the same value in every reference frame, and a tensor calculus was required to formulate the mathematical transformation.

As ontologists, however, we start by assuming that space and matter are substances existing in time, and since that means that light may have different (one-way) velocities, different reference frames are not ontologically equivalent. Thus, it is not appropriate to call it a theory of relativity. On the contrary, it will explain the general equivalence of reference frames, or the premise of Einstein’s argument, as an appearance constituted by space and matter as ontological causes, much as it did in explaining the premises of Einstein’s argument in STR.

The key to the spatiomaterialist theory of gravitation is its explanation of the apparent truth of STR.

In its ontological explanation of the truth of the special theory, spatiomaterialism rejects Einstein’s assumption that the velocity of light is the same relative to every inertial frame and assumes, instead, that it is due to an inherent motion in space. It also assumes (or shows) that the motion of material objects through space causes four Lorentz distortions in them. The Lorentz distortions enable it to explain why inertial frames are empirically equivalent locally, and by taking into account how clocks are mis-synchronized on moving reference frames by adhering to Einstein’s definition of simultaneity at a distance (that is, ignoring the difference between the one-way velocities of light in each direction), they also explain why inertial frames appear to be equivalent globally, that is, why the (net) Lorentz distortion always seem to be occurring in the other member of any pair of inertial frames.

These assumptions and conclusions are all taken for granted in explaining the truth of the general theory of relativity, and only one additional ontological assumption is required to explain gravitation. That is the assumption that the accumulation of matter at certain locations in space has an effect on space, mediated by the inherent motion in space, that, in effect, accelerates the inherent motion in the nearby space toward it.

There are various consequences of this assumption. They are described in the following sections, including their role in explaining the new phenomena predicted by Einstein. One consequence has to do with the velocity of light. Another has to do with effect on material objects that are forced to remain at rest relative to space itself in a gravitational field. The third is a result of how the effect of matter accumulation on space is mediated by the inherent motion itself. Finally, I will show how it explains the special phenomena that occur in very strong gravitational fields, such as black holes. At the end, I will return to the issue about the nature of the argument and show how this ontological explanation of gravitation explains “general relativity” in the sense of the observational equivalence of different models of GTR, which Einstein used to derive his conclusions.

In constructing its theory of gravitation, spatiomaterialism takes its lead, as Einstein did, from the assumption that reference frames free-falling in gravitational fields are equivalent (locally) to reference frames in inertial motion. Einstein called this the “principle of equivalence.” But given its explanation of the truth of STR, this principle has a somewhat different meaning, for spatiomaterialism holds that different inertial frames, despite being observationally equivalent, are ontologically different.

When inertial frames have different velocities relative to one another, at least one must be moving relative to space, and since that means having a velocity relative to the inherent motion in space, we had to assume that material objects suffer Lorentz distortions as a result of their motion relative to the inherent motion in space, in order explain why they appear equivalent (locally and globally). Now, in order to explain all the old and new gravitational phenomena, we must assume yet another interaction between space and matter — an interaction that makes it appear that free falling frames are observationally equivalent, locally, to inertial frames outside gravitational fields.

Whereas Einstein took gravitation to involve an interaction between matter and spacetime, spatiomaterialism takes gravitation to involve an interaction between matter and space. Spatiomaterialism assumes that, instead of curving spacetime, accumulations of matter (mass and energy) change the velocity of the inherent motion in space.

I am speaking as if the inherent motion were something actually moving though space while space endures, as a substance, through time, but I have admitted that, if you prefer, it can be taken as just a spatio-temporal aspect of substantival space having to do with how fast what occurs in one location in space can affect what happens elsewhere. If space is to mediate the relations and interactions among bits of matter, some such limit on the velocity of their effects on one another is necessary, because otherwise spatiomaterialism would have to give up its assumption that space is a substance made up of many particular substances (one for each location in space and all connected as described by Euclidean geometry). There is no doubt that space involves an “inherent motion” in the sense of having a spatio-temporal aspect about how parts of space are related.

The only issue is whether there is anything actually moving through space other than bits of matter. That can be doubted, because, thus far, at least, the only candidates for what moves across space are bits of matter. Setting material objects aside (because the move slower than the inherent motion), we have, thus far, come across nothing that actually moves across space at that maximum velocity except light (and the forces exerted by material objects with an electric charge), which are forms of matter. The gravitational force is not an exception, for even though it also propagates at the velocity of the inherent motion, it is also a form of matter even on this theory (as I suggested in Forms of matter). But it does no harm to think of this aspect of the nature of space as an inherent motion, for we have already recognized that space is a substance enduring through time and seen that it must have a spatio-temporal aspect to the relations of its parts. Moreover, in explaining how quantum mechanics can be true in a spatiomaterial world, we will find that something other than matter also moves across space with the inherent motion.

Thus, I will continue to speak of space as if there were an inherent motion through every location, moving at the same velocity both ways in every direction in three dimensional space. It is something we can imagine, because as rational beings, we are able to think about space, time and motion, and thus, it will enable me to describe the effect of matter accumulation on space in a qualitative way, in terms of its effect on the inherent motion and, thereby, on all the electromagnetic interactions that are mediated by it.

Those with a more reactionary bent may, however, want to call the inherent motion in space by its traditional name. It is actually an ontological explanation of the ether. The luminiferous ether was supposed to be a material substance of some kind at rest in absolute space that mediated electric and magnetic forces like a very elastic material substance. To be sure, we have no need to postulate any form of matter to play the role of the ether, because we take space to be a substance, and its inherent motion can mediate electromagnetic interactions. But on the other hand, it would be appropriate to speak of the inherent motion in space as the ether, and that means that the new assumption being made here could be described just as well as an acceleration of the ether. (I would use this term, except that it is likely to inflame the antagonism of Einsteinians, who sometimes like to portray their denial of absolute space as merely discrediting a foolish metaphysical belief in unobservable entities.)

The assumption that spatiomaterialism makes in order to explain gravitation, therefore, is that the accumulation of matter exerts a force on other nearby bits of matter by way of its effect on the inherent motion in space that changes the velocity of the inherent motion in space as if the inherent motion itself were being accelerated toward the center of gravity at the rate described by Newton’s law.

The inherent motion flows both ways in every direction, and the gravitational change in the velocity of the inherent motion is different in opposite directions. The inbound velocity of the inherent motion is greater than it would be outside the gravitational field, and the outbound velocity is correspondingly less than it would be outside. Thus, it is as if the inherent motion itself had an inbound velocity.

Since the inherent motion is a velocity both ways in every direction at every location in space, there is always some pathway for material objects relative to it in which the two one-way velocities of inherent motion are equal in both directions. Let us call that motion relative to space “rest relative to the inherent motion” (or for reactionaries, “rest relative to the ether”). The effect of the force of gravity is, therefore, equivalent to accelerating rest relative to the inherent motion in space, so that it has velocity relative to space in a gravitational field.

(It might, therefore, be better to describe the effect of the force of gravity as accelerating the ether, because it is rest relative to the ether that is undetectable. But that could be misleading. It might suggest that ethereal matter is accumulating at the center of gravity, whereas the inherent motion is just the way in which bits of matter coincide with space, and thus, the acceleration of the inherent motion is just a change in how bits of matter coincide with space. But it is useful to keep in mind that there is an inertial frame at rest relative to the inherent motion, and it is, in effect, what is accelerated by the accumulation of matter.)

The inbound velocity of the inherent motion at any point depends on how much it has increased as a result of accelerating all the way in from infinitely far away as a result of its acceleration.

The amount of acceleration varies directly as the product of the amount of matter (mass and energy) making up the objects accelerating one another and inversely as the square of the distance between them in space (though the force is exerted by way of the inherent motion).

At any point in a gravitational field, therefore, the increase in the inbound velocity of the inherent motion is equal to the escape velocity at that point. That is, relative to space, the inherent motion is moving toward the concentrated matter at the velocity of light plus a velocity that is equal to the outbound velocity a material object would have to have at that point relative to space to escape gravity and eventually come to absolute rest outside its influence. The decrease in the outward-bound velocity of the inherent motion in space is likewise the escape velocity, making the outward bound velocity of the inherent motion the velocity of light minus a velocity equal to the velocity a material objects would have to have to move outward and just escape the gravitational filed.

Since the gravitational variation in the velocity of the inherent motion at different points in space is equivalent to the acceleration of the inherent motion, any matter that coincides with space by way of the inherent motion also accelerates at the same rate. That includes, as we shall see, all forms of matter.

Photons are accelerated because they coincide with space in such a way that they are carried along by the inherent motion in space.

Material objects also coincide with space by way of its inherent motion. This is implicit in the spatiomaterialist explanation of the truth of STR. What makes it impossible to detect its velocity relative to the inherent motion experimentally are Lorentz distortions that material objects suffer because of their motion relative to the inherent motion. Indeed, some of those distortions depend on the difference in the one-way velocities of light in opposite directions in the direction of its motion relative to the inherent motion. Thus, when the inherent motion itself is accelerating inward, any material object that coincides with space by way of the inherent motion is also accelerated in the same way. And since electric charges move with the material objects and exert their forces by way of the inherent motion, their electric fields are accelerated along with them.

Since acceleration of matter by way of the acceleration of the inherent motion is a form of potential energy, the gravitational field is itself a form of matter. It is the form of matter I called “gravitational matter” at the beginning of the ontological explanation of the truth of the laws of physics (see Forms of matter), and the quantity of matter involved in constituting the potential energy of gravitational field is counted as part of the total matter (mass and energy) accumulated at the center of accumulation. Thus, as the kinetic energy of material objects increases because of their acceleration, the potential energy not only declines, but becomes less than zero (or maximum potential energy), and the total quantity of mass and energy is, thereby, conserved.

If the center of matter accumulation itself is in motion relative to space, then it already has a velocity relative to the inherent motion in space and all the effects of its gravitational field are affected accordingly.

Gravitation involves, according to this ontological explanation of the truth of the general theory, a second interaction between space and matter. The first was the reaction of space to material objects that acquire a high constant velocity relative to the inherent motion: it imposes the Lorentz distortions on such material objects. The second is more complex, because matter first causes a change in space, and then space, in turn, causes a change in matter. That is, accumulations of matter accelerate the inherent motion in space toward themselves, and the acceleration of the inherent motion not only accelerates the bits of matter it contains, but also changes the velocity of light at any point in space (because the inherent motion accumulates inward velocity over the entire gravitational field). It is as if space had a compound effect on the matter it contains, because either effect can occur separately, and both can happen at once.

The first effect occurs separately when material objects have a constant velocity relative to the inherent motion outside of a gravitational field.

The second effect occurs separately when material objects are at rest relative to the inherent motion being accelerated into a center of mass that is at rest in absolute space.

Both effects occur either when material objects have a constant finite velocity relative to an inherent motion that is being accelerated into a center of gravity that is at rest, or when the accumulation of matter itself has a constant velocity relative to the inherent motion in space outside gravitation.

Let us consider the consequences of this additional assumption about the nature of space and matter.

This ontological assumption explains why Newton’s law is approximately true in all those areas where it is recognized to be a good approximation, because it differs from Newton’s theory only in its assumption that gravitation acts by way of the inherent motion, that is, that it accelerates the surrounding inherent motion in space and that it does so as a force that is itself propagated by that inherent motion.

It also explains Einstein’s equivalence principle ontologically. It entails that local experiments on free falling frames come out the same as on inertial frames outside gravity, for in both cases they have a constant velocity relative to the ether.

But the spatiomaterialist theory also explains intuitively certain new phenomena used to confirm Einstein’s GTR, including the three new kinds of phenomena that have been used to confirm the general theory as well as the predictions about black holes.

Variation in the velocity of light. The most immediate effect of the acceleration of the inherent motion is on the velocity of light. The photon coincides with space by having some direction in the inherent motion wherever it is located and being carried along by the inherent motion in space. Thus, the motion of the photon relative to space manifests the inherent motion in space any motion that the inherent motion itself has relative to space because of the gravitational field.

Since the inherent motion is different at different locations in space as a function of the force of gravity, a photon traveling inward toward the center of matter will accelerate as it moves, acquiring a velocity relative to space that is higher than the velocity of light outside of the influence of gravitation. Correspondingly, a photon moving outward will leave the center of mass with a velocity relative to space that is less than it would have outside of gravitation, and it will accelerate all the time it is moving outwards until it reaches the velocity of light outside gravitation just as it escapes the gravitational field.

The quantity of the increase (decrease) in the velocity of light at any point in space relative to what it would be if there were no gravitational force depends on the escape velocity, that is, how much velocity a bit of matter would acquire as a result of being acted on by the gravitational force as it moves across the gravitational field.

Consider for simplicity’s sake a center of matter (mass and energy) that is at rest in absolute space. The theory is that when matter accumulates in space, it acts on the surrounding space in a way that is equivalent to accelerating the inherent motion in space toward it, giving the inherent motion itself a velocity relative to absolute space. The rate of acceleration is determined by the force of gravity (which declines as the square of the distance from the center of gravity), and that means that the photon starts accelerating infinitely far away from the gravitating body and accumulates speed as it continues to accelerate inward (with its rate of acceleration becoming greater as the gravitational force increases), so that at points nearer the center of gravity, the photon has an instantaneous, inward velocity that is equal to the velocity of light outside gravitation plus the escape velocity at that point in the gravitational field.

If the gravitating body is not at rest in absolute space, but is itself moving relative the inherent motion in space, that will also alter the velocity of light the same way at every point throughout its gravitational field.

When enough matter accumulates to accelerate the inherent motion itself to a velocity in space that is faster than the velocity of light outside any gravitational field, it is called a “black hole.”^xxiii The so-called Schwartzschild radius of a black hole at rest in space is the surface in space at which the inward velocity of the virtual inherent motion equals the velocity that light would have in that direction at that location, if the inherent motion were at absolute rest. Inward-bound light crossing that surface would have a velocity relative to space twice what light would have outside of gravitation, and thus, it is impossible for light being carried in the opposite direction by the inherent motion to cross that surface. Outward bound photons at the Schwartzschild radius of a black hole would be at rest relative to space.

Gravitational bending of light rays. The effect of the acceleration of the inherent motion on the velocity of light explains the most famous new prediction of the general theory, namely, the bending of light rays in a gravitational field.

Given that light, as a form of energy, has a mass and exerts a gravitational force, Newton’s law can be used to predict that light will be bent from its straight path by the force of gravity, much like a material object. But the general theory of relativity predicts that the light ray will be bent at about twice the rate predicted by Newton’s theory. And in a famous expedition in 1918, Eddington found that Einstein was correct by measuring the direction of a ray of light from a distant star as it passed behind the sun during an eclipse and the distant star could be seen.

The greater effect of gravitation predicted by Einstein is what would be expected on the spatiomaterialist explanation of gravitation, because two factors are involved in determining the pathway of the photon.

First, as the light ray passes the gravitating body, it is pulled sideways into the center of gravity by the inward acceleration of the inherent motion in the transverse direction, which diverts it from a straight path, much as expected on Newtonian grounds.

Second, as the photon is approaching the center of gravity, the inward acceleration of the inherent motion gives light an inward velocity higher than it would have outside the gravitational field. But since the inherent motion on the other side of the center of gravity has been accelerated in the opposite direction, the photon slows down as it passes the gravitating body to a velocity that is lower than it would be outside gravitation, and then it gradually speeds it up again to the normal velocity of light relative to space as it moves out of the gravitational field on the other side. The result of these changes in the velocity of light is that the photon spends a disproportionately longer period of its entire trip near the center of gravity where the sideways acceleration of the inherent motion toward the center is greatest than it does farther away when the sideways acceleration of the inherent motion is minimal. That explains the higher value of bending predicted by Einstein.^xxiv

Time delay in radar signals. The effect of the acceleration of the inherent motion on the pathways of photons can also explain the time delay in radar signals reflected back to earth from planets on the far side of the sun when the paths of those signals lie near the sun.

There is a spatial symmetry about the velocity changes that occur both times the radar signal approaches and recedes from the sun. The signal gains velocity as it approaches the sun, because the inherent motion is accelerating under gravity in that direction. But it quickly comes to have a lower velocity than light outside of gravitation as it passes by the sun, because of the inbound acceleration of the inherent motion on the other side of the sun. And then the signal regains velocity as it recedes, because the inward velocity of the inherent motion on the other side is lower the father away from the sun.

It might seem that there should be no net effect on the total time it takes for the light signal to pass by the sun, because the higher velocity of its approach to the sun will be canceled out by the lower velocity of its retreat from the sun on the opposite side. After all, the approaching signal travels just as far at each higher velocity as the receding signal travels at comparably lower velocities.

There is, however, a net slowing down of the period required for the entire trip, because the equal distance on each side of the sun entails that the light signal spends more time traveling at slower velocities than it does traveling at faster velocities. Hence, it cannot make up all the time it loses going slower in the time it spends going faster. This happens both ways on its round-way trip to the distant planet, causing an overall delay in the radar signal’s return that does not occur when its path is not near the sun.^xxv

Time dilation caused by acceleration relative to the inherent motion. Another famous prediction of Einstein’s general theory of relativity is the so-called “gravitational red shift,” or a time dilation in gravitational fields. That is, all physical processes on material objects are slowed down at a rate that depends on the potential energy of the gravitational field (which would vary directly with the altitude, if the force of gravity were constant). It predicts that such a time dilation will be observed both in objects at rest in a gravitational field and in objects in free fall in a gravitational field.

Gravitational time was observed by Pound and Rebca (1960) demonstrating a difference in the rate of oscillation of iron nuclei at the top and bottom of a tower at Harvard.

It was also observed in signals sent by a hydrogen maser shot up above the earth and allowed to fall back by Vessot (1980).

Gravitational time dilation can be explained by the spatiomaterialist theory of gravitation, but it implies that physical processes are actually slowed down only when material objects are at rest in a gravitational field. Objects in free fall in a gravitational field are not affected. But there is an appearance of a time dilation in objects in free fall that is caused by the change in the velocity of the light by which the speed of falling clocks is observed. Let us, therefore, consider each case separately.

Real gravitational time dilation. The principle of equivalence implies that material objects at rest in a gravitational field will suffer a time dilation, and the ontological explanation of the equivalence principle according to the spatiomaterialist theory of gravitation implies that the rate of time dilation is proportional to the energy that would be required to accelerate the object to keep in at rest given its velocity relative to the inherent motion.

This distortion is like the Lorentz time dilation, except that it depends on resisting the gravitational acceleration of the inherent motion rather than having a constant velocity relative to it. According to the spatiomaterialist theory, a clock at rest in a gravitational field, for example, will be slowed down compared to a clock in free fall. If a free falling clock happened to have an initial upward velocity in a gravitational field like a ball thrown into the sky and it was synchronized with a clock at rest on its way up, then, when it passed the same rest clock again on its way down, the rest clock will have fallen behind by an amount that depends on the period between the measurements and the energy required each unit of time to resist the acceleration of the inherent motion and keep it from falling in gravity, given the velocity of the accelerated inherent motion at that point.

The “gravitational red shift” in objects at rest is usually explained as a consequence of Einstein’s equivalence principle. Consider two clocks at rest at different altitudes in a gravitational field and what happens to a regular signal (such as photons of a certain frequency) sent between them, say from the upper rest clock to the lower. (See Diagram of Gravitational red shift.) The equivalence principle implies that, when this interaction is observed from a free falling frame, it must obey the same laws that hold for inertial frames outside gravitational fields.

Consider, therefore, a free falling frame as long as the distance between the two rest clocks, and suppose that it had been shot upwards so that its inertial motion brings the top of the free falling frame momentarily to rest in space alongside the upper rest clock just as it sends a photon of a certain frequency toward the bottom rest clock. If the photon were intercepted by the bottom free falling clock, it would have the same frequency observed when it left, because that is what would be observed if the inertial frame were outside the gravitational field. But that is not how the photon would appear to the bottom rest clock, as can be predicted by observers on the free falling frame. All the time that the photon is traveling downward, the free falling frame is also accelerating downward, and thus, when the observer at the bottom of the free falling frame sees the photon being received by the bottom rest clock, that clock will be moving upward toward the photon. Such motion would cause a Doppler effect, and so the free falling observer predicts that the photon will be measured by the bottom rest clock as having a higher frequency than the photon sent by the upper rest clock. Indeed, this is what the rest observer does find, according to GTR and actual experiment.

In this case, it is a gravitational blue shift, but if the signal had been sent upward, it would be a red shift. (By the time the photon arrived at the top rest clock, the free falling frame whose bottom clock was momentarily at rest beside the bottom rest clock when the signal was sent would have accelerated down­ward, and so the top free falling observers would see the top rest clock as receding upward when the signal arrives, entailing the prediction of a Doppler red shift, that is, a lower frequency of light received by observer located by the top rest clock.)

What is the cause of the red/blue shift observed by the receiving rest clock?

GTR explains the frequency change by the spacetime curvature between the two clocks, but it does not say whether it results from a change in the frequency of light signals during the flight or a difference in the intrinsic rates of rest clocks at different altitudes. Will (1986, p. 49-50) says that “it doesn’t matter” whether the “light signal changes frequency during the flight” or the “intrinsic rate . . of the clocks change”, because there is “no operational way to distinguish between the two descriptions”.

Spatiomaterialism, however, cannot be indifferent, for it assumes that space and matter are substances that exist only at the present moment, and that means that the red/blue shift cannot involve any actual change in the frequency of signals as they travel across space through time. The frequency, or period between signals, cannot change, regardless how the velocity of light may change along the path, as long as each signal follows the same path in real time. The only possible spatiomaterialist explanation is that the frequency shift is an appearance due to an actual slowing down of the rest clock (and all processes involving material objects at rest).

Spatiomaterialism explains why the clocks at rest are slowed down by their relationship to the inherent motion. The inherent motion is accelerating at the location of the clock, which is evident in the free falling frame, and thus, the rest clock must be accelerated relative to it in order to keep it at rest. In order to understand the relationship between these two reference frames, let us consider the equivalent situation outside of gravitation according to the spatiomaterialist theory.

The relationship between these two reference frames in the gravitational field is not equivalent to one reference frame being accelerated relative to some inertial reference frame outside gravitation unless both frames are also in motion relative to the inherent motion in space, because at any point in a gravitational field, the inherent motion has acquired a certain velocity relative to absolute space. Thus, let us consider two reference frames outside of gravity that have the same velocity relative to the inherent motion as those in the gravitational frame, and let us suppose that one of them is accelerated relative to the other. In such a case, the Doppler effect would cause the same red (or blue) shift, depending on which way one frame was accelerated relative to the other during the brief interval of measurement.

Outside a gravitational field, the Doppler effect would not be interpreted as a time dilation, because it would be explained by the change in the velocity of one of the frame relative to the inherent motion due to its acceleration during the interval of measurement. The situation in the gravitational field is different because the acceleration of one frame relative to the other does not change the velocity of either one of them relative to the inherent motion.^xxvi Instead, it is the inherent motion itself that is being accelerated. Thus, the red (or blue) shift cannot be explained as a result of the change in velocity relative to the inherent motion due to the acceleration of the frame at rest in gravitation, as it is outside gravitation. It can only be the result of a slowing down of physical processes on the reference frame at rest in gravitation. Thus, it is a real time dilation.

Rest clocks at different altitudes in a gravitational field suffer different rates of time dilation, even though they may be resisting the same rate of acceleration in the inherent motion (as in a uniform gravitational field). This can be explained on the spatiomaterialist theory, because they have different velocities relative to the inherent motion. Outside a gravitational field, according to Newtonian physics, different amounts of energy are required for the same acceleration in objects when the objects have different velocities. The force per unit time is the same, but since at higher velocities, the force must be exerted over a greater distance, and thus, the energy consumed in exerting the force over that period of time is greater. That is, the rate of gravitational time dilation is proportional, not the force required to accelerate the rest clock, but to the amount of energy required. (At lower altitudes, the force has to act over a greater distance relative to rest in the inherent motion in order to keep the clock at rest.) This explains why the rate of time dilation is proportional to the potential energy for its location in the gravitational field (or the kinetic energy an object falling from outside the gravitational field would have at that point).

Apparent gravitational red shift. An actual gravitational time dilation occurs only when the clock is being accelerated against the acceleration of the inherent motion. A clock in free fall in a gravitational field will actually tick away at the same rate as a clock outside of the gravitational field. But a clock free falling in a gravitational field will appear to suffer a gravitational time dilation, because the motion of the clock across the gravitational potential means that any signals it sends out at regular intervals will be received later than they are expected, making it seem like the clock is slowed down.

Consider a clock in free fall sending signals out of a gravitational field. To observers outside the gravitational field, those signals will make it appear that the clock is suffering a time dilation, though it is not, because in addition to the normal Doppler shift expected from the velocity it acquires from free fall, signals sent back from lower altitudes will also travel the additional distance at lower velocities of light because the outbound velocity of light is lower (because the inbound velocity of the inherent motion is greater the closer it is to the center of gravity). Each signal will be delayed a bit longer than expected.

Or consider a clock shot upwards in a gravitational field that sends regular signals to earth (Vessot’s experiment). The signals received from the clock on earth will be affected by several factors apart from gravitation, including its location at the moment the signal is sent and its instantaneous velocity. These factors can be calculated and compared with the signals actually received. The actual signals will seem to be arriving sooner that expected the higher the clock goes, making it seem that the clock must be speeding up as it rises out of the gravitational field. But that is not proof that objects in free fall suffer a time dilation. Instead, it merely indicates that the light signal is traveling faster toward earth than the velocity of light outside of gravitation, and the higher the clock rises, the more different this factor makes (though the effect decreases as the altitude increases, because the signal travels the additional distance at a velocity that is closer to what it is outside gravitation).

The spatiomaterialist explanation of gravitational time dilation in general relativity resembles its explanation of the global equivalence of inertial frames in special relativity, because in both cases it recognizes both real and apparent distortions.

In special relativity, the Lorentz distortions are real in inertial frames that are moving relative to the inherent motion. But to observers on such a moving inertial frame, the inertial frame at rest relative to the inherent motion appears to be suffering Lorentz distortions. (The appearance is caused, as we have seen, by the mis-synchronization of clocks on the moving inertial frame and how that combines with its real Lorentz distortions.)

In general relativity, the gravitational time dilation is real material objects that are at rest in a gravitational frame, because that is how accelerate reference frames are related to the inherent motion. But free falling clocks appear to be suffering a time dilation, because as the clock falls, the signals travel pathways from the clock to the stationary observer at various velocities that are either faster or slower than the velocity of light outside of gravitation, depending on where the is located when the signal is sent.

Propagation of the gravitational force through the inherent motion. The final famous prediction of Einstein’s general theory of relativity is precession of the perihelion of Mercury’s orbit around the sun As Mercury orbits the sun, the main axis of its elliptical orbit rotates slowly around the sun (in the same direction as Mercury itself). It is a very small rotation (about 43 seconds of an arc per century, setting aside the other perturbations that Newtonian physics can also explain. This phenomenon also has an explanation in terms of the acceleration of the inherent motion in space according to the spatiomaterialist explanation of gravitation.

The gravitational force is exerted by a center where matter has accumulated by way of the inherent motion, that is, at the outbound velocity of light in the inherent motion it affects. The force is like a pulse of attraction propagating outward from the gravitating body, accelerating the inherent motion toward itself wherever the pulse reaches. The force is steady, because one pulse follows another continuously. But the gravitational force exerted anywhere in the field imposed by these pulses is exerted locally, by the inherent motion though which matter of any kind coincides with space at that point.

Gravitational waves. It helps to have a concrete model of how the gravitational force is exerted, and so let us think of it as being exerted by a flow of outbound pulses through the inherent motion affecting the velocity of inherent motion itself that it passes through. That will enable us to see why there are gravitational waves, as predicted by Einstein’s general theory of relativity.

When a gravitating body is at rest in space, its force field is basically spherical. The center of matter exerts a gravitational force on the surrounding space by way of the inherent motion (at the velocity of outbound light in it), and the acceleration it imposes on the inherent motion itself falls off at the square of the distance. Though the acceleration felt at any point in the gravitational field depends on a force that started propagating from the central body earlier, the acceleration at that point does not change over time, because each pulse of gravitational force is followed by another pulse the next moment.

At any point in the field, the arrival of a gravitational pulse accelerates the inherent motion inward (increasing its inbound velocity as it pulls it inward), but the pulse then moves on to the next location in space and does the same thing to the inherent motion located there. At each moment at any point in space, the inherent motion itself that arrives from farther out (because of the last pulse) is subject to the next pulse of gravitation, and so the inherent motion itself is accelerated inward, giving it a higher inbound velocity as it moves closer to the gravitating body. The gravitational field is, therefore, like a flow of gravitational pulses outward in the inherent motion everywhere pulling the inherent motion itself toward the gravitating body. Thus, it is a steady gravitational force field, which would affect objects in the way Newton’s law predicts.

However, when a gravitating body is moving back and forth across space (for example, when a pair of dense astronomical bodies are in orbit around one another), the pulses of forces propagating outward from the gravitating body come from different locations from one moment to the next, and thus, there is a wavelike change in the acceleration of the inherent motion at a distance. Thus, any material objects located there will feel a gravitational force that is changing directions from moment to moment.

Since the gravitational wave can accelerate material objects, it carries potential energy across space, and thus, it is a form of matter (which we are calling “gravitational matter”). If the gravitational field were imposed by a gravitating body at rest in space, the gravitational matter constituting it would be counted as part of the total quantity of matter (mass and energy) accumulated at its center (because the gravitational force is accelerating the inherent motion toward itself). But the gravitational matter making up waves is not counted in the rest masses of the gravitating bodies generating it (because the gravitational force is not accelerating the inherent motion toward itself. Thus, gravitating bodies lose energy as they exert gravitational waves. (The astronomical bodies orbiting one another will slow down and eventually fall into one another.)

Precession of the perihelion of Mercury. This explanation of how the force of gravitation is exerted can explain the precession of the perihelion of Mercury (or any planet around a star). The inherent motion itself is accelerated by gravitation, and thus the force of gravitation that is felt by any bit of matter depends on the acceleration of inherent motion in the part of space where it is located at the time.

Since the sun is so much more massive than Mercury, we can treat it as if it were at rest in space. Thus, although it is sending out pulses of gravitation through the inherent motion that accelerate the inherent motion it reaches towards itself, the gravitational field is basically spherical, with the strength of the gravitational force falling off at the square of the distance. This is the gravitational field through which Mercury moves.

Mercury is moving roughly perpendicular to the sun’s radial force field, and if that were all that determined the gravitational force that Mercury feels, Mercury would follow the pathway predicted by Newton’s law of gravitation (because its being the result of a pulse of gravitation propagating from the sun does not make any difference to the force that Mercury feels).

Mercury is also, however, another gravitating body. It is sending out pulses of gravitational attraction radically in the inherent motion, accelerating the inherent motion itself towards itself. Insofar as its pulses are oriented in the same direction as those propagating radially from the sun, this will make no difference, because Mercury’s force will be acting on an inherent motion that is everywhere being accelerated toward the sun. However, Mercury will also be accelerating the inherent motion toward itself in directions perpendicular to the sun’s radial forces. And since the sun’s radial pulses of gravitational forces travel by way of the inherent motion, they follow the path of light rays, and since Mercury will be bending light rays that pass by it (just as the sun does; see Gravitational bending of light rays), Mercury will be bending the sun’s pulses of gravitational forces toward itself as they pass by.

The acceleration of the inherent motion toward Mercury changes the location of the sun’s gravitational forces, but not the direction in which those forces accelerate bits of matter. As radial forces, they are normally pointing at the sun. But consider what happens to the inherent motion ahead of Mercury as it moves perpendicular to those radial forces. As it accelerates the inherent motion toward itself, it shifts the location of the inherent motion itself (the bending of the light rays), and thus, the gravitational force that would be exerted in those parts of space are no longer directed at the sun, but are slightly offset. They point to a location relative to Mercury that the sun would otherwise have only later in its orbit. Thus, when Mercury coincides with the part of space in which the displaced inherent motion is located, the force of gravitation will not be in the direction of the sun, but slightly offset.

To be sure, there is a symmetry about the acceleration of the inherent motion in front of Mercury and behind in its direction of motion. After all, light rays are bent towards it as they pass either in front or behind Mercury. But there is an asymmetry caused by Mercury’s motion. It is moving toward the inherent motion accelerated towards it in front, and it is moving away from the inherent motion accelerated towards it from behind. Thus, Mercury is affected by the displaced gravitational forces ahead of it, because it is moving into the parts of space where they are located. And it is moving away from the parts of space where the displaced gravitational forces behind it are located.

The net effect of the asymmetry caused by Mercury’s motion into the inherent motion it has accelerated towards itself in front of it as it moves is that its change of location relative to space amounts to a greater change of location relative to the inherent motion. The gravitational pulses, like light rays, are pulled closer together in front of it, so that its velocity relative to space makes a greater change in the direction of the gravitational force it feels than would otherwise be the case.

Since through its orbit, the direction of the sun’s force is always displaced in the same direction (as if Mercury were farther along in its orbit than it actually is), the sun’s gravitational force is always making Mercury change direction faster than it would otherwise, and thus, the orbit as a whole precesses around the sun in the same direction as Mercury itself.

The alteration in the direction of the effective gravitational force of the sun on Mercury is the major factor accounting for the precession, but there are two additional factors making it different from Newtonian expectations, which are relatively minor.

First, the propagation of Mercury’s pulses of gravitational attraction outward in the inherent motion is not quite at the velocity of light, because its acceleration of the inherent motion has given it an inbound velocity. In front of Mercury as it is moving though the inherent motion perpendicular to the sun’s radial acceleration, Mercury’s outbound pulses of gravitation have a velocity that is less than the velocity of light outside of gravitation by the escape velocity at each point in its outbound propagation.

Second, since Mercury itself is a material object, its motion relative to the inherent motion subjects it to Lorentz distortions, including a relativistic mass increase. Thus, it takes a greater gravitational force to change its direction.

Phenomena in Strong Gravitational Fields. The acceleration of the inherent motion in space is what replaces the curvature of spacetime in the spatiomaterialist explanation of gravitation. But we have considered mainly phenomena involving weak gravitational fields and velocities much slower than light, and its assumption about the nature of the gravitational force also explains other new GTR phenomena involving strong gravitational fields and high velocity.

In strong gravitational fields, for example, the velocity of the inherent motion itself (the ether) relative to space can approach the velocity of light mediated by the inherent motion, and thus, spatiomaterialism implies that a time dilation will occur even in free falling clocks, if they have a sufficient high velocity relative to the inherent motion in space.

Consider, for example, a free falling clock that is shot upwards out of a gravitational field so that it rises and falls back. At the top of its trajectory, the cock will be momentarily at rest relative to space, and even though it is not being accelerated against the gravitational attraction, it may be suffering a Lorentz time dilation. In this case, it would be caused by its constant velocity relative to rest in the inherent motion, which is rushing inward because of its acceleration by the gravitating body.

This Lorentz time dilation is different from the gravitational time dilation discussed above, which is caused by being accelerated in a gravitational field. But both factors may be contributing to the red shift that observers outside the gravitational field observe in light signals sent outward by such objects.^xxvii But since the Lorentz time dilation is a second order effect (a function of v²/c²), while the gravitational time dilation is a first order effect (a function of v/c), it doesn’t become significant until the emitter’s velocity relative to the inherent motion approaches that of light itself in the inherent motion. In strong fields, however, the Lorentz time dilation may be a more significant cause of red shift than the gravitational time dilation.

Indeed, material objects in strong gravitational fields with very high velocities relative to the inherent motion will suffer all the Lorentz distortions: length contraction, mass increase, and flattening of electric force fields, as well as time dilation.

I have already mentioned that the acceleration of the inherent motion can give the inherent motion itself (the ether) a velocity relative to space that is as great as the velocity of light outside gravitation (that is, in the ether). This is what happens at the Schwartzschild radius of a black hole. No light can escape a black hole, because everywhere on that spherical surface surrounding the black hole the outbound velocity of light mediated by the inherent motion is canceled out by the inbound velocity of the inherent motion itself. Any such photons would be at rest in space, even though they are moving at the velocity of light in the inherent motion.

Nor could anything else escape the black hole, since doing so would require moving through the inherent motion faster than the velocity of light. That is why it is called an “event horizon”.

Free falling material objects cannot even be momentarily at rest at the Schwartzschild radius, for the Lorentz distortions caused by their velocity relative to the inherent motion at that point would require their lengths to be zero, their physical processes to have stopped, and their masses to be infinite.

Inside the event horizon, light traveling any direction in the inherent motion would have an increasing velocity relative to absolute space toward the center of the black hole. And any bits of matter being accelerated by that acceleration of the inherent motion would move and interact with one another as they do outside gravitational fields (except for tidal forces, which bring their radial pathways closer together), as implied by Einstein’s equivalence principle. But when the bits of matter reach the center of the black hole, they must come to a stop. Physics does not say what happens then. Material objects cannot withstand the forces on them at the center, and presumably, they would collapse spatially, making the gravitational forces infinite. Thus, the center of a black hole is aptly called a “singularity” in absolute space.

Since neither light nor gravitational pulses can propagate outbound from beyond the Schwartzschild radius, the only indication of the amount of matter that has fallen into the black hole is the size of the Schwartzschild radius.

Spatiomaterialism can also explain what is happening around rotating black holes. Rotating black holes are formed by matter spiraling in, and there is an asymmetry about the gravitational field they set up which draws bits of matter falling toward the back hole in the direction of its rotation.

The reason is that the force of gravitation exerted by matter falling into a black hole propagates outward at the velocity of light in the inherent motion, and since at the Schwartzschild radius, the inherent motion itself is moving inward at the velocity light would have in the inherent motion if it were outside gravitational influences, only the forces propagated outward just before passing across the radius have an effect on the inherent motion outside. And since the matter is spiraling past the Schwartzschild radius, it has a greater effect behind than in front of its direction of motion. Thus, other bits of matter in that region of space feel an attraction that is not directly into the black hole, but which pulls it around the black hole in the direction of the matter that preceded it.

Empirical equivalence of different models of the general theory of relativity (GTR). This explanation of the old and new gravitational phenomena has assumed that nothing exists but two, opposite kinds of substances enduring through time. But the capacity of spatiomaterialism to explain those phenomena does not necessarily mean that it is equivalent to a single model of GTR on the received geometrical interpretation (which explains gravitation as a curvature in four dimensional spacetime). Thus, it remains to be seen why there are infinitely many different, observationally equivalent models of GTR for any particular universe, or why “general relativity” (in one sense) seems to be true.

Since this explanation of gravitation is based on the spatiomaterialist explanation of the truth of STR, space is assumed to be a substance, and we are liberty to take as our reference frame the inertial frame at rest in space outside of gravitational influences where the one-way velocity of light is the same both ways in every direction. That inertial frame is at rest relative to the inherent motion in space, and the inherent motion itself is at rest relative to space (in other words, that inertial frame is at rest relative to the ether, which, in turn, is at rest relative to space). The times and places of events assigned by observers on such an “absolute reference frame” would be accurate, because his clocks would not by mis-synchronized

Consider a gravitational field imposed by a gravitating body of some kind. It will be accelerating the inherent motion (or ether) toward itself according to the inverse square law. Of all the reference frames that would be accelerated toward the gravitating body, the one with the most accurate times and places of events would be the one that is at rest relative to the inherent motion itself (or the ether) as it is being accelerated toward the center of gravitation. To be sure, such a reference frame could not have clocks synchronized everywhere, since any large rigid object would be torn apart by the difference in forces acting at different points. But if observers on that reference frame could use GTR (or this ontological explanation of the gravitational force) together with light signals received from other objects to figure out where and when events occur throughout the gravitational field. That is, they would determine the “simultaneity hypersurface in curved spacetime” from their reference frame, and since that would correspond to what is really happening to substances at that moment as they endure through time, their reference frame can be called the “absolute model” for GTR, by analogy to the inertial frame of the absolute observer in STR.

The reason that there are many different empirically equivalent models for any such situation is that there are other reference frames which differ from the absolute reference frame only by have a velocity relative to the inherent motion itself that is being accelerated inward. They are empirically equivalent locally, because they suffer Lorentz distortions that mask their velocity relative to the inherent motion. And observers on each of them could use GTR together with information received from events elsewhere to determine their “simultaneity hypersurface in curved spacetime.” They would all disagree with one another, like different inertial observers outside gravitation, and there would be no way for them to tell by experiment which reference frame was the absolute reference frame.

That is, each possible model of GTR is adapted to the trajectory of one of the many different particles that could be in inertial motion at any point, and their different velocities relative to the inherent motion would give them, incipiently, at least, different standards of simultaneity (that is, each determines a different “simultaneity hypersurface in curved spacetime”). Any pair of such reference frames may have a high velocity relative to one another as they pass one another at that point, but each would observe Lorentz distortions occurring in the other reference frame, and thus, the symmetry between them would make it impossible to for them to tell which reference frame is at rest relative to the inherent motion in space that is being accelerated toward the center of gravitation.

This explains why models based on different reference frames are empirically equivalent as far as different velocities relative to the inherent motion is concerned. But neither can anything known about the effects of the gravitational force be used to distinguish one reference frame from another. Even of observers on the reference frames accepted the spatiomaterialist explanation of the nature of gravitation as an acceleration of the inherent motion by the gravitating body, that would not single out the absolute reference frame from the rest. (Or if the observers think in terms of GTR and see gravitation as a “curvature of spacetime” caused by gravitating bodies, that does not compromise their empirical equivalence.)

The absolute model cannot be assumed to be the one based on the local inertial frame that would result from accelerating all the way in from being at rest outside the gravitational field, for the gravitating body may itself have a non-zero velocity relative to the inherent motion in unstressed space.

It might seem possible to measure an object’s velocity relative to the inherent motion by using the gravitational time dilation of objects at rest in the gravitational field to determine their velocity relative to the inherent motion. But that will detect only the increase in the velocity of the inherent motion as a result of being accelerated toward the center of gravity to that point from outside the gravitational field, and that will not determine whether the gravitational field itself is in motion relative to the inherent motion outside gravitation.

Or it would be possible, in principle, to use the difference between light signals and gravitational signals to detect absolute rest, if gravitational forces propagated at a different velocity from light. But since the force that accelerates the inherent motion in space propagates through the inherent motion at the same velocity as light, its effects are explained equivalently by each model in the same way as light.

The equivalence of inertial frames that Einstein meant by “general relativity” can be explained, therefore, by special relativity. That is, the empirical equivalence of different models of GTR can be explained as the empirical equivalence of local inertial reference frames that have different constant velocities relative to the accelerating inherent motion. There is no way to determine which of their standards of simultaneity is correct, for there is no way to detect rest relative to the inherent motion. And none of the interactions between space and matter that constitute the force of gravity betrays which reference frame is the absolute model.

Though gravitation just happens to work in such a way that absolute rest relative to the inherent motion cannot be detected, the fact that it works that way could explain why Einstein was able to deduce his law describing the unexpected effects of gravitation from the assumption that all different local inertial frames are equivalent, or “general” relativity.

The spatiomaterialist explanation of gravitation has been presented as an ontological explanation of the truth of Einstein’s general theory of relativity. Since what is crucial to such an ontological explanation is identifying the aspects of the substances constituting the world to which the theory corresponds, I have presented only a qualitative argument. I have shown how GTR could be true, even if nothing existed but substances enduring through time, and every possible photon has a determinate location and velocity in absolute space at each moment as it is present (because the inherent motion itself is accelerated and, thus, moving through space). Though I have said enough about the quantitative factors to make clear how it would predict the same quantitatively precise measurements, I have not shown mathematically that it is equivalent.

That is an exercise I leave up to mathematically inclined readers. It affords an opportunity to refute ontological philosophy, for if it can be shown that there is no way that the acceleration of the inherent motion in space can yield the quantitatively correct predictions for all the relevant phenomena, we will have defaulted on the mortgage we took out to use spatiomaterialism as the foundation for the necessary truths of ontological philosophy, and the project will have failed. I see not reason to belief that that can be done. But like any basically empirical argument, ontological philosophy is vulnerable to empirical falsification, and thus, it must stand up to such challenges.

We can also see, at this point, why philosophers of science have not recognized the superiority of substantivalism about space to substantivalism about their spacetime. Instead of inferring to the best ontological explanation of everything in nature, they have let their ontology be determined by realism about the highly mathematical theories that physics has accepted as the best efficient-cause explanation of what happens in nature. Philosophers of spacetime simply assume that every theory about space and time, including Newton’s (and, thus, spatiomaterialism), can be represented as just another variety of spacetime theory using differential geometry.^xxviii

What spatiomaterialism offers, however, is a different kind of model of GTR. It explains ontologically why Einstein’s field equations are true by showing how gravitational phenomena can be constituted by space and matter as substances that exist only at the present moment. To treat spatiomaterialism as the belief in a “simultaneity hypersurface in a four dimensional spacetime manifold” is to abstract from such basic ontological issues as the nature of existence and time and to judge these theories only as efficient-cause explanations, that is, by their predictions of precise measurements.^xxix

And when we judge all these theories by their capacity, as ontological theories, to account for everything observable about the world, including real change, the empirical superiority of an ontology of enduring substances is obvious, as we have seen, because of its explanation of the nature of time and existence.

Spacetime, whether curved or flat, cannot explain how the present is different from the past and the future, because spacetime cannot be a substance enduring through time as long as time is part of its structure. Thus, neither can it explain real change, because nothing ever comes into existence as time passes nor goes out of existence. (And as we have seen, attempts to avoid falsification by our experience of real change by adding subjective substances to the ontology makes it more complex encounters problems relating eternal and enduring substances as a single world, and is in any case ad hoc.)

Spatiomaterialism differs ontologically from Einstein’s GTR in just the way required to explain real change. Though it explains gravitation in much the way Einstein proposed — as an effect of the container of material objects on the path they follow — it replaces curved spacetime with an acceleration of the inherent motion itself. Since that is nothing but an aspect of space and matter as substances enduring through time, given how they are related, it explain why the present is different from the past and the future and “real change” is ontologically possible.

Quantum Mechanics. Quantum mechanics is the other great revolution in contemporary physics. Classical physicists would have admitted that the existence of ordinary material objects is a phenomenon that still needed an explanation, and as it turns out, that explanation came with the quantum revolution. Not only does quantum mechanics describe the electromagnetic forces responsible for the structure of all ordinary objects down to molecules and atoms, but the mathematics that is now used (in a gauge field theory called "quantum electrodynamics") is the model for explaining even the short-range forces (the strong and the weak forces) which responsible for the nucleus and deeper structure of material objects. The issues involved in explaining the truth of quantum mechanics is taken up in this chapter, and the two short-range forces, along with the basic particles of physics, will be explained in the next. The challenge posed by quantum mechanics and what is at stake in explaining its truth ontologically are discussed in the first section, and the rest of the chapter suggests one way, at least, in which its truth can be explained by spatiomaterialism. But at the outset, it should be noticed that spatiomaterialism already provides an explanation of how those forces are related to gravitation.

One of the greatest current mysteries of contemporary physics concerns the relationship between the force of gravity and the other three basic forces of nature. The problem is that the electromagnetic force and the two short range forces are explained by the exchange of a distinctive kind of particle (the gauge boson, such as the photon, in the case of electromagnetism), and the general theory of relativity does not lend itself to representation as a gauge field theory. The most promising way to represent gravitation as the exchange of such gauge bosons (called “gravitons” in the case of gravitation) would incorporate all four basic forces and the objects on which they act. But this so-called “superstring theory” requires the postulation of ten or more dimensions to space, and it seems to be completely immune from possible empirical falsification. There is nothing to recommend it but the mathematical uniformity in the representation of all four basic forces of nature, and as we have seen exclusive reliance on mathematics does not necessarily lead to the best explanation. .

Spatiomaterialism offers a solution to this problem, if quantum electrodynamics and the two short range forces are explained as interactions mediated by the inherent motion in space (that is, space as the "ether"), as I have been assuming, because this ontological explanation of relativity theory would also explain how the other three forces are related to gravitation. Gravitation is not a gauge theory, because the gravitational force acts on the inherent motion itself, that is, on space, not on bits of matter directly. It is by changing the “medium” (or "ether" as a condition of space) in which gauge particles are exchanged that gravitation accelerates bits of matter. It is not necessary for centers of matter accumulation to exchange gravitons with individual bits of matter in the region to accelerate them.

What makes the problem of relating gravitation and the other forces seem so intractable is the assumption that it requires the discovery of a law of nature from which Einstein’s general theory of relativity as well as the gauge forces can all be derived. The discovery of a basic law covering all the basic kinds of interactions among bits of matter has long been the so-called “holy grail” of physics, and that is the assumption that has led to attempts to formulate a gauge theory of gravitation. It seemed that such a basic law of physics could be discovered only if gravitation could be represented mathematically in the same way as the other forces. That is the goal of superstring theory.

Spatiomaterialism would solve this problem ontologically, rather than mathematically. The solution does not require the discovery of a new law of nature from which all the other laws follow, but only an ontological explanation of the truth of the laws that have already been discovered, for that reveals how gravitation is related to the other three forces. We have seen how the truth of general relativity can be explained ontologically, and thus, if spatiomaterialism can explain the truth of the other basic forces of nature in terms of the inherent motion in space, there is an ontological explanation of the relationship between the two kinds of forces. It is the recognition of the inherent motion (or "ether") as an aspect of the essential nature of space that makes this possible. By contrast, the gauge field theories are, in effect, the attempt to represent space as nothing but the forces by which particles interact.

If the explanation is ontological, what makes the problem of reconciling gravitation and the other forces of nature seem so intractable is, once again, the empirical method of physics, that is, the method of inferring to the best efficient-cause explanations of what happens in nature (and letting ontology be determined by realism about its theories). It was inevitable that physics would eventually find itself in this predicament, because physics first became a science by taking advantage of the power of mathematics to describe regularities about change. By insisting on mathematical theories that make surprising, quantitatively precise predictions of measurements, physics was able to discover the most abstruse facts about how bits of matter move and interact with one another. That is what enabled modern physics to go beyond the ancient atomists in understanding the nature of the elementary objects. But despite the acuity of its vision of regularities, physics was blind to a more basic aspect of the world. It failed to recognize that the job of science is not just to describe the regularities by which it is possible to predict and control what happens in the world, but also to describe the basic substances that constitute those regularities (not just the particles to which they refer, but all the substances that cause them ontologically). It comes from a failure to recognize that ontology can be explanatory in its own right and that ontological-cause explanations are a deeper kind of explanation from efficient-cause explanations, that is, from the same oversight that led to the Einsteinian revolution in the first place.

The challenge of quantum mechanics. Like the Einsteinian revolution, quantum mechanics might also be thought to pose a challenge for ontological philosophy. The quantum revolution has also overthrown assumptions of classical physics about the nature of the world, and if spatiomaterialism were unable to explain ontologically why the laws of quantum mechanics are true, physics might provides a reason for denying that ontological philosophy can use spatiomaterialism as the foundation for doing philosophy in a new way, despite its explanation of relativity theory.

The quantum revolution does not, however, challenge spatiomaterialism in the same, direct way as relativity. Quantum mechanics has not led to any consensus among physicists about the nature of what exists that is incompatible with spatiomaterialism.

The Einsteinian revolution is generally assumed to be the discovery of something that directly contradicts spatiomaterialism. In contemporary physics, absolute space and absolute time have explicitly been replaced by spacetime. But absolute space and time are entailed by the assumption that space and matter are substances enduring though time. Thus, in order to defend the use of spatiomaterialism as the foundation for this philosophical argument, I had to show that what Einstein’s two theories imply about the world could be explained on the assumption that space and time are absolute.

The quantum revolution has not led to ontological beliefs that directly contradict spatiomaterialism. This is partly because there is no consensus among physicists concerning what quantum mechanics implies about the nature of what exists. There is no dispute about the laws themselves; they are among the most precise and highly confirmed in physics. But scientific realism about quantum mechanics does lead to general agreement in ontological beliefs. There are so many disputes about the kinds of entities that are required for the laws of quantum mechanics to be true and they are so intractable that most physicists beat a hasty retreat to their empirical method and take cover by simply pointing out that its laws are the best way of predicting and controlling the relevant phenomena.

To be sure, there are ontological interpretations of quantum mechanics that are incompatible with spatiomaterialism. For example, some philosophers take measurements in quantum mechanics (involving the so-called “collapse of the wavefunction”) to be an event that depends on a conscious mind coming to know something about the world, and that is to assume that mind is a fundamentally different kind of substance from matter, which is is a form of immaterialism that spatiomaterialism rejects. Another interpretation, called the “many worlds view,” interprets measurement in quantum mechanics (again, the collapse of the wavefunction) to be the occasion of the universe splitting into different universes in which each of the different possible outcomes of each measurement are realized, which is not compatible with the world being constituted by substances. However, the possibility of such views is hardly an objection to spatiomaterialism, as long as it is possible to give an ontological interpretation of quantum mechanics that is compatible with spatiomaterialism. Thus, the issue is whether all possible ontological interpretations are incompatible with spatiomaterialism. It was the universal assumption that Einsteinian relativity is incompatible with space being absolute that forced us to take out a mortgage on spatiomaterialism, promising to show how it can explain Einstein’s two relativity theories ontologically as a condition of using it as the foundation for ontological philosophy.

To be sure quantum mechanics did overthrow the classical view of the nature of matter. But that does not necessarily challenge spatiomaterialism, because spatiomaterialism is no more committed to the classical view of matter than it is to the classical view of space. The relevant issue is whether it is possible to explain the truth of the laws of quantum mechanics by making assumptions about the nature of matter (and space) that are consistent with spatiomaterialism.

Materialism in general is not generally thought to be what is refuted by quantum mechanics. On the contrary, many physicists who are quite confident of the truth of quantum mechanics would consider themselves “materialists” in the broad sense in which that term is used to classify ontological positions.

The question is what more specific essential nature material substances must have in order for quantum mechanics to be true. It is clear that the regularities described by quantum mechanics cannot be explained ontologically by the kinds of material objects and light waves recognized by classical physics. But spatiomaterialism does not have to defend that view of matter. Indeed, as we have seen, its explanation of why the laws of classical physics are true (insofar as they are true) depends on assumptions about the nature of matter that are not part of classical physics. I assumed, for example, that kinetic energy is a form of matter that exists in addition to the rest masses of material objects, and that potential energy is as form of matter (force field matter) that is already counted in the rest masses of the objects exerting the forces. And in explaining the truth of the special and general theories of relativity, I have made further non-classical assumptions about the nature of the world — for example, that there is an inherent motion in space and that it can itself be accelerated and have a velocity relative to space.

This is not to say that there is nothing puzzling about quantum mechanics. There are two, basically different ways that it might seem to challenge spatiomaterialism directly. One has to do with a long recognized indeterminacy about its predictions, and the other is a more recently discovered problem about action at a distance (deriving from Bell’s theorem).

Indeterminism. The laws of quantum mechanics do not describe nature as having deterministic causal connections among states of affairs. Those laws often imply only that, given everything that can be known about a given situation, any of a number of different states might follow (or precede) it. The most that can be done is to assign a probability to each of those possible outcomes.

This is fundamentally different from classical physics, for its laws were deterministic. As Laplace pointed out in the eighteenth century, if the basic laws of classical physics are true, then given a complete description of the current situation (even the state of whole universe), it would be possible, in principle, to predict any future state (or even any earlier state). The state of the universe (or any closed system) at any one moment determines its state at every other moment.

Even in very limited situations, the laws of quantum mechanics do not usually support such deterministic predictions. Given a complete quantum mechanical description of a situation, there is a range of possible events that can happen (such as what measurements will reveal), and there is no way of saying which one it will be (though it is possible to assign probabilities to the alternatives). Thus, physics no longer assumes that complete knowledge of the current state of the universe would make it possible to predict what would happen.

This lack of precise predictability comes from the nature of the Schrödinger equation. Its solution for a given situation is a wavefunction which is a complete quantum description of that situation (in pre-relativistic quantum mechanics). It describes precisely how the quantum system evolves as time passes, just like a wavefunction in classical physics. But the Schrödinger wavefunction is not classical, because it involves complex numbers (containing i, or the square root of minus one), and the space in which the wave is contained is a “configuration space,” which is a space with three times as many dimensions as there are particles involved in the situation being described. There is no obvious way to relate such a wavefunction to the natural world. The standard interpretation of the Schrödinger wavefunction takes the square of the amplitude of the wavefunction (for a single particle) in any small region of space to represent the probability of finding the particle at that location. (And there are mathematical operators on the wavefunction that predict measurements, but they cannot predict precisely both of any pair of complementary variables, such as the position and momentum of an electron.)

This limitation on precise predictions of what will happen is summed up in the famous Heisenberg uncertainty principle. This principle can be taken as reflecting either an indeterminism about the world itself or as merely an incompleteness in what can be known about it. Though in either case, it is a limitation in principle, rather than practice, a mere incompleteness in our possible knowledge about the world would not contradict spatiomaterialism. Substances enduring through time could still constitute causal connections, even if some aspects of those substances cannot be measured precisely. Furthermore, even if this uncertainty did derive from an indeterminism in the nature of what happens independently of how it is known, it would not necessarily be incompatible with spatiomaterialism.

Indeterminism would contradict spatiomaterialism if it was incompatible with the world being constituted by substances enduring through time. Such an extreme indeterminism would be true, if the predictions supported by quantum mechanics corresponded to all the causal connections that there are between the properties that hold at one moment and the those that hold at the next. To hold that what is unpredictable is not determined at all is incompatible with any explanation of the world as constituted by substances enduring though time, because it is to assume, in effect, that something comes from nothing. What is unpredictable about the next moment would not depend in any way on what existed at the previous moment, and since it would have to come from nothing at all, extreme indeterminism would contradict the assumption that the world (and all its aspects) are constituted by substances enduring through time. Though this does not bother epistemologically minded naturalists, it would be a death blow to ontological naturalism.

A less extreme form of indeterminism is compatible with an ontological explanation of the natural world, though it is still hard to swallow. Indeterminism might hold that what is unpredictable according to the Heisenberg principle is a result of an inherent randomness in the essential nature of the matter making up the world. This would be more than a mere limitation in what we can know about the determining conditions, because it also would be a limitation in what even God could know. There would be no need to believe that something comes from nothing, because what exists at the next moment would be constituted by the same substances that constituted the world at the previous moment. But here would be no aspect of the nature of those substances at the previous moment that determines which of certain aspects it will have the next moment, because the randomness would be an aspect of the essential nature of the kind of matter that constitutes the world. The randomness would be a temporally complex aspect of the essential nature of matter, for it would make the connections between properties that substances have at different moments random. It would be as if matter itself contained a randomness generator that even God could not use to predict what will happen (though God would presumably still know the future, since he is the creator of all the moments of the world). Though such a view about the nature of matter would be consistent with spatiomaterialism, it would not be as good as one that could give a genuine ontological explanation of what happens, that is, which explains what happens as aspects of the world that follow from the natures of the basic substances as they endure through time constituting the world.

However, The Heisenberg uncertainty principle does not preclude a genuine ontological explanation of what is unpredictable. To hold that quantum uncertainty is merely a limitation in what beings like us, who are parts of the world, can know about the world is to hold that what happens does have a cause, but that we cannot know precisely what it is. This is to interpret the probabilistic nature of quantum mechanics as an incompleteness in our knowledge, rather than as indeterminism about the world. It assumes that there is some “hidden variable” that is actually determining what happens, though for some reason, that variable cannot be measured. That is not incompatible with spatiomaterialism, because the reason for the Heisenberg uncertainty could be that the interactions required for scientists, as material objects in space, to know about particular conditions in the world so disturb the world that they alter the conditions being known. That limitation must, of course, be caused by the basic nature of those interactions. But that does not mean that it is impossible to identify the nature of the hidden variable. It means only that its quantity cannot be measured accurately in any particular case. And having inferred to spatiomaterialism as the best ontological explanation of the world, we may be in a better position to identify the nature of the hidden variable that makes quantum mechanics incomplete.

Bell’s theorem. Though the traditional puzzles about the apparent indeterminism of quantum mechanics do not necessarily contradict spatiomaterialism, there is a more recently discovered implication of quantum mechanics that may. It occurs when particles separate from one another in a way that gives them opposite orientations of a quantum property called “spin.” John Bell showed that when such particles move away from one another in opposite directions, it is possible for a measurement made of one particle at one location to predict (probabilistically) measurements that are made at another location more accurately than would be possible if the particles had the properties being measured from the time they parted from one another. These “Bell correlations,” as I will call them, seem to imply that spin is not a property that the particles carry with them locally, but one that depends on the entire system, including both particles rushing away from each other.

This suggests according to a standard interpretation of quantum mechanics that the measurement of one particle affects the other particle (that is, that such effects are part of what is called the “collapse of the wavefunction”). But if measurement does have such effects, then it would have to be able to have its effect faster than the velocity of light, and that seems to contradict the principle of local action. I have assumed that what happens in one part of space cannot affect what happens elsewhere any faster than the velocity of light, for that velocity is determined by the inherent motion in space.

There is, however, something suspicious about the Bell correlations. There is no other evidence of faster than light effects in nature. Furthermore, it has been shown that, whatever is going on, Bell correlations are the kind of signal that can be used to communicate information. They are peculiarly lacking in further consequences.

It is not clear, therefore, that this departure of quantum mechanics from Bell’s theorem (about what local action entails) depends on one measurement affecting the other measurement causally. However, worries about the possibility of action at a distance will probably not be put to rest completely unless it is explained how it is possible for quantum mechanics to make such predictions. Thus, there something that needs explaining.

There is, therefore, reason to explore the ontological explanations of quantum mechanics that are opened up by spatiomaterialism. We would be justified in using spatiomaterialism as the foundation for ontological philosophy without explaining why quantum mechanics is true. But if its explanation of the aspects of the natural world to which the equations of quantum mechanics correspond did help clear up the quantum puzzles, there would be an additional reason for believing that spatiomaterialism is true.

In the first section, I will review the traditional puzzles about the nature of matter posed by quantum mechanics.

In the second section, I will introduce several new assumptions about the nature of space and matter and show how they would enable spatiomaterialism to explain the forms of matter that were assumed in explaining the truth of the laws of classical physics.

The third section will return to the quantum puzzles and show how the proposed ontological assumptions would explain those puzzling phenomena ontologically, including a response to the challenge that seems to be posed for spatiomaterialism by the more recent discovery of Bell correlations.

This more detailed ontological theory about the nature of matter is offered in a speculative vein. It differs from the ontological explanation of relativity theory, because no such explanation must be given in order to use spatiomaterialism for philosophical purposes. And it differs from the arguments to come about global regularities, because they attempt to prove that certain proposition are ontologically necessary truths. The reason that this ontological explanation of quantum mechanics is not ontologically necessary is that there may be other ontological explanations of quantum mechanics that are also consistent with spatiomaterialism (and what is says about relativity theory). Thus, the most I would claim to show is that some such ontological explanation is true. It may not be this one, but it will be clear, I believe, that there is some way of explaining the truth of quantum mechanics on a spatiomaterialist foundation. And since speculation is valuable as a way of exploring the possibilities, this particular version of spatiomaterialism may contribute to the discovery of the more complete truth about the natural world.

This explanation of quantum mechanics is, like its explanation of relativity theory, ontological, rather than mathematical. I will be trying to show how the new phenomena predicted by quantum mechanics can be constituted by space and matter as substances enduring through time, not that there is a better efficient-cause explanation of what happens. It does not claim to make any new predictions of what happens in the world.

Though I will give reasons for believing that this ontological explanation is quantitatively accurate (or can be made so), I will not try to show in detail how the formidable mathematical formalism of quantum mechanics relates to the world. Such a mathematical argument would take us too far afield. And in any case, it has already been done by David Bohm. (See Bohm, 1993, with Basil J. Hiley.) That is, the ontology I will be proposing is a variation on the ontology that Bohm shows to correspond to the Schrödinger equation, the basic equation of quantum mechanics, and thus, if Bohm’s ontology is a possible explanation of the truth of quantum mechanics, then so is this one.

There are many good accounts of quantum mechanics, but a reasonably accessible one that I have recently found useful is Jim Baggott's The Meaning of Quantum Theory.

In most cases, it will be clear that the kinds of assumptions I will be making can be refined to made them quantitatively adequate. This is much the same attitude I took in explaining ontologically the truth of general relativity, except that in the case of quantum mechanics, I also leave open the choice between various more detailed, alternative ontological assumptions. Thus, in order to show that it is not possible to explain the truth of quantum mechanics ontologically in this way, it would be necessary to show that none of these possibilities can be quantitatively adequate for the whole range of quantum phenomena.

Nor do I claim that the ontological theory being presented here is the best spatiomaterialist explanation of quantum mechanics, only that it (or one much like it) is possible in the sense of accounting for all the relevant phenomena. There may be ways in which space and matter existing together as a world can explain the truth of quantum mechanics more simply. That would be interesting and preferable. But it is not the crucial point, because the possibility of such an ontological explanation is all that is relevant to rest of ontological philosophy. And seeing how it is possible is the first step toward discovering the best such theory.

Quantum puzzles. Of the various quantum puzzles, the most basic is probably wave-particle duality. The atom itself is, however, the most important, puzzling consequence for the ordinary world. The traditional way of summing up what is most puzzling about quantum mechanics is the Heisenberg uncertainty principle, but recently the most discussed is called “Bell’s inequality.” All of them are described here as a way of introducing quantum mechanics as it is currently understood, and after explaining the spatiomaterialist theory of quantum matter, I will show how they can be solved.

Wave-particle duality. According to Bohr, the basic puzzle of quantum mechanics is the dual nature of the basic entities it describes. They all appear to be like both particles and like waves. What classical physics took to be waves turn out to have a particle-like nature as well, and what classical physics took to be particles turn out to have a wave-like nature as well. Bohr thought that both appearances of the underlying reality are due in part to our measuring apparatus and the classical expectations on which they are constructed. But wave-like and particle-like natures are apparently incompatible, and since both of these classical conceptions of reality are needed to make all of the possible predictions, he called the basic puzzle of quantum mechanics “complementarity.” Bohr was the originator of the so-called "Copenhagen interpretation" of quantum mechanics, which holds that the reality behind these complementary phenomena is incomprehensible to us.

The particle-like nature of electromagnetic waves. Light has long since been thought to have wave-like nature in classical physics. Early in the nineteenth century, Thomas Young showed that light passing through two narrow, closely spaced holes (or slits) produces a pattern of light and dark lines on the screen that finally intercepts them, and he explained it by the wavelike nature of light. The places on the screen where the waves emerging from each slit interfere constructively are bright, while the places where they interfere destructively are dark. When one slit is blocked, the interference pattern disappears.

Diffraction phenomena also indicate the wave like nature of light. Light rays passing through a hole that approximates its wavelength will be spread out as it leaves the hole, with the range of the spread varying inversely with the size of the hole. When the hole is large, the light hitting the distant screen is like a point, but when the hole is small, the diffraction is great.

Moreover, as we have seen, light had been explained by Maxwell as the wavelike coupling of the electric and magnetic forces described by his equations. Indeed, it enabled him to predict the velocity of light.

The particle-like nature of light was the first of the discoveries that eventually culminated in quantum mechanics. Instead of propagating like a wave in an elastic medium, as the classical model assumed, it became clear that light is actually made up of distinct particles, which are now called “photons”. This particle-like nature means that the energy and momentum carried by light do not combine continuously, as they do in ordinary waves, but come in separate units, called “quanta”. The size of the quantum of light is now represented by Planck’s constant, h, which is part of every new equation used in quantum mechanics. It appears in the new equations for the energy and momentum of light. The energy, E, is given by E = hf (where E is energy, f is frequency), and the momentum, p, is given by p = h/ (where p is momentum, and is the wavelength).

Max Planck first discovered the particle-like nature of light in 1900, though he did not fully understand what he was on to. He discovered the constant named after him by tinkering with a classical equation for calculating the amount of energy given off at each frequency in so-called blackbody radiation, that is, a hot body in which no frequency of light should be favored. (It is best approximated by a box with mirrored interior walls in which light of all possible wavelengths for a box with certain temperature are being reflected back and forth.) The classical equation assumed that the frequencies of light being given off varied continuously from the lowest to the highest, with the peak intensity depending on the temperature. That assumption worked well enough for the low frequencies, but at high frequencies, it led to the conclusion that the total energy given off should be infinite. This absurdity was called the “ultraviolet catastrophe.” Planck discovered a formula that avoided the catastrophe and predicted the total quantity of energy given off at each frequency by introducing a constant, h, into the formula which restricted the frequencies of light. That is the source of the equation for the energy of light: E = hf. (Though its meaning is still obscure, it can, perhaps, be seen as requiring the photons to differ from one another by that constant amount.)

Albert Einstein made it clearer that what Planck had discovered was the particle-like nature of light by using Planck’s constant is his own explanation of the photoelectric effect (in 1905, the same year that he published his special theory of relativity). It had been known that light being intercepted by material objects could release electrons from the material objects, but it was found that the release of electrons did not depend on the total energy of the light waves (the intensity of the light), as one would expect on the wave hypothesis. It depends on the frequency of the light. Below a certain frequency, no electrons are released, regardless how intense the light may be at that frequency. Whereas light with a higher frequency would release electrons even though the intensity was much less. Einstein showed that the release of the electrons depended on the absorption of single photons, each of whose energy depended on Planck’s constant: E = hf.

Much later (in 1923), Arthur Compton showed that photons also have a momentum like particles. He shot high energy photons (x rays) at electrons and used arguments based on the conservation of momentum and energy to predict correctly the amount by which their energies would be changed by such scattering.

The particle-like nature of the light does not change its wave-like properties. Indeed, it turns out that interference effects still occur when light is sent through the two-slit apparatus one photon at a time. Over time, they still accumulate in fringes on the distant wall.

The wave-like nature of particles with rest mass. Material objects are understood in classical physics as having definite locations in space at each moment and to follow definite trajectories as they move from one place to another. But the behavior of objects with rest mass on the smallest scale is peculiar in the opposite way from photons, according to quantum theory. Just as light waves have a particle-like nature, so material objects have a wave-like nature.

The wave-like nature of particles with rest mass was predicted in 1923 by de Broglie. What Einstein’s special theory of relativity implies about the relativistic increase in mass leads to the conclusion that the energy of a photon is equal to the product of its momentum and the velocity of light, or E = pc. Since the velocity of light is equal to the product of the frequency and wavelength, or c = fit follows that the momentum of a photon is p = h/De Broglie went on to suggest that the same relationship holds of particles with kinetic energy. He argued that particles, such as electrons, protons and material objects with mass generally would also have a wave length that varied inversely with their momentum in the same way.

Interference and diffraction phenomena were the kind of empirical evidence that was taken as showing that light has a wave-like nature, and soon after de Broglie’s prediction, it was shown that the electrons forced to pass through very small holes do exhibit diffraction, that is, the smaller the hole, the more they spread out. Eventually, even interference phenomena were demonstrated with electrons. When electrons moving at a certain velocity are projected through narrow, closely spaced, parallel slits at a screen (where the distance between the slits approximates their de Broglie wave length), they also form an interference pattern on the far wall, as if they were waves. Even when the electrons were sent one at a time, they tended to land on the distant screen only along certain fringes, leaving lines between them without any hits. Thus, each particle is like a wave. The same has been show to hold for neutrons, though in the case of ordinary sized objects, the wavelengths are so small that interference effects are undetectable.

The structure of the hydrogen atom. The laws of quantum mechanics were discovered mainly by attempting to explain the structure of the hydrogen atom. It had been established by Ernest Rutherford that the atom is composed of a massive, positively charged nucleus surrounded by far less massive electrons, and Niels Bohr hoped to explain the chemical properties of atoms by the nature of the interactions between the electrons and the nucleus. It was clear that atoms could not be explained in classical terms on the model of the solar system, since according to Maxwell’s equations, the orbital motion of an electron would generate (as the acceleration of a negatively charged particle) an electromagnetic wave which would drain its energy until the electron was located at rest with the nucleus. In fact, atoms with electrons located around it are quite stable, and when such atoms are excited (by supplying energy to them), they give off electromagnetic radiation at a certain set of distinctive frequencies.

Bohr explained the frequencies of the spectrum of hydrogen atoms (in 1913) by assuming that electrons can have only certain orbits, each characterized by an energy level that corresponds to the total energy of an electron with kinetic energy in a force field with potential energy imposed by the nucleus. (The total quantity of energy is negative, because the kinetic energy of the particle is not great enough to replace all the negative potential energy that would be required to free it, and according to our assumption about the nature of potential energy, the negative sign for potential energy indicates that the nucleus and electron have less rest mass.) The energies of the possible orbits were determined as a function of Planck’s constant, and a number was assigned to each possible orbit, starting with the lowest energy orbit and counting upwards (n = 1, 2, 3, . . ). Bohr showed that the spectral lines of the hydrogen atom could be explained by the differences in the energies of these permitted electron orbits.

The basic puzzle of quantum mechanics is the structure of the atom itself, that is, what is going on that only certain energy levels are possible for electrons bound to a nucleus by electromagnetic forces.

Given the structure of the atom, however, there is another problem, for it does not seem possible that electrons could be jumping from one orbital to another. When a photon is absorbed or emitted by an atom, an electron changes from one permitted orbital to another (so that the atom changes from one energy state to another). But the photon has a particle-like nature, and the particle seems to change its position and motion in an instantaneous, step-like change, that is, without accelerating nor even moving continuously from one state to the next. It hard to see how the electron’s change of orbital can be explained as the motion of a material object, since a material object can change location only by moving across space continuously as time passes time.

Another puzzle has to do with the timing of the emission of photons. When an atom or molecule is in an energy state that can decay into a lower energy state, it is not possible, even in principle, to say exactly when it will decay. The timing can be assigned a probability, but the theory has nothing to explain why it happens at one moment rather than another within that range.

Electron jumps also seem to be involved in the phenomenon of tunneling. “Tunneling” refers to situations in which electrons seem to jump across barriers imposed by force fields. On classical principles, crossing such a force field would require more energy than the electron has. Nevertheless, some electrons do jump across. Only a few electrons do so, and there is no way to predict which ones will jump. But it is so regular that this phenomenon is used as a kind of microscope for mapping the surfaces of material objects.

Erwin Schrödinger thought that it would be possible to avoid these puzzles about electron jumps and explain everything deterministically by following up on de Broglie’s suggestion and explaining the behavior of the electron in an atom as a wave. Using the model of the classical equation for waves and taking the electron wave to be in a potential field, Schrödinger presented an equation in 1925 that explained the energy levels of the permitted orbitals of electrons in the force field imposed by the nucleus of the hydrogen atom. The time-independent Schrödinger equation (with the temporal changes factored out so that it represents only the spatial structure of the wave) portrays the electron bound to the nucleus of the hydrogen atom as a standing wave, like a plucked string on a guitar. This made it possible for Schrödinger to explain the numbers that Bohr had assigned to the permitted orbitals of electrons as the energy states in which the electron could be such a stable, standing wave. The lowest energy level corresponds to the string with no nodes (that is, half the wave length for its energy), the next one to a string with one node, and so on. The problem of quantum jumps seemed to be solved, because the transitions between such energy states of atoms were explained as smooth and continuous transitions of waves.

Schrödinger believed that his wavefunction showed that electrons were not particles at all, but could be explained purely as waves in an electromagnetic field. This did not explain why electrons appear to be particles, for example, how they leave vapor trails in a Wilson cloud chamber or interact at a certain point on the distant wall in the two-slit interference experiment. But it is possible to explain why electrons seem to have a determinate location by holding that they are a "superposition" of waves with slightly different wavelengths, because in regions where such wave interfere constructively, they clump together in what are called “wave packets.” Since the locations where such a set of waves interfere constructively have more or less precise locations in space and seem to move through the space occupied by the waves, the Schrödinger wavefunction could explain the appearance that electrons move like particles. (This was not a fully adequate explanation, however, because such wave packets also tend to disperse over time, and yet electrons actually turn up later at definite locations.)

However, it was not possible to interpret the Schrödinger wavefunction as the description of a classical wave. One problem was that it contained complex numbers. There is no way to measure quantities multiplied by the square root of minus one, and yet those complex numbers are essential to the wavefunction, since they describe the phases of the waves that are superimposed in the quantum system and, thereby, determine the interference phenomena.

Furthermore, the Schrödinger wavefunction described a wave in a space that can have more than three dimensions (or what is called “configuration space). When more than one particle is involved, the space occupied by the wave described by Schrödinger’s wavefunction has three times as many dimensions as there are particles. There is no obvious way to relate such an equations to the actual three dimensional world.

What is now the orthodox interpretation of the Schrödinger wavefunction was first proposed by Max Born in 1926. He took the square of the (time-independent) wavefunction in some region of configuration space to be a measure of the probability of finding that the particle located in that region of configuration space (thereby predicting a measurable property, such as location, momentum or kinetic energy). The predictions are confirmed by measurement.

Since the predictions are merely probabilistic predictions, however, Born took the Schrödinger wavefunction to be a representation, not of the world itself, but of what we can know about it. This avoided the problems of quantum jumps and wave packets that spread out, because what really happens is not knowable. And insofar as it is taken realistically, it implies that what happens is not fully determined by the state that precedes it.

Heisenberg uncertainty principle. An entirely different mathematical representation of these same quantum phenomena was developed by Werner Heisenberg. His “matrix mechanics” is basically an algorithm for making predictions of measurements without any attempt to explain what is going on beneath the observable surface. Though Schrödinger showed that Heisenberg’s matrix mechanics and his own wavefunction are mathematically equivalent, matrix mechanics makes the limitations on what can be known about the classical properties of the entities described by quantum mechanics clear. In arguing against Schrödinger, he defended what has come to be known as the Heisenberg uncertainty principle.

In matrix mechanics, there are pairs of variables called “complementary” or “conjugate” variables, because the measurement of one affects the measurement of the other. That is, the results of measuring one variable and then the other would be different if they were measured in the opposite order. The position and momentum of an electron are complementary variables, meaning that the position and momentum of an electron cannot both be measured with arbitrarily high precision But the more precise one measurement is, the less precise the other is. Using Born’s probabilistic interpretation of the wavefunction to express the “uncertainties” in such measurement, Heisenberg derived a general principle about complementary variables: the product of the uncertainty about the position and the uncertainty about the momentum cannot be less than Planck’s constant divided by four pi.

Heisenberg’s uncertainty principle holds in a parallel way for other conjugate variables, such as energy and time, angular momentum and orientation, and cycle and phase. In each case, one variable is more particle-like and the other is more wave-like, and thus, the variables are said to be complementary.

Heisenberg apparently took his uncertainty principle to be a basic postulate from which all of quantum mechanics could be developed. He rejected talk about the wave-particle duality and took a purely instrumentalist approach which simply denied that there is any aspect of the world that is not described by his matrix mechanics (or by their equivalents in using the Schrödinger wavefunction).

The equivalence of Heisenberg’s matrix mechanics and Schrödinger’s equation means that the Heisenberg uncertainty principle can be derived in a similar way from Schrödinger’s equation.

The solution of Schrödinger’s equation for a given situation yields a wavefunction, which is a complete description of the quantum system. But in order to predict a measurable property, it is necessary to apply an appropriate mathematical operator to the wavefunction. The operator yields an “expectation value” for that property, which may be a precise value or an average value.

But some pairs of operators are not commutable, such as the position and momentum of a particle. Though it is often possible to make precise predictions of these properties, the prediction of one makes it impossible to predict the other. That is, when one property is predicted by one operator, the mathematical operation changes the wavefunction and so the prediction made for the other property is not the same as it would have been if the second property had been predicted first. Since the order in which the operators are applied to the wavefunction makes a difference in what they predict, it is impossible to predict both properties at once. Thus, the conjugate variables to which Heisenberg’s uncertainty applies turn out to be the pairs of properties predicted by non-commutable operators.

When the operator yields an expectation value that is just the average result for an entire series of experiments, it can often be represented as a superposition of different wavefunctions for each of which the operator gives an expectation value. When the measurement is made and one of them turns out to be true, the wavefunction is said to “collapse,” because the system turns out to have one or another of precise predicted outcomes. This is called the “collapse of the wavefunction,” because it is assumed that prior to the measurement, what actually existed was a superposition of different wavefunctions.

This interpretation of the measurement of a quantum system exacerbates the problem, for the superposed states of the system can evolve in radically different ways. In the most famous example, a cat is locked in a box with a devise triggered by an unpredictable beta decay that will, with 50% probability, release a poison that kills the cat within a certain period of time. But until someone looks to see what has happened, there is a superposition of the two states, one with a dead cat and another with a living cat, and reality only resolves itself into one or the other possibility at the moment someone looks. This implausible implication of measurement being the collapse of the wavefunction is called the problem of "Schrödinger’s cat."

The Heisenberg uncertainty principle is, perhaps, the most general statement of the puzzles of quantum mechanics, and a genuine ontological explanation of quantum mechanics, if there is one, should reveal the source of this limitation on our knowledge.

Bell correlations. Recently, attention has focused on a final quantum mystery, called “Bell’s Theorem” or “Bell’s Inequality.”^xxx John Bell showed that quantum mechanics entails, in certain circumstances, a statistical correlation between events occurring at a distance that seems to be possible only if the events have effects on one another that travel faster than the velocity of light. It holds for interactions in which particles move away from one another in opposite directions with opposite orientations of a “spin”.

Spin. Spin is a quantum property that was first recognized with the discovery of quantum field theory. The Schrödinger wavefunction is the law of non-relativistic quantum mechanics, and a more complete law was discovered by Paul Dirac when he combined the Schrödinger wavefunction with Einstein’s special theory of relativity, that is, taking the relationship it describes between space and time into account.

There was an asymmetry between the time-dependent and time–independent wavefunctions derived by solving Schrödinger equation. The time-independent wavefunction, describing the spatial aspects of the standing wave, is a second order differential equation, whereas the time-dependent wavefunction, describing how the quantum system unfolds in time, is a first order differential equation. Dirac derived a time-dependent wavefunction that was a second order differential equation, making time and space symmetrical, as they are in the special theory of relativity.

It is puzzling just what makes Dirac's derivation work, but it involved several profound discoveries.

Dirac discovered that there are twice as many solutions for the wavefunctions than had been thought, half of them corresponding to negative energy. This was the discovery of antimatter, such as, for example, the positively charged electron as the negative partner of the negatively charged electron, called the "positron."

Dirac discovered that quantum particles have another property, called “spin,” which was a new quantum number that was needed for wavefunctions to describe fully any quantum situation. That is, spin is a new quantum number (namely, s) needed to describe the atom (along with Bohr’s numbers for the energy states of atoms (n), a number for the orbital angular momentum of the electron (i), and a number for its magnetic moment (m)).

It is believed that the intrinsic spin of an electron has little to do with a spinning electrical charge. The spin of a particle is defined operationally as the strength of the magnetic force that results when a magnetic field is imposed on the particle. Particles, such as the electron, that have ½ spin (called “fermions”) have one of only two possible magnetic moments (positive and negative). Since there is no way for them not to have a magnetic moment, it is hard to see how they could be a classical material object with a charge that is somehow actually spinning.

Bell’s Inequality. John Bell discovered a curious consequence of quantum mechanics involving spin. The spin of a particle (either a rest mass or a photon, which has a spin of 1) would seem to a property that the particle carries with it, but a prediction made on this assumption contradicts quantum mechanics. And it seems to have been disproved empirically. This suggest that spin is a property that depends, not on the particle itself, but on what happens elsewhere in a much more inclusive system involving both particles.

The system is one in which two objects are generated in a way that requires them to have opposite orientations of spin, and they move away from one another in opposite directions. Since space is three dimensional, the spin of a particle can be measured from three different, mutually perpendicular directions. If one particles is measured as having as having spin, say, up, in some direction, then the other particle will never turn out to have anything but the opposite, down, orientation of spin when it is measured in the same direction. This holds regardless which of the three independent directions in space the magnetic field is oriented, and quantum mechanics does not permit one to infer from its spin in one direction what its spin in any other direction is. Thus, if spin is a property that the particles already have when they part from one another, the outcome of measuring the spin of the particles that moved off one way from their creation from one direction should not enable us to predict the spin of the other particle when measured from a different direction. Bell showed that, on this assumption, a certain inequality must hold about the frequency with which measurements of spin in one particle in one direction would correlate with measurements of the spin of the other particle in one of the other directions.

However, quantum theory predicts and experiments have confirmed that this inequality will be violated. When two objects are generated in this way, and the spin orientation of one of these objects is measured in one direction, it is possible to predict the outcome of a measurement of the spin orientation (up or down) of the other object in an independent direction of three dimensional space more often than the Bell inequality allows. It is not a reliable prediction in any particular case, but statistically it is more frequent than would be possible, if the spin orientations of both objects were already determined when they parted and they were simply carried away with them, as the principle of local action would require.

Though the two measurements can be made as far apart in space as one likes, it seems that the only way the measurements could be correlated is if the measurement of one object were somehow affecting the state of the other. And since the two measurements can be made to occur as near to one another in time as one likes, there are instances of this phenomenon in which such an effect could hold only if something travels between them faster than the velocity of light. This puzzling correlation is not only a consequence of quantum theory, but has also been confirmed experimentally, and thus, it seems that we must give up the principle of local action. But it seems to violate the principle of local action. Since the different outcomes are a superposition of different wavefunctions, this is seen as just another puzzles about the so-called "collapse of the wavefunction."

The puzzles of quantum mechanics have to do with understanding what in the world corresponds to the Schrödinger equation. The “Copenhagen interpretation” of quantum mechanics, developed by Bohr, is the received view. It simply denies that it is possible to describe the nature of what exists except by applying the classical conceptions of particles or wave, which if not strictly speaking incompatible, are, at best, complementary. Defenders of the Copenhagen interpretation see the puzzles of quantum mechanics as deriving from its departures from classical physics, as if classical physics were based on intuitions ( or a form of imagination) that is anthropocentric and, thus, merely subjective. And some go on to insist that the uncertainty is a real indeterminism about what happens in the world.

The chief opponent of this view was Einstein. He was resisting the reification of quantum uncertainty as indeterminism when he claimed, “God does not play dice with the universe.” A view of the world as being constituted by substances of some kind is what kept Einstein from accepting quantum mechanics as the complete description of what exists. His acceptance of spacetime as a substance made him most sympathetic to Spinoza, for Spinoza believed that the world is a single substance. But what seems to have kept Einstein from admitting that such a substance could have indeterminism as a basic property were his ontological instincts.

In what follows, I will elaborate the the assumptions of spatiomaterialism in a way that explains ontologically why quantum mechanics is true. It is, as I have warned, more speculative than the rest of the argument of ontological philosophy. But it may suggest the power of an ontological approach and vindicate Einstein’s view of the nature of the world in at least one respect.

The theory of quantum matter. In order to show the possibility of a spatiomaterialist explanation of quantum mechanics, I will describe one way that the relevant phenomena might be constituted by space and matter as substances enduring through time. This will require a refinement of the assumptions made thus far about the natures of both matter and space. It is a refinement is a basic aspect, because it has to do with how these substances endure through time.

Space and matter were postulated in Spatiomaterialism as substances with essential natures that are opposite in a most fundamental way. The parts of space all have essential natures that include geometrical relationships to one another, so that the existence of one depends on the existence of all the others. But the parts of matter can all exist independently of one another. Being opposite in that way, it was possible to explain why bits of matter have spatial relations to one another and how change is possible by assuming that bits of matter exist together with space as a world by each coinciding with some part of space or another. These are the basic assumptions of spatiomaterialism, and it is possible to make further assumptions about the natures of space and matter, as long as they are consistent with these basic assumptions.

I made further assumptions about the nature of space and matter in order to explain how the laws of classical physics are true. I assumed that the nature of matter coincides with space in all the forms that are counted by physics in its principle of the conservation of mass and energy: rest mass, kinetic energy, two kinds of force-field matter (electric charges and gravitational fields), and two kinds of waves of forces (electromagnetic waves and gravitational waves).

I made another assumption about the nature of space and matter in order to explain Einstein’s special theory of relativity ontologically. I assumed that space has an inherent motion (or “ether”) which determines the velocity of light), and that material objects suffer Lorentz distortions as a function of their velocity relative to the inherent motion. (In order to suggest the inevitability of the Lorentz distortions, I anticipated a conclusion that I will defend here, namely, that material objects are constituted by unit-like interactions that are equivalent to the two-way electromagnetic interactions involved in the an interferometer.)

I made yet another assumption about the nature of space and matter in order to explain Einstein’s general theory of relativity. I assumed that centers of matter exert a force on the surrounding space that accelerates the inherent motion (or ether) and, thereby, accelerates all the bits of matter that coincide with space by way of it.

In order to explain ontologically the truth of the laws of quantum mechanics, I will make further assumptions about both space and matter.

Space. As we have already assumed, space has an inherent motion. This aspect of the nature of space determines the velocity of light. This assumption about the motion of electromagnetic waves (or photons) is crucial to the spatiomaterialist explanation of relativity theory, because it is the motion of objects with rest mass relative to the inherent motion that gives rise to the Lorentz distortions which explain the phenomena of special relativity. And the acceleration of the inherent motion itself relative to space is what explains the gravitational phenomena covered by general relativity.

The inherent motion of space is what plays the role that the ether was supposed to play in classical physics. The inherent motion mediates all the motion and interactions among bits of matter, because it is the aspect of space by which bits of matter coincide with parts of space. Since the inherent motion goes both ways in every direction of three dimensional space, there is a certain velocity at any point that is at “rest” relative to the inherent motion itself (that is, at rest in the ether). Relative to that inertial frame, light has the velocity, c, both ways in every direction in three dimensional space. But rest relative to the inherent motion may not be rest relative to space, because in gravitational fields, the inherent motion (or ether) is in motion relative to space and even accelerating. That aspect of its nature can, however, be set aside for now, because the inherent motion in substantival space that is the relevant aspect in explaining the quantum nature of matter.

To make it concrete, consider what the inherent motion must involve in order to explain electromagnetic waves. It must exist at every location in space at every moment. It must always have the same velocity in space (except, of course, for the changes that occur in gravitational fields). In each part of space, it must sweep through space in every possible direction, that is, both ways in every direction in three dimensional space. And it must be able to carry electromagnetic waves of every possible wavelength and every possible phase of every wavelength across every point in space, preserving their wavelengths and phases. (And as we shall see, it must do this for photons of two kinds, one of each possible orientation of spin.)

Since the inherent motion is sweeping through every part of space at the same time, what is sweeping through any part of space in any given direction is like of a wave front. The same motion sweeps through all the points in every two dimensional plane of which it is part. Indeed, there is such a wave front sweeping in every direction through every point of space.

Nor is it inappropriate to speak of the inherent motion as having waves, since it carries every possible wavelength of light, and as we shall see, the wavelengths of those wave fronts make a difference in what happens. It takes a certain period time for a photon (a complete cycle of electromagnetic radiation) to pass any given point, and since the photon is carried along by the inherent motion, such a cycle marks out a certain distance (its wavelength) over and over along its path. Indeed, since this is always happening, there is always already a series of wavelengths implicitly marked out in space by the inherent motion at any given wavelength, each going through a cycle at the same time as all the others, that is, at the present moment. This pattern holds for every wavelength and for every phase of each wavelength both ways in every direction. And it holds both ways in every direction for each point in space.

I elaborate this implication of postulating the inherent motion in order to make explicit what all I will not try to explain about the nature of space. By calling it an “inherent motion in space”, I mean that it is an aspect of the nature of space itself. That means, at a minimum that it is occurring at every location in space, whether there is any light there or not. But what is more, it means that space is what causes light to move as it does. The inherent motion at any location in space carries light along with it, when matter of that kind happens to coincide with that part of space. Unless the inherent motion of space were responsible for the velocity of light, it would not be possible to explain relativistic phenomena ontologically.

The inherent motion, therefore, marks out distances in space according to any cycle of changes occurring locally as time passes. This is to talk about the inherent motion as if it were a real set of events taking place in space, and as I said earlier, it may be possible to formulate a simpler spatiomaterialist explanation in which the inherent motion is merely a spatio-temporal aspect of the nature of space as a substance, that is, a geometrical structure about space and time. The inherent motion is, after all, basically a relationship between distances in space and periods of time that are built into the essential nature of space. That is to add a temporal aspect to the spatial relationships that space was originally assumed to have in Spatiomaterialism in order to explain the three-dimensional geometrical structure of space.

Each part of space has not only an essential geometrical relationship to every other part of space at the present moment, but also an essential relationship to future and past moments in the existence of every other part of space. To be sure, the past and future states of parts of space do not exist, because nothing exists but what exists at present, if substance endure through time. That means that one location’s relationship to future or past states of another location is a temporally complex property of space, which determines the maximum velocity with which what happens in one part of space and affect what happen in other parts of space. But that temporally complex property corresponds to a temporally simple relationship that actually exists among the parts of space as time passes. That is what I mean to emphasize by talking about the wave patterns set up in space by the inherent motion sweeping though every part of space, both ways, in every direction. These patterns may be nothing more than simply how all the parts of space endures through time, but speaking of these patterns as being laid out by the inherent motion in real time dramatizes the role they play in explaining the regularities described by quantum mechanics. And at this point, clarity about what is being assumed is more important than simplicity, since it is not necessary to have the simplest ontological explanation in order to show that there is such an explanation.

Matter. In order to give a deeper explanation of the nature of matter, we must distinguish between two kinds of matter, which I will call “force-field matter” and “quantum matter.” Three of the six forms of matter that were distinguished in order to explain the truth of classical mechanics are forms of force-field matter (electric fields, gravitational fields, and gravitational waves), and three are forms of quantum matter (rest mass matter, kinetic energy matter, and photons). Force-field matter has already been explained ontologically as involving a property (or temporally variable condition) of parts of space (though there is more to be said about it). And it is the nature of quantum matter that will bear the major burden of this ontological explanation of the quantum mechanics.

Force-field matter. By “force-field matter,” I mean forms of matter that are constituted by a changeable property or condition of parts of space. The property of space acts like a force, because it changes the way in which bits of matter coinciding with that part of space move and interact. Consider the three forms of force-field matter:

Gravitational fields. Gravitational matter is one kind of force-field matter, and we can set it aside, because it has already been explained. Gravitational matter is the matter that exists as the force field that gravitating bodies impose on the surrounding space, accelerating the inherent motion (the ether) toward themselves. Like any form of potential energy, the quantity of matter involved in a gravitational field is already counted in the rest masses of the objects exerting the forces. That is, their rest masses decline as the bodies attract one another, acquiring kinetic energy at the expense of potential energy (though as we shall see, force-field matter is not actually converted to kinetic quantum matter until the material objects acquire kinetic energy relative to the inherent motion by colliding with other material objects near the center).

Gravitational waves. Since gravitation is a force that propagates with the inherent motion of space, gravitating bodies can set up gravitational waves, which exist independently of material objects with rest mass, for example, from binary stars, which are in orbit around one another. But this is still a form of force-field matter, not quantum matter, because the gravitational force propagating at the velocity of light acts on space, not on bits of matter directly. It is by accelerating the inherent motion in the parts of space it encounters that gravitation accelerates bits of matter, not by interacting with bits of matter directly.

Electric fields. An electric charge also imposes a force field on the space surrounding the material objects that has the charge, and that is another form of force-field matter. The electric field is another property (or variable condition) of space which affects other material objects with electric charges. Electromagnetic matter contained in electric charges is already counted in the rest masses of the objects that have the charge, and matter is conserved, because as we have seen, the consumption of potential energy is counted as a negative quantity.

The electric field is more complex than the gravitational field, as we have seen, because changes in the electric field cause magnetic forces. But that connection between electric and magnetic forces, which is described by Maxwell’s equations, can be explained as another aspect of the nature of space. That is, changes in the electric field caused by the motion of an object with rest mass propagate as a result of the inherent motion in space, and thus, the electromagnetic interactions are relative to the inherent motion (as we have assumed in explaining Einsteinian relativity).

Quantum electrodynamics is the gauge field theory that is currently accepted by physics as an explanation of the electric charge and its behavior, and such a theory lends itself to a spatiomaterialist ontological explanation, because it portrays forces as being exerted by the exchange of particles, called the "boson" of the gauge field. In this case, it is a virtual photon. The electric charge is described as having a certain orientation in a complex vector plane, and the forces exerted on the charged particle by the virtual photons are just what is required for the orientation of the charge to be unchanged in that complex vector plane by its change of location. Those forces turn out to the forces described by Maxwell’s law. But since the force field is explained as virtual photons emerging from space as a result of the charged particle's motion at its location in the field, the gauge field theory is the kind of explanation that can be given an ontological explanation by spatiomaterialism. (More will be said about the nature of the electric charge and the gauge bosons that mediate interactions among charged particles as required as we go along and, more completely, when we take up the basic particles. See Change: Basic Objects.)

Quantum matter. The nature of quantum matter is the basis of this ontological explanation of quantum mechanics, and the remaining three forms of matter (rest mass matter, kinetic energy matter, and electromagnetic waves) are all forms of quantum matter. Like the new assumption about the nature of space, this new assumption about quantum matter recognizes a temporal aspect to the nature of matter, though it is a temporal property suited to the opposite nature of matter.

Parts of space are all connected geometrically, and since the inherent motion connects them all temporally as well, the endurance of space through time is characterized by the inherent motion (or the spatio-temporal geometry) described above. Much the same way of enduring through time also characterizes force-field matter, since force-field matter is spread out continuously in regions of space through which the inherent motion is constantly flowing. But since bits of matter can exist independently of one another, there is another way in which they can have a further temporal aspect to their nature.

The new assumption is that quantum matter is just a series of cyclic events that occur over time. That is, bits of quantum matter endure through time as a series of unit-like events whose cyclic nature entails that each event gives rise to another event of the same kind (unless it interacts with another bit of matter in some way and another kind of cyclic event ensues). Since these events follow one another as time passes, cycles of events (of the same kind) are a way of counting time, much as the inherent motion in space allows periods of time to be counted by the distance it crosses. These events will be called “quantum event,” because these are the smallest changes that can take place in a spatiomaterialism world (except for the inherent motion itself in smaller parts of space). Quantum events cannot be divided up in to smaller events, and so they are elementary units. But since they are cyclic events, each gives rise to another event, and since they reproduce in time, they explain the endurance of bits of (quantum) matter through time. The way that matter endures through time as a series of cyclic quantum events is mainly what the “quantum” in quantum mechanics is referring to, according to this spatiomaterialist explanation of quantum mechanics.

An “event” has both a spatial and a temporal dimension. It begins at some place and time and ends at some place and time. What happens in a quantum event is that a force is exerted and change is caused. The force may cause a change in another force, as illustrated by the photon, in which electric and magnetic forces are coupled in cycles. Or the quantum event may be a force that changes the motion of an object with rest mass, as we shall see holds in the case of the motion of an object with rest mass.. Different forms of quantum matter are constituted by different kinds of quantum events, as we shall see. But since they are elemental events, they all have the same, smallest size. That size is what is represented by “Planck’s constant”, h.

Planck’s constant is a certain size in a parameter called “action”. Though action was recognized early in the Newtonian era as one kind of physical quantity, it has nearly dropped out of contemporary physics (except for the constant h), apparently because it need not be mentioned in describing efficient causes. Action is, however, defined in terms of a certain physical quantities that are mentioned as efficient causes (such as spatial relations, mass, force, velocity, acceleration, momentum, and energy). For our purposes, the most useful way to think of action is as the product of force times distance times time, as if a force were acting on something (such as a unit mass) for a certain distance over a certain period of time.

In units that physicists take to be basic, action has the dimensions of mass times distance squared per unit time (or mass times distance squared per unit of time squared, all times time). And in addition to thinking of it as force times distance times time, it can be seen as momentum (or mass times velocity) times distance (that is, as the integration of a change in momentum over the distance it occurs). Alternatively, it can be seen as energy (mass times velocity squared) times time (that is, as the integration of a change in energy over the period of time it occurs).

In speaking of momentum and kinetic energy, I assume that we are talking about matter that is nearly at rest in the ether, where Newtonian laws hold and momentum is approximately equal to mass times velocity and kinetic energy is approximately equal to one-half of mass time the square of velocity. This is not quite true, because according to the special theory of relativity, mass increases with velocity. However, by starting with rest mass as the quantity of matter constituting particles at rest in the inherent motion, it will be possible to explain why mass increases with velocity, because we will be able to explain the extra mass as the matter making up its kinetic energy.

The idea is, therefore, to interpret the quantum of action as an event, that is, as a change of some kind that takes place in the world as a result of something being done. This may be a little vague, but remember that we are taking now about the most basic elements of what exists in the world, and the nature of quantum events can be made clear only by considering their various kinds. But since action is measured in units that include both space and time, it is possible to think of these events as having determinate boundaries in space and time, that is, as beginning at some place and time and ending at some place and time. That gives these events determinate locations in the geometry of space and time as determined by the velocity of light, that is, by the inherent motion.

Planck’s constant is a certain size of action, and we can explain why it appears in all the equations of quantum theory, if we assume that quantum events have an all-or-nothing character about them. Bits of quantum matter endure, we assume, because they are constituted by quantum events with a cyclic nature. Although cycles of quantum events may follow one another continuously in time and space, there is a unit-like nature about them, so that either a whole quantum event occurs, or it does not occur at all. This means, on the one hand, that nothing can happen that involves less than a unit of action (except possibly the inherent motion), and on the other, that everything that does happen to quantum matter is made up in some way of a certain number and kinds of these elemental units of action.

The assumption that quanta all have the same amount of action is not as restricting as it may seem, because quanta have widely varied temporal and spatial dimensions. They can take place in a short distance in a brief period of time, if the force is great enough, or they can take place over a longer distance in a longer period of time, when the force is weaker. But in order to spell out the assumption that they have a unit-like nature, let us think of quanta as having end points in space and time, so that quantum events can be fit together as complete cycles in the spatio-temporal geometry of the inherent motion of space in different ways. This model may be too crude. It is unlikely that quantum events have anything as abrupt as definite points at which one cycle ends and another begins. But that is a way of keeping in mind the unit-like nature of these events, even if it is just a place-holder to be replaced by a better explanation of where and how one quantum event ends and another quantum event begin.

For example, a better model of their unit-like nature would, perhaps, be one in which interactions between different bits of matter can occur only when whole cycles of the different bits of matter are lined up somehow according to the spatio-temporal geometry of the inherent motion in space. That is, given their precise locations in space and time, the points at which quantum cycles stop and start would depend on what they are interacting with and the direction from which they are interacting, so that different starting points and stopping points might hold if they were interacting with quantum cycles of bits of matter from different directions in space, of different kinds, or with different phases to their cycles. (Lining particles up in this way could be, as we shall see, the role of their intrinsic spin and its magnetic moment in mediating interactions of bits of quantum matter.)

Matter is a substance, because it exists continuously over time, never coming into existence nor going out of existence. We are assuming that one form of matter can be converted into another, including conversions between quantum matter and force-field matter (that is, between potential and kinetic energy). But when matter exists in the form of quantum matter, the endurance of bits of matter through time is explained by the cyclic nature of the quantum events that constitute their existence. That is, given that the quantum event starts at some place and time, there is a certain place and time where the cycle is complete, and at that point, another quantum event begins. Since quantum events are related cyclically, they can reproduce themselves in time. However, quantum cycles succeed one another not only temporally, but also spatially, so that nothing is flitting about discontinuously from place to place in space. Other things being equal, quantum events give rise to other quantum events of the same kind and dimensions as themselves.

Bits of matter do, however, interact. I will say more about how they interact in a moment, but in general, what happens is either the conversion of matter between quantum forms and force-field forms of matter and/or changes in the kinds of quantum matter. Force-field matter is laid out in space, changing its shape with the motion of the material objects that are imposing the forces. And since material objects, their motion and photons are just cycles of quantum events reproducing themselves in time, what changes are the kinds, numbers, and dimensions of the quantum events constituting them.

Since the quantum events have a unit like nature, what happens to bits of quantum and force-field matter in space involves fitting quantum events together in space and time according to certain laws as if the endurance of the world through time were the result of building a brick wall into the future. Some bricks are simply stacked on top of one another, as quantum cycles reproduce themselves in time. But when bits of matter interact, the bricks fit together in more complex ways, changing the sizes and locations of the bricks in the next row. The space on which the wall is being built also plays a role, because the sizes of the brick may also change with their locations (as in force fields), and the effects of space on their sizes changes with the locations of the bricks affecting space (as in changing location in a force field). Nature is a master mason, never failing to lay in the next layer of bricks according to fixed rules, and thus, there are regularities about change as the brick wall is built into the future. And the structures formed by them can be quite stable over time.

In order to spell out the details of these “rules of quantum masonry,” I will describe each of the forms of quantum matter and then take up the issue about how they interact with one another. Some of the quantum puzzles will be explained along the way, and in the end will, we will see how their interactions explain the structure of the atom, the Heisenberg uncertainty principle, and the Bell correlations.

To explain the endurance of matter by the cyclic nature of quantum events may, however, make it seem that matter is not a substance at all. If quantum events are ultimately just the exertion of a force in some part of space making some other event occur that is also constituted by forces, it is conceivable that quantum matter is just a property of parts of space, much like force-field matter. Could matter be entirely reducible to space? This is not what we assumed when we took spatiomaterialism as the foundation for this ontological way of doing philosophy.

The reduction of matter to space is, however, something that ontologists should welcome, if it is possible, for it would be just as complete as spatiomaterialism, but a simpler, and, thus, better ontological explanation of the natural world. It is more or less what Einstein was trying to do during the latter part of his life in attempting to construct a unified field theory. He wanted to describe matter another kind of curvature of spacetime, along with gravitation. If something like that comes of this ontological explanation, then spatiomaterialism will turn into spatialism.

However, I will put this possibility aside. In the first place, we would be getting ahead of ourselves to assume at this point that spatialism is true. We have yet to see how matter can be explained by cycles of quantum events. And second, even if an ontological explanation of quantum mechanics like this stands up in the end, it does not seem to me that that would make spatialism true. You may be able to reduce the inherent motion in space to spatio-temporal geometry, but the unit-like nature of quantum events will keep them from being reducible to properties in space. Each quantum event occurs over a period of time, and since quantum events cannot exist unless the whole event occurs, to postulate their existence is tantamount to holding that what exists includes entities with a temporal dimension to their essential nature. Bits of matter-time may be less problematic than spacetime, but in a world in which nothing exists but the present moment, they are, strictly speaking, not possible. Thus, this unit-like nature can be explained only by postulating the existence of a substance with a part-whole relationship of some kind that make it appear to be made up indivisible cycles of events. Whatever its nature, it basically different from the essential nature from space. Space is incapable of explaining the unit-like nature of quantum events, because it must exist only at the present moment in order to have an inherent motion that flows continuously. The only plausible way of explaining the all-or-nothing character of quantum events is to postulate another kind of basic substance, distinct from space, which can coincide with parts of space, for in that case, we can believe that, despite seeming to have a temporal dimension to their nature, quantum events also exist only at the present moment. There is, however, no need to settle this issue now.

Forms of quantum matter. I will focus first on the nature of quantum matter, since force-field matter depends on the existence of the bits of quantum matter constituting a particle with rest mass in nearby parts of space and it is fairly clear how it can be explained. Quantum matter includes electromagnetic waves, material objects with rest mass, and their kinetic energy.

The total matter is ultimately equal to the total quantum matter. Force-field matter is already counted in the masses of the objects exerting the forces, and gravitational waves eventually die out as they are converted into other forms of matter.

The quantity of quantum matter in any region of space is measured by the number of quantum events per unit time, for that is equal to the quantity of energy, given the definition of “action.” Since we will assume that all quantum matter is constituted by quantum events, the equivalence of energy and mass by Einstein’s equation, E = mc², implies that each unit of mass must be equivalent to a certain number of quantum events per second.

The quantity of force-field matter involved in constituting the electric charge can be measured as potential energy, that is, in terms of the number of quantum events per second that can be converted from it, and that quantity must be subtracted from the total quantum cycles constituting rest mass.

After describing the nature of each form of quantum matter, I will take up the nature of electromagnetic interactions, bringing force-field matter back into the picture. But along the way, I will point out how this theory explains the peculiar nature of matter at the scale of the quantum and solves certain quantum puzzles.

Light. Light is the easiest form of matter to explain on the assumption that “quantum” refers to elementary events with the size indicated by Planck’s constant, for light can be explained as being made up of photons, each of which is the size of a quantum.

Light was understood as a wave in classical physics. According to Maxwell’s equations for electromagnetism, the change in the electric force has as its effect a magnetic force, and the change in the magnetic force has as its effect an electric force. Thus, the two forces interact, and their interaction can couple them in cycles of changing electric and magnetic forces that propagate through space at a fixed velocity, the velocity of light. Its wave-like nature is apparent in such phenomena as diffraction and interference.

As we assumed in explaining Einsteinian relativity, the velocity of light is explained ontologically by the velocity of the motion inherent in space itself. Let us, therefore, think of the electric and magnetic forces involved in electromagnetic waves as being carried along with the inherent motion in some direction. That will allow us to explain electric and magnetic forces as properties of parts of space, except for the way that they are coupled together in units as photons (or rather aspects of the inherent motion in space).

The particle-like nature of light waves can be explained on the assumption that each cycle of electric and magnetic forces is a single quantum event that occurs as a whole, if it occurs at all. Since these quantum events are cyclic, when one event does occur, it is followed, other things being equal, by another quantum event of the same kind. But since these quantum events coincide with space by way of the inherent motion, the next cycle of electric and magnetic forces occupies the next part of space in its direction. As the cycles reproduce themselves in time, therefore, they move across space, constituting an electromagnetic wave in time and space.

This ontological explanation of light accounts for the quantum equations used to describe the energy and momentum of photons. Energy is proportional to the number of quantum cycles per unit time, and that is what the equation for the photon’s energy says: E = hf (where f is the frequency of the light). The shorter the period of each quantum cycle, the more units of action that can occur in a unit of time, and thus, the more energy it carries.

The momentum of the photon can be explained in a parallel way, except relative to the direction of space in which the photon is moving. The dimensions of the quantum as a unit of action implies that the momentum of a quantum cycle is proportional to the number of quantum cycles per unit distance (in the direction of motion), and that is what the equation for the momentum of the photon says: p = h/l, where l is the wavelength of the light and 1/l is the number of cycles per unit length). In other words, the momentum is inversely proportional to the wavelength. Photons with shorter wavelengths have more momentum.

Since the velocity of light is constant, fl = c (where c is the velocity of light), and thus, the energy and momentum of the photon are proportional to one another: E = pc. In other words, the shorter the photon’s quantum cycle in time and space, the higher its energy and momentum, respectively. But since it is still the size of a quantum, the decreased size of the event in space and time means that the forces involved in each cycle are greater (since action is the product of force, space and time).

Since each cycle of electric and magnetic forces is a quantum event, no part of it can exist unless the whole cycle does. This unit-like nature to the events that constitute the existence of a photon is explained ontologically by how bits of matter coincide with space, and so it depend as much on the nature of space as it does not the nature of matter. (More precisely, the energy of the photon depends on the bit of matter apart from space, whereas its momentum also depends on space, because momentum is a result of the interaction of electric and magnetic forces being carried along by the inherent motion.) This suggests a straightforward ontological explanation of the phenomena that led to the recognition that light is made up of particle-like units.

Planck. What Planck discovered about blackbody radiation can be explained ontologically as a discovery about how photons coincide with the same part of space. What he discovered is that photons of different frequencies can all coincide with the same part of space as long as there their frequencies differ from one another by at least one quantum of action per second. This limitation on the frequencies that can exist in the same part of space avoids the so-called ultraviolet catastrophe, that is, why the total energy of photons at higher frequencies does not become infinite.

On this ontological explanation, what coincides with space are not just the changing electric and magnetic forces of electromagnetic waves, but rather complete cycles of such forces. And since the inherent motion contains each quantum of action is part of a wave pattern of a certain size that extends though the space in its direction, this limitation is a minimum difference that holds for the sizes of the wave patterns that can exist in that region of space.

Though this is a limitation on the variety of possible photons that can coincide with any part of space, the inherent motion in space is still handling a lot of different kinds of photons. In addition to all the frequencies of light in any direction that can exist at any part of space, photons of each frequency can have different phases (that is, different points in space where the cycle begins) as well different orientations of spin. Not only must the inherent motion be able to carry photons of all these kinds at once in any given direction, but it must also be able to carry the complete variety of photons in every direction in three-dimensional space. Indeed, at any given location it must be able to carry photons of all kinds both ways in every direction, and it must do so at every location in the region of space all the time. That is just how the parts of space are connected (though the inherent motion itself may be moving across space and being accelerated in a gravitational field).

Einstein. Einstein’s explanation of the photoelectric effect was that in order for light to free electrons from matter, the light had to have a high enough frequency, because the electron had to receive all the energy it needed to overcome the force binding it to the atom from a single photon. Lots of low frequency photons would not work.

This particle-like behavior of light is just what would be expected, if light is constituted by cycles of quantum events, because in order for light to interact at all, a whole quantum event of one kind must become a quantum event of another kind, in this case, it is the kind of quantum event that constitutes kinetic energy. And a single photon can supply the force needed to accelerate the electron, because photons with a higher frequency have smaller temporal and spatial dimensions and, given that each photon is a quantum of action, the forces constituting them must be correspondingly greater.

Compton. When a photon does interact, it is the whole photon that interacts. When a photon is scattered by an electron, for example, a whole photon is absorbed and a whole new photon is generated (one that is 180^o out of phase with the original). The Compton effect has a straightforward ontological explanation, because the scattering of the high energy photon by an electron, like an elastic collision between two material objects, conserves both energy and momentum. The mass of the electron limits how much energy and momentum can be carried away, and that can be confirmed by measuring the direction and wavelength of the reflected photon.

Rest mass. Material objects with rest mass are another form of matter that was recognized in explaining the truth of classical physics, and our reason for thinking that rest mass is just another form of the substances that are counted in the principle of the conservation of energy was the equivalence of mass and energy (E = mc²) entailed by Einstein’s special theory of relativity. But having set aside force-field matter, we are now explaining those forms of matter as forms of quantum matter, and that requires us to hold that material objects with rest mass are constituted by quantum events in some way. And there is an obvious way to do so.

The rest mass of a particle can be explained as the number of cycles of quantum rest mass events per second, just as for the energy of photons. Such quantum cycles would, of course, have to coincide with space in a different way from photons, because objects with rest mass can remain at rest (or more precisely, have a constant velocity relative to the inherent motion in space). The simplest way to explain why such objects can be at rest is to hold that the quantum cycles constituting them go around in circles (or some such closed path), instead of moving across space with the inherent motion like photons. Moreover, since such quantum events would follow a closed path, like a circle, which brings the action back to where it began to start the next cycle, it is clear how quantum rest mass cycles can succeed one another in time.

In order to show that objects with rest mass can be explained as form of quantum matter, it will be necessary to show how all the basic particles recognized by physics can be explained by quantum rest mass cycles in this way. But that is a task that will not be taken up until the next chapter on contemporary physics, Cosmology: Basic Objects. For purposes of explaining quantum mechanics proper, we shall need only three kind of basic particles with rest mass: electrons, protons and neutrons. They are the near basic constituents of ordinary material objects of all kinds, and together with the electromagnetic force, including the photon, they can explain all the processes that occur in ordinary objects, from atoms to human beings. That is the range of phenomena covered by the quantum mechanics of electromagnetism.

Such ordinary phenomena do not include, of course, the sun, radioactivity, nuclear power and the like. These other phenomena depend on interactions among more basic particles than nucleons and their electromagnetic interactions with electrons. These more basic particles are recognized by physics, and they must all be explained as cycles of quantum events (and how quantum cycles coincide with space) in order for this ontological explanation of quantum matter to be complete. There is a way of doing that in which even the electron does not turn out to be basic, as explained in Cosmology: Basic Objects.

For the present, we shall simply take it for granted that electrons and nucleons can be explained ontologically as objects constituted by quantum rest mass cycles.

Visible light is made up of photons with frequencies of about 10¹⁵ cycles per second and energies about a few electron volts. Electrons have an energy of about one half million electron volts, and thus, the frequency of its quantum rest mass cycles must be on the order of 10²¹ cycles per second. And since protons have a rest mass about two thousand times that of electrons (or about 938 million electron volts), the frequency of their quantum rest mass cycles must be on the order of 10²⁴ cycles per second. However, nucleons have a complex structure, and on this ontological explanation of them, their quantum rest mass cycles do not follow a circular pathway. It is a more complex pathway that may involve three or six quantum events to complete.

Electrons and protons carry an electric charge, as well as rest mass. The conservation of electric charge is explained by the gauge field theory for electromagnetism, and though what I will say about the electric charge is compatible with that theory, I will not try to explain it until we take up the basic particles. (See Change: Basic Objects: Gauge Field.) We shall just take the electric charge for grated.

Kinetic Energy. The assumption that kinetic energy is a form of matter was made in order to explain ontologically the basic laws of classical physics. We explained the principle of the conservation of mass and energy ontologically by the endurance of material substance, and that forced us to recognize that kinetic energy is a form of matter. What needs to be shown here is how kinetic energy matter can be explained as a form of quantum matter.

The received view is that the motion of a material object is nothing but its change of location in space over time. But that is not possible for an ontological explanation of the world that explains change by the endurance of substances through time, that is, as “real change,” because it must assume that nothing exists but what exists at the present moment. However, if nothing exists but the present moment, material objects are never in motion, and so wherein does its motion consist? To call motion “instantaneous velocity” is merely to name what needs to be explained.

Thus, ontology must recognize that the motion of objects with rest mass is not just their change of location over time, but rather is due to another form of matter that endures through time. That is, we must think of motion as an additional bit of matter that coincides with the material object and the part of space where the object is located. But it is a different form of matter, because it coincides with space in a way that moves the rest mass along in a certain direction at a certain rate.

This is to resurrect the notion that inertia is a kind of force that keeps the object with rest mass moving, and it explains, as we shall see, the difference between the rest mass of a material object and its inertial mass. But since heat is known to be the kinetic energy of material objects at the micro level, it is also, in effect, to vindicate the notion that heat is a caloric fluid, as we shall see in explaining Material global regularities.

De Broglie’s equation. Kinetic energy can be explained in terms of quantum cycles by supposing that there are quantum events that change the locations of material objects by a certain distance in a certain time. Newton’s first law of motion requires that material objects in motion continue in motion, and in order to explain why that law is true, we assumed that kinetic energy matter endures through time like any other form of material substance. But now we are explaining how quantum matter endures through time by the cyclic nature of quantum events, and so we must explain kinetic energy as a series of cyclic changes, each step of which can exist only as a whole. Let us call them “quantum kinetic cycles.” They will explain ontologically the truth of the de Broglie equations for the momentum and kinetic energy of particles with rest mass, which parallel the equations for photons.

De Broglie first proposed that particles with rest mass have a wave-like nature, much like photons. His equation, p = h/l, which was derived from the equation for photons, described the momentum of the particle as being inversely proportional to its wavelength, and that can be explained ontologically by the nature if the cyclic quantum events that constitute kinetic energy. The wavelength of the particle can be explained ontologically as the distance that the quantum kinetic cycle moves the particle during each kinetic cycle. And we can explain ontologically why the de Broglie equation is true, if we assume that for a unit mass, the length of the quantum kinetic cycle in the direction of its motion is inversely proportional to the momentum of the material object. Like photons, therefore, momentum is proportional to the number of quantum kinetic cycles that occur within a unit of space (in the direction of motion).

Just as the momentum is related to the spatial dimensions of the quantum events constituting kinetic energy matter, so the kinetic energy itself is related to their temporal dimension. The kinetic energy of the particle is inversely proportional to the period of its quantum kinetic cycle, so that its kinetic energy would be proportional to the number of cycles that occur in a unit of time, also like photons. In this case, E = hf, where f is the frequency of the kinetic cycle, or the inverse of its temporal size.

In sum, the faster the particle with rest mass moves, the shorter the distance covered by each quantum kinetic cycle, and the shorter the period required for each quantum kinetic cycle that moves it across space. But since each quantum kinetic cycle is a quantum of action, the shorter its temporal and spatial dimensions, the stronger the force that is acting to move the rest mass across space in each cycle, that is, the more inertia it has.

Quantitative relationship of momentum and kinetic energy. The cycles of quantum events that are responsible for the motion of objects with rest mass explain their momentum and energy, therefore, in much the same way as the momentum and energy of photons. But there is an important difference. In photons, there is a constant relationship between energy and momentum (described by the Einsteinian equation, E = pc), but no such relationship holds for particles with rest mass. Unlike photons, rest masses can have various velocities in any direction, and their momentum and kinetic energy do not have a constant relationship. On this ontological explanation, that means that the temporal and spatial dimensions of the quantum kinetic cycles by which the rest masses change location in space do not have a constant relationship.

From the equations for classical physics, we know that the momentum of a moving object is proportional to its velocity (p = mv), while the energy of its motion is proportional to the square of the velocity (E = ½mv²), and as promised when the laws of classical physics were being reduced to spatiomaterialism, this kinetic theory of matter explains why momentum and energy are related in this way.

To go faster, a particle with rest mass must have shorter quantum kinetic cycles in space, because their wavelength varies inversely with momentum. But with greater speed, therefore, quantum kinetic cycles carry the particle a shorter distance across space during each quantum event. In order for the velocity to be higher, the particle must cover more space in the same length of time, and that means that the period of each quantum kinetic cycle in time must decrease even faster than its length decreases in space. In fact, it is only possible if the period of the quantum kinetic cycle decreases in proportion to the square of velocity.

For example, if the velocity of a unit mass is doubled, the wavelength of each quantum kinetic cycle is cut in half. But that means that the period of each quantum kinetic cycle must be one-fourth as long as the previous quantum kinetic cycles, for otherwise the object will not travel twice as far in the same period of time.

Thus, the way kinetic quantum events must fit together in space over time in order to explain the motion of particles with rest mass explains why the kinetic energy increases with the square of the velocity, while momentum increases directly with velocity. It is a result of how the change in the spatial dimensions of quantum kinetic cycles must affect their temporal dimensions in order for momentum to be inversely proportional to their de Broglie wavelength. (And the reason that the kinetic energy of a particle is not equal to the frequency of its quantum kinetic cycles, but only half, is that only half that much energy is required to accelerate a particle to that “frequency.” More energy is required to accelerate objects at higher velocities, as we noted in explaining why the gravitational time dilation varies with altitude in a gravitational field, not with the strength of the force.)

Rest mass. This description of quantum kinetic cycles has assumed that the particle being moved has one unit of rest mass, but particles of different kinds have different masses and according to classical physics the mass of the particle helps determine its momentum. Its momentum is the product of its mass and velocity. For example, when two material objects have the same velocity, but one has twice the mass of the other, the one has twice the momentum and twice the kinetic energy of the other object. This can be explained ontologically on the assumption that the particle’s motion is due to quantum kinetic cycles, but it will require us to take into account the relationship between the quantum cycles making up the rest mass and the quantum cycle constituting its motion.

We are assuming that the rest mass of a particle is proportional to the frequency of the quantum cycles constituting its rest mass. In an object with twice the rest mass, there are twice as many quantum rest mass cycles per second. Though rest mass and kinetic energy are both a series of cycles of quantum events, and though the total matter is equal to the total of both kinds of quantum cycles per second, they are different forms of matter and each has an existence that is distinct from the other. But in order to explain the role of rest mass in determining momentum, we must assume that the quantum rest mass cycles determine a scaling factor for quantum kinetic cycles. For example, when two material objects have the same velocity, but one has twice as many quantum rest mass cycles as the other, the one must have quantum kinetic cycles whose wavelengths and periods that are half the other object.

This scaling factor would explain why the momentum and kinetic energy of particles is proportional to the rest mass. But it is only a scaling factor for the quantum kinetic cycles required to move the object across space. The period of its rest mass cycles are not changed by the motion of the particle with rest mass. Quantum kinetic cycles are additional quantum events whose size depends on how many rest mass cycles occur during each unit of time as well as how far the object is moved during each unit of time.

Inertial mass. This is only a first approximation to the explanation of how the size of the quantum kinetic cycles depend on mass as well as velocity, because kinetic energy is an additional quantity of matter that coincides with the object with rest mass and that kinetic matter must itself be moved along with the object with rest mass. Thus, since the total number of quantum cycles per second that is being moved along by the kinetic matter includes both the quantum rest mass cycles and the quantum kinetic cycles of the objects, the scaling factor for quantum kinetic cycles must depend not only on the total rest mass cycles but also on the total quantum kinetic cycles. Let us call that combined total quantum cycles the “inertial mass” of the material object, to distinguish it from the rest mass. And let as refine our ontological explanation of momentum and kinetic energy to make them proportional to the inertial mass of the material object, rather than its rest mass.

The rate for the conversion of matter between mass and energy is given by Einstein’s formula, E = mc², and the simplest explanation is that it describes the rate at which additional quantum kinetic cycle contribute to the scaling factor. That fixes the number of quantum rest mass cycles for each unit of mass and constrains the explanation of rest mass by quantum cycles.

[However, the relationship may be more complex. It is possible that the quantum rest mass cycles constituting particles have a special nature (presumably because of how they depend on weakons and neutrinos and the unique structures that result), and each quantum rest mass cycle contribute more to total mass than a single quantum kinetic cycles. Let us proceed, however, on the simple assumption.]

[There is, however, no reason to doubt that the quantum kinetic cycles are simply added to the quantum rest mass cycles in determining the total mass (or energy, if you will) of the object. To be sure, the Einsteinian formula, E² = p²c² + m_o²c⁴, suggests that the contributions of rest mass ( m_o²c⁴) and the object’s motion (p²c²) to the total energy (E²) is more like orthogonal components of total energy as a vector sum. But this formula represents the object’s motion in terms of its momentum, that is, its spatial aspect, not its total energy. Energy is the temporal aspect of the quantum cycle, and both kinds of energy are included in this total. Furthermore, this equation merely describes the dynamic invariant that holds among inertial frames corresponding to the kinematic separation s (where s² = c²t² – x², and the parallel is m_o²c⁴ = E² - p²c²). But on the spatiomaterialist explanation of special theory of relativity, the tradeoff between total energy and momentum (in the temporal and spatial dimensions) that makes inertial frames equivalent in this way is just an appearance. Not only rest mass, but also the total energy and momentum have absolute values, though they cannot be determined empirically, that is, measured.]

This ontological explanation of inertial mass would account for the Lorentz distortion in the masses of material objects with a high velocity relative to the ether, or what is called the “relativistic mass increase” (which was promised in Change: Special theory of relativity). The reason that inertial mass increases with velocity is that the total mass of the material object includes both its rest mass (the quantum cycles constituting its mass when it is at rest relative to the inherent motion) and the mass of its kinetic energy (the quantum kinetic cycles that give the object a velocity relative to the inherent motion).

Thus, not only is more energy required to accelerate a material object by a fixed amount at higher velocities relative to the ether because of the laws of classical physics (with higher velocity the force has to be applied over a longer distance in the same period of time to increase its velocity the same way), but more energy is required to accelerate a material objects by a fixed amount at very high velocities because of the relativistic mass increase entailed by Einstein’s special theory of relativity (with very high velocities, the mass of the kinetic energy that must be accelerated along with its rest mass becomes significant). As the material object approaches the velocity of light, the mass of the kinetic energy matter (and, thus, the inertial mass) becomes infinite.

Interference phenomenon. Finally, this explanation of kinetic energy as a form of quantum matter affords an explanation of interference phenomena (and diffraction) with material objects, that is, the phenomenon that most clearly demonstrates the wave-like nature of particles.

In order for quantum kinetic cycles to explain the wave-like nature of moving material objects, we must take into account the role of the inherent motion. Quantum kinetic cycles move objects with inertial mass relative to the inherent motion in space, but they are usually much slower than the motion that sweeps each point both ways in every direction. Let us assume, therefore, that as that motion sweeps through a material object in any direction, it picks up the wavelength of its quantum kinetic cycle and lays out, in the space beyond it, waves with the same wavelength (until it runs into another object). Since the wavelength varies inversely with the product of the inertial mass and velocity, the waves laid out in space by the inherent motion, in effect, broadcast information about the particle’s momentum and phase of its quantum kinetic cycle in every direction in the ether. (Since the inherent motion flows in all directions, waves are laid out in all directions indicating its momentum in each direction, including those opposite to the direction of the particle itself.)

In order to explain how the inherent motion picks up the wavelength of the quantum kinetic cycle, we must assume that it interacts with the quantum kinetic cycle as a whole. It is as if the inherent motion timed how long it took to pass through the whole kinetic cycle and laid down a mark in space each time the same period had passed again. But notice that this period is not the period of the quantum kinetic cycle itself. The material object takes much longer to cross the distance covered in a single quantum kinetic cycle than the motion inherent in space, and thus, the inherent motion will take many trips across the distance covered by each quantum kinetic cycle before it is succeeded by another quantum kinetic cycle. This effect on the inherent motion would not be possible, if the kinetic cycle did not have a quantum nature, existing as a whole or not at all, for it must interact with both ends of the path across which the material object is being moved during each cycle. In other words, the kinetic energy, which is inversely proportional to the period of the quantum kinetic cycle, is not broadcast to other regions of space by the motion inherent in space. Only the momentum is. And that is fitting, since momentum is the spatial aspect of quantum kinetic cycles, whereas energy is the temporal aspect.

In order to explain the interference phenomenon exhibited by objects with inertial mass in the two-slit experiment, we must recognize that the inherent motion sweeping through a material object in each direction, picking up the wavelength of its quantum kinetic cycle, is part of a wave front. When particles with a certain velocity are moving toward the barrier with two, closely spaced slits, some particles pass through, and their collisions with the wall lying beyond the barrier indicates that the two pathways are interfering with one another like waves. The particles collide with the distant wall only along certain fringes, and not between them. This would be just what is expected, if we assume that the particle tends to move along the path of waves that have been laid out by the inherent motion. The wave fronts broadcast by the particle are intercepted by the barrier except for the two slits. The inherent motion stops laying out wavelengths in space where it is intercepted by the barrier, but it continues laying them out where it flows through the slits. Thus, on the other side of the barrier, there are two wave fronts laying out the same wavelengths, one emanating from each slit, and they interfere with one another like light waves. Assuming that the particle tends to fall in step with the waves that have always already been laid out in the space between the barrier and the distance wall, therefore, its path is diverted away from paths on which the wave fronts interfere destructively toward those paths on which the wave fronts interfere constructively. That is, the particle always tends to be where its wave front is strongest.

If we use the crude picture of quantum cycles as having a definite starting point and ending point, we can think of the particle as being subjected to a force at the completion of each quantum kinetic cycle, if it finds itself in a position where the waves being laid out from the two slit are interfering destructively, which changes its direction slightly. But when it ends a quantum kinetic cycle where the waves from the two slits interfere constructively, it simply goes with the flow. Thus, the effect is to channel the particle along a certain path way. The actual path will vary from particle to particle with the same momentum depending on the direction its emerges from the slit it passes through, and so it results in a fringe of more and less likely points of interception by the distant wall.

In other words, in both photons and material objects, the cause of interference phenomena is the inherent motion. In the case of photons, the inherent motion carrying the relevant wavelength goes through both slits setting up a pattern of spacetime cells where they interfere constructively, and the direction of the photon is diverted slightly in those regions. It is the same in the case of particles with inertial mass, except that the relevant wavelength is due to the quantum kinetic cycles of the particle. In both cases, therefore, the interference phenomena also occurs when particles (photons or objects with rest mass) are sent through the slits one at a time. It depends on the geometry of the inherent motion moving in certain directions laying out a waves of a certain length in space. And in both cases, if one of the slits is blocked — or even if an apparatus is set up that can detect which slit a particle goes through — the interference effects disappear.

Schrödinger’s equation. The quantitative adequacy of the wave pattern laid out by the inherent motion to explain interference and similar quantum phenomena has already been demonstrated, in effect, by David Bohm (1993), for this role of the inherent motion is an ontological explanation of what he calls the “quantum potential.”

What happens in these experiments on particles with rest mass can be described by the Schrödinger wavefunction, and Bohm shows mathematically how such a wavefunction can be divided into a part that is due to the causally relevant factors described by classical physics and another part which he calls the “quantum potential.” The quantum potential is a rather strange force, because unlike classical forces, its strength does not decline with distance. The quantum force can be quite strong, but its casual role does not come from its strength, but rather from its spatial structure. Bohm describes the quantum potential as “active information,” for he assumes that the particle moves with its own energy and momentum, while the quantum potential merely informs it about how to do so in detail. The particle has a definite position and momentum at each moment, but its classically determined path is affected by the quantum potential that exists along with it. The Schrödinger wavefunction holds for all particles with the same momentum in the two-slit experiment, but the effect of the quantum potential on any particular particle cannot be predicted, because it depends on a so-called “hidden variable”.

The quantum potential is the key to Bohm’s explanation of how the Schrödinger wavefunction can be understood as referring to a fully deterministic process, and this ontological explanation of interference phenomena is an example of how spatiomaterialism would interpret what Bohm means by the quantum potential. The quantum potential describes the waves laid out in space by the inherent motion for any relevant wavelength of kinetic quantum cycles or photons. The effect of the waves laid out by the inherent motion makes the quantum potential look like “active information” (or a “pilot wave,” as de Broglie called it), because the particle follows the nearest path to its classically determined path in which the waves coming from various directions reinforce, avoiding those in which they cancel out. But to explain the quantum potential by the inherent motion is to disagree with Bohm on one point, for he holds that the quantum potential is simply a manifestation of a “nonlocality” about what happens that simply exists in the quantum system and does not depend on anything traveling across space over time. But on this ontological theory, it is due to the inherent motion.

Furthermore, the inherent motion explanation of the quantum potential makes it possible to hold that the hidden variable, which determines how any particular particle is affected by the quantum potential described by the wavefunction, is the particular phase of its quantum kinetic cycle. That is, any particular particle has a definite position and momentum at the beginning and end of its quantum kinetic cycle, and the Schrödinger wavefunction describes precisely what happens to it as a result of the quantum potential. But it is not possible to measure which phase any particular particle has, and since that wavefunction also describes what happens to all other possible particles with the same momentum (the complex numbers enable it to take all the different possible phases into account), the outcome can be predicted only probabilistically.

Solutions to quantum puzzles. The nature of the three forms of quantum matter has explained several quantum puzzles, and Bohm’s interpretation of the Schrödinger wavefunction points the way to a solution of those that remain. We have seen how both photons and particles with rest mass have both a wave-like and particle-like nature, though they are fundamentally different forms of matter on this explanation and have fundamentally different explanations. Photons are waves that have a particle-like nature because each such bit of matter is a complete cycle of quantum events, whereas particles with rest mass have a wave-like nature because their motion is constituted by another form of matter attached to the rest mass that endures through time as a series of cycles of quantum events. This points the way to a certain kind of ontological explanation of quantum mechanics, and in order to test its adequacy, let us consider how it would handle the three quantum puzzles: the structure of the atom, Heisenberg’s uncertainty principle, and the Bell correlations.

Structure of the atom. Bohm’s interpretation of the Schrödinger equation is the key an ontological explanation of the structure of that atom. Schrödinger’s equation determines a wavefunction for the conditions that hold in atoms, with a positively charged nucleus surrounded by electrons (but since it is too complex to solve when many electrons are involved, each electron is usually treated separately, taking the mean position of the other electrons as boundary conditions). The time-independent Schrödinger wavefunction for the atom has an amplitude for the electron that varies with locations in space, and as Max Born suggested, the square of that amplitude (when normalized) in any region of space can be interpreted as the probability of finding an electron located there. The wavefunction describes various orbitals, or regions of space relative to the nucleus where two electrons (with opposite orientations of spin) are most likely to be found. This is the structure that explains the periodic table of elements and is used to explain chemical bonds among atoms.

The orbitals of the atom are identified by quantum numbers, such as the principle quantum number (indicating the energy levels: n = 1, 2, 3 . .), the orbital angular momentum quantum number (l = 0, 1, 2, . . ), and the magnetic quantum number (m, which determines the orientation of the orbital angular momentum as a magnetic moment it has in a magnetic field imposed in some direction). Electrons also have an intrinsic spin quantum number, s = ½, and two electrons, with opposite orientations of spin can occupy each orbital. Here is a rough description of the possible orbitals.

Electrons occupy shells, corresponding to different energy levels, and in the lowest energy shell (n = 1), there is only one orbital (the s orbital), which can contain two electrons (with opposite intrinsic spin). It has no orbital angular momentum (l = 0). The probability of finding the electron in the s orbital is highest at the center of the nucleus, and the probability of finding it farther away falls off exponentially.

In the second shell (n = 2), with the next higher permitted energy, there is not only an s orbital, but also three different p orbitals. The p orbitals correspond to electrons having an orbital angular momentum (l = 1, as if they were in orbit around the nucleus), and each such orbital has a node running through the nucleus, indicating that a p electron will never be found to be located where the nucleus is. Moreover, in the plane in which it has its orbital angular momentum, the real (that is, non-complex) component of the wavefunction’s amplitude has the p electron located in one or another region on opposite sides of the nucleus, that is, 180^o apart. Thus, since there are three p orbitals at the second energy level, atoms in which the second shell of electrons is full have (real valued) orbitals arranged in 3-D space that look like three, mutually perpendicular barbells.

In the third shell, at the next energy level, there is another s orbital, three p orbitals, and five d orbitals with a more complex geometrical structure, and so on through the energy levels of the atom. Since each orbital can contain two electrons (with opposite intrinsic spin orientations), the number of protons in the nucleus determines the structure of the lowest energy atom of each elemental kind.

In order to explain the structure of the atom ontologically, we need to recognize that it is constituted by three forms of matter and an interaction between them that can be seen as involving something in the nature of a photon (that is, virtual photons).

Rest mass matter. The particles with rest mass include the neutrons and protons that make up the nucleus as well as the electrons. But each proton and electron carries an electric charge, which is a form of force-field matter that helps constitute each particle, though as we have seen, the quantity of such matter is already counted in the rest masses of the particles.

Kinetic energy matter. Both the nucleus and the electrons are in motion as a result of their interaction, but the nucleus is so much more massive than the electrons that its quantum kinetic energy cycles are very small compared to those of electrons (and can be ignored in estimating quantities). Bohr assumed that electrons are in motion relative to the nucleus in order to explain the structure of the hydrogen atom, and despite doubts about electrons following determinate trajectories like classical material objects, it is clear that electrons have some kind of motion. (Electrons must move in order to have orbital angular momentum, and unless electrons in the s orbital had some kind of motion, there would be no explanation of how there could be s orbitals at higher energy levels.) Thus, according to this ontological explanation of the forms of matter, the electrons bound to the nucleus in an atom must have kinetic matter in addition to their rest mass matter, that is, the electrons are moved around by quantum kinetic cycles.

Force-field matter. Since protons and electrons carry opposite electric charges, they jointly impose a force field on the part of space occupied by the atom. The forces that these particles exert on one another change how they move, and the attraction of positive and negative charges is great enough to bind the electrons to the nucleus (with the negative potential energy representing the loss of some force-field matter that was counted in their rest masses as independent objects). But part of the force-field matter that the particles have given up still exists in the atom as the kinetic energy matter by which the electrons (and the nucleus) move across space as time passes, and the motion of electrons relative to the nucleus entails a change in the force field that is jointly imposed by them.

Virtual photons. The interaction between these particles is a process that is continually converting potential energy into kinetic energy and kinetic energy into potential energy, that is, converting matter between force-field matter and quantum kinetic cycles. Electrons (and the nucleus) are continually either giving up force-field matter and acquiring kinetic energy matter or giving up kinetic energy matter and acquiring force-field matter, and such transfers of matter are represented in the gauge field theory for electrodynamics as bosons, called "virtual photons."

The structure of the atom can be explained by the quantum nature of the kinetic energy matter of the particles with rest mass and the gauge bosons that transfer momentum and energy between them and force-field matter. Both the changes in the locations of the particles and the changes in the motion of the particles occur in a step like way, because they both involve quantum events. That can explain the structure of the atom, because those quantum events must fit together neatly in the spatio-temporal geometry determined by the inherent motion in space in order for them all to coincide with the same part of space. It is as if the quantum events constituting the atom were spatio-temporal bricks, and the existence of an atom were a result of their fitting together both spatially and temporally like a brick wall being built into the future. The masonry is so neat and well organized that the wall can be built indefinitely high, making the atom stable.

The quantum nature of kinetic energy matter means, as we are conceiving it in our possibly too crude way, that electrons (and nucleus) change location in a step-like way, that is, covering some whole distance in a period of time as a single, indivisible event. It is as if the electron must first complete an entire quantum kinetic cycle before it can change its momentum, and when it does change momentum, it must complete another complete quantum cycle before it can change again. Thus, only at certain locations and at certain moments does the electron change how it is moving.

Any changes that occur in an electron’s motion depends on the electric forces being exerted by all the electrons and protons, that is, on the field that they jointly constitute (because they are all made partly of force-field matter). These forces cause electrons to change how they move (that is, change their momentum), and that depends on some kind of (virtual) photon which gives the electron momentum and energy or takes it away. But on this model, such interactions occur only at the end of each quantum kinetic cycle, and it is a step-like change that determines the nature of the next quantum kinetic cycle. The quantum nature of the process makes the quantity of the change clear, because according to Newton’s laws of motion, the amount of energy and momentum that is transferred to the electron each time would depend on how much of energy and momentum the electron picked up from the force field matter in space during its previous quantum kinetic cycle. The change in the electron’s kinetic energy would depend on the distance it covered in the force field during the last kinetic event, and the change in the electron’s momentum (including its change of direction) would depend on the period spent being subject to the force field during the last quantum kinetic cycle. (Or more precisely, since the strength of the force varies over that distance and period, the change in energy would be the integral of the force over that distance, and the change in the electron’s momentum would be the integral of the force over that period of time).

This way of thinking about the quantum nature of the kinetic cycles may be an overly crude way of portraying the electromagnetic interactions, but the step-like changes bring out how the interaction involves not just the electron, but a complete quantum event making up its kinetic matter. The change occurs in a cyclic fashion, in which the last quantum kinetic cycle combines with the force-field matter to determine how much the next quantum kinetic cycle differs in momentum and energy. Such electromagnetic interactions are geometrically complex, because changes in electric forces cause changes in magnetic forces, which affect their motion, and what is more, these particles also have magnetic moments due to their intrinsic spin, which affects them in a different way. The way that these forces work is what is described by the gauge field theory for electrodynamics. The transfer of matter from force-field matter to kinetic matter or back is mediated by the gauge boson for the electromagnetic field, that is, by the exchange of a particle between them. This particle is like a real photon, because it is constituted by electric and magnetic forces interacting in some way. But it is unlike the photons that constitute light, because the momentum and energy it carries is not related by E = pc. They cannot have a constant proportion, because the energy and momentum needed to change the motion of objects with inertial mass as required by Newton’s laws do not have the same proportion in every case. (That is, momentum is a function of velocity, whereas energy is a function of the square of velocity, and so the proportion between them will vary with the velocity involved.) But this is just the nature of virtual photons, as opposed to real photons, which can exist independently and make up ordinary light. The matter constituting virtual photons can come from the force-field matter included in the rest masses of the particles, but they must have whatever unit-like nature is required to transfer all of the momentum and energy picked up from the force-field matter during the last quantum kinetic cycle at the moment that cycle ends, whatever the real nature of this possibly crude representation may be.

[When electrons do finally exchange a photon with the nucleus and their next quantum kinetic cycle is changed, they have a different location from where they were at the end of the last quantum kinetic cycle and their motion is changed for the next quantum kinetic cycle. This step-like change in their motion is the effect of virtual photons on the electron, but since the electron is a charged particles, it is also helping to impose the force field from which the virtual photons arises. And that is something that we must assume the electron does constantly, not just at the end of each quantum kinetic cycle, for as we shall see when we take up the gauge field theory, the electric charge is explained ontologically as a pulsation of electric forces emanating from the center of rest mass that is synchronized with electric charges throughout the universe. That is, all negative electric charges exert their maximum electric force at the same time in a cyclic way, and what makes positive electric charges opposite is that they exert their maximum electric force 180⁰ out of phase. (The synchronization of their pulsations is what is represented by their "orientation in complex vector fields," and the virtual photons of the gauge filed theory are the forces that must be exerted on charged particles as a result of their motion in order to conserve electric charge, that is, to keep their pulsations in synch with the universal pulsation of electric charges everywhere despite their motion.) In any case, in order to be able to explain quantum electrodynamics in this way, we will assume that electron is exerting its electric force in synch with the universal pulsation, and thus, it must occurs constantly during each quantum kinetic cycle. And that means that we are assuming that the electron has a determinate location at each moment during each quantum kinetic cycle. (For furthere discussion, see Change: Basic Objects: Gauge Field.)]

If the interactions among these forms of matter must have the unit-like nature that we are assuming explains Planck’s constant ontologically, the structure of the atom can be explained as a result of how all the kinds of quantum events involved fit together in the spatio-temporal geometry determined by the inherent motion in the part of space where they exist. This means that the interactions between the electrons and the nucleus would have a cyclic character, and all the interactions between electrons and the nucleus (as well as between the electrons themselves) would give them quantum kinetic cycles that are synchronized and related spatially, so that they fit together neatly in space and time like spatio-temporal brick in the atom as a brick wall being built into the future. But since there are slightly different combinations of momentums (quantum kinetic cycles) and positions (the locations where one quantum kinetic cycle ends and another begins), there is no way to say precisely where any particular electron is at any time.

Without trying to explain the orbitals in detail, it is clearly possible that the electrons are following determinate pathways as a result of interactions of this kind, changing their quantum kinetic cycles in a step-like way while all the time helping constitute the electromagnetic force field by way of their (pulsating) electric charges.

Though electrons in the s orbital are most likely to be found in the nucleus, that does not mean that they do not have a regular motion at all. Assume that each such electron is in a cyclic interaction with the nucleus in which it is accelerated first in one direction across the nucleus and then back in the opposite direction. The changes in how it moves come at the end of each lap when it is maximally far away from the nucleus, and it does not change its velocity during the trip, because it is a single quantum kinetic cycle (at least in the lowest energy state). That is, where one quantum kinetic cycle ends and another one begins, the electron changes its momentum all at once, without slowing down or speeding up. The reason it is most likely to be found at the center of the nucleus is that it can have any direction of back and forth motion through the nucleus, and the nucleus is the one part of space traversed by every possible pathway. At higher energy levels, the electron would be moving faster, and thus, it would have quantum kinetic cycles that are shorter and quicker, and at the n=3 energy level, it means that the electron has a good chance of being located either with the nucleus or at a distance from it, but not in between.

Electrons in the p orbital at the n=2 higher energy level have an orbital angular momentum. But it may seem that they cannot have a circular orbit around the nucleus in the relevant plane, because its orbital is usually represented as being a sphere located mostly on opposite sides of the nucleus. But the regions on opposite sides of the nucleus are just the real component of the amplitude its Schrödinger wavefunction, and the complex component puts it on opposite sides of the nucleus in the same plane, except for being rotated by 90⁰. The p orbital could, therefore, be a result of two quantum kinetic cycles, each trying to pull it back and forth across the nucleus in perpendicular directions (as in the s orbital), but perpendicular to one another. The quantum interactions with the nucleus that keeps changing their quantum kinetic cycles would have to be synchronized to occur 90⁰ out of phase to have this result, but that could be just the condition of such quantum events being able to coincide with the same part of space at all.

Even though different p orbitals are rotating electrons in independent planes of three dimensional space, they may also be synchronized in a certain way so as to keep the electrons from exerting too great a repulsive force on one another. (The general synchronization of these quantum kinetic cycles and changes in them is evident in the s electron at the third energy level, for its probable location is either outside the lower level shell or at the nucleus, suggesting that it is continually moving through those shells in some way.)

The reason that two electrons can fit into each orbital is that, with opposite orientations of spin, they can be synchronized in exactly the same way, but 180⁰ out of phase or in the opposite directions. Their opposite orientations of their intrinsic spins would exert a force (a "magnetic moment") that lines them up in opposite ways in the magnetic field, and that suggests that the magnetic fields plays the central role in making it possible for the exchange of virtual photons to generate such a neat pattern in the spatio-temporal geometry of the inherent motion.

Much more needs to be worked out in order to show how all the electrons in the orbitals could be following determinate trajectories determined by quantum kinetic cycles, but there seems to be no reason to deny that they have such step-like trajectories, even if they cannot be measured precisely. And it could be extended to include the other orbitals of atoms and the molecular orbitals that explain chemical bonds among atoms and groups of atoms.

Quantum jumps. Finally, the puzzle about the electron jumps entailed by the step-like changes in the energy level of atoms would be solved. All the changes in momentums of electrons, even those within its energy level, are step-like jumps. They occur at the end of one quantum kinetic cycle (in our possibly crude way of thinking about it) and before the next quantum kinetic cycle begins. It is clear that the change in energy state is a change in the orbital occupied by an electron is a step-like change, because it occurs with the absorption and emission of a single photon of the appropriate energy (and momentum). But that is just what would be expected, if the atom has a structure that is determined by the way that the quantum events of the various forms of matter constituting the atom must fit together in order to coincide with the same part of space given the spatio-temporal geometry determined by the inherent motion in space. The electron absorbs or emits a real photon, which changes its next quantum kinetic cycle so that it is part of a different orbital. The only possible changes are step-like changes, because they are changes in the structure of the atom.

The structure I have tried to describe here is the same structure that is determined by the “quantum potential” that David Bohm found in the Schrödinger wavefunction by mathematically separating out the classical forces. That left a force with a localized effect that did not decline with distance in the way electric forces do, but spread throughout space. Though Bohm thinks of it as “active information” which tells the electron how to play out its classical role, it can be explained, as I have suggested here, by recognizing that kinetic energy exists as a form of quantum matter by which objects with rest mass coincide with space, because that determines the same structure in the inherent motion in space. Quantum kinetic cycles and the inherent motion in which they are fit together are, in other words, another ontological explanation of Bohm’s quantum potential.

Lorentz distortions. By the way, this explanation of the structure of the atom affords an of the inevitability of the Lorentz distortions. In explaining the truth of Einstein’s special theory of relativity, I showed that the Lorentz time dilation and length contraction would be inevitable in the atom, if the electrons were bound to its nucleus by a unit-like two-way electromagnetic interaction. (See Change: Special theory of relativity.) That is apparently the implication of the Schrödinger wavefunction that describes the motion of such an electron subject to the positive charge of the nucleus, as can be seen in the s orbital.

The s orbital corresponds to a standing wave (as in a plucked string) without a node, and that means that the path of the electron is only half the total Schrödinger wavelength. (A standing wave of the complete cycle would have a node, because one half would be positive amplitude and the other half would have negative amplitude.) Since the momentum of an electron cannot change during a quantum kinetic cycle, it seems that either a single cycle of the wavefunction must be responsible for both legs of its trip across the nucleus, or else a complete cycle of the wavefunction is responsible for each leg. In either case, the electromagnetic interaction between the electron and the nucleus involves a two-way motion across the s orbital.

Such a two-way, unit-like interaction would cause Lorentz distortions in the atom, as explained in the discussion of special theory of relativity, because the inherent motion is what mediates changes in the force field (and quantum potential) caused by the electron motion. Thus, when the atom has a high velocity relative to the inherent motion, the periods of the cyclic interactions between the electrons and the nucleus increases (causing a time dilation), and the difference between the one-way velocity of light in opposite directions in space changes in the longitudinal distance across which they act (causing a length contraction).

As we have seen, the relativistic increase in inertial mass is simply the addition of quantum kinetic cycles to the rest mass cycles, which determines the scaling factor for quantum kinetic cycle and determines the force required to change its momentum. Thus, the quantum nature of matter affords an ontological explanation of the Lorentz distortions, which should eliminate the suspicion that they are simply ad hoc assumptions contrived to defend classical physics from the Einsteinian revolution.

Heisenberg’s uncertainty principle. The Heisenberg uncertainty principle holds that it is not possible to measure both the position and momentum of a particle, or indeed both members of any pair of complementary variables, with arbitrarily high precision. According to the Copenhagen interpretation, this is because these classical properties do not describe the real nature of what exists at the most elementary level. Position and momentum are just properties we read into the world by using instruments designed to measure material objects according to principles of classical physics. Since both position and momentum are needed to predict what a classical particle will do, the Heisenberg uncertainty principle entails, at least, a limitation in what can be known, and it can be taken to mean that what exists at one moment does not determine what happens the next moment, or the denial of determinism.

The Heisenberg uncertainty principle is equivalent, as mentioned above, to the non-commutability of operators on the Schrödinger wavefunction:

When the Schrödinger equation is set up for a given situation, such as an atom or the two-slit experiment, the time-dependent Schrödinger wavefunction is a complete description of how interactions unfold over time. They unfold in a completely deterministic way, just like a classical wave function, except that the Schrödinger wavefunction uses complex numbers to describe the wave and it describes a wave in a configuration space with as many dimensions as three times the numbers of particles involved.

In order to make predictions from the Schrödinger wavefunction, mathematical operators must be applied. They generate real numbers as expectation values for the relevant property. But what is predicted is either just a mean value for many such measurements, that is, a probabilistic prediction, or if it does predict a precise value for the property involved, that property is one of a pair of complementary properties, and the other member of the pair cannot be predicted precisely.

In other words, classical properties come in complementary pairs that do not commute. The values predicted for such properties depend on which complementary operator is applied first. The application of an operator changes the wavefunction, so that the next operator is actually applied to a different wavefunction.

When a measurement is actually made, the quantum system turns out to have a property with a determinate value. The standard interpretation of what happens in such an measurement is called the “collapse of the wavefunction.”

What actually exists in the system represented by a Schrödinger wavefunction is assumed to be a superposition of all the states that might be revealed by a measurement. That is, states corresponding to all possible outcomes of measurements actually exist at the same time. Thus, what happens when a measurement is actually made is that the wavefunction collapses into one of those superposed states. The system is changed, and then another wavefunction describes the system, representing a different superposition of states.

Since there is nothing to determine which way the wavefunction collapses, this view denies determinism. In effect, it explains the truth of the Heisenberg uncertainty principle by the actual indeterminacy about what happens.

There is, however, no collapse of the wavefunction, according to ontological explanations of quantum mechanics along the lines presented here. In any quantum system, every particle with rest mass has a determinate position and momentum and follows a classical trajectory, and measurements reveal properties that the system actually has. Instead of giving the system the measured property, as the “collapse of the wavefunction” interpretation implies, measurement discovers which property the system already had.

This way of interpreting measurements of quantum systems is entailed by an ontological explanation, because it explains the properties and regularities described by physics as aspects of the substances constituting the world (and if it is to be genuinely explanatory, it cannot depend on any randomizing factor assumed as part of the basic nature of the substances constituting the world). But the price of holding such a view is explaining why the Heisenberg uncertainty principle is true. And that can be accomplished by explaining why the operators corresponding to complementary variables are non-commutable.

The ontological explanation of complementarity is just the quantum nature of matter. What “quantum” refers to ontologically are the elementary events of which everything but space is composed. Each quantum event is a unit, which either occurs as a whole or not at all, and every such quantum event has the size of a single quantum of action, denoted by h, Planck’s constant. This explains, as we have seen, both the particle-like nature of photons as well as the wave-like nature of particles with rest mass. In the case of such particles, the complementarity comes from the quantum nature of their kinetic energy, that is, from the nature of the form of matter that changes the locations of particles with rest mass. Kinetic energy is constituted by quantum kinetic cycles, implying that the motion of a rest mass involves a series of cyclic quantum events, each of which is a unit of action that moves the rest mass across space a certain distance during a certain period of time.

What ultimately causes the Heisenberg uncertainty is the quantum kinetic cycle. The velocity of a particle with rest mass moving through space depends on the wavelength of its quantum kinetic cycle, but the particle can have a range of different positions in space at the beginning and end of each quantum kinetic cycle. That is, each quantum kinetic cycle involves a certain phase as well as a certain wavelength. But since the particle is located in a potential field, in order for its energy level to be fixed, a different location at the end of each cycle may require a slightly different wavelength the next cycle. Thus, the quantum state of the particle is some combination of wavelength and phase at its energy level, but there are many combinations that might satisfy those conditions.

Both complementary properties cannot be measured with arbitrary precision at the same time, because they are different aspects of the same bit of matter, which is a series of cycle of quantum events, each of which can interact only as a whole. Either it interacts in a way that reveals the wavelength of quantum kinetic cycle, which leaves its phase undetermined, or else it interacts in a way that determines its phase (that is, the position of the rest mass at the beginning or end of a quantum kinetic cycle), and its wavelength is undetermined. But both cannot be measured at the same time, because a quantum event interacts only as a whole. And complementary aspects cannot be measured is succession, because such interactions change the cycles of quantum events.

The Schrödinger equation describes the motion of particles with rest mass in a potential field where there is a continual exchange between kinetic energy and potential energy, and on this ontological explanation, the wavefunction that holds for any given system describes the quantum kinetic cycles that result for such an interaction. I have suggested what such an explanation implies about the atom and the two-slit experiment, but it can be generalized.

One way that the Schrödinger wavefunction is different from a classical wavefunction is that it is complex. There are complex numbers, involving the square root of minus one, that cannot be eliminated, and that makes its relationship to the actual world problematic. On this ontological interpretation, however, they represent the different possible phases of the quantum kinetic cycles constituting the momentum of the rest mass cycles. That is, on our crude interpretation, the starting points and ending points of the quantum kinetic cycles can have different locations in space and time and still be quantum kinetic cycles of the kind that can exist under those circumstances. The complex numbers are a mathematical device for representing all those different possible phases and keeping track of how they affect one another.

The other way in which the Schrödinger wavefunction is different from a classical wavefunction is that it describes a wave in a configuration space with three times as many dimensions as there are particles in the system, and that also makes its relationship to the actual world of three dimensions problematic. On this interpretation, however, each of the 3-dimensional spaces is used to keep track of how the phases of the quantum kinetic cycle a particle involved in the system unfolds in time. Though the quantum kinetic cycles of all the particles depend on classical forces and laws, each particle needs a 3-D space of its own in order to represent all its possible phases separately.

When a mathematical operator is applied to the wavefunction and a prediction is made about the value of some property, the different possible phases for all the particles are all reconciled with one another, working out the interference effects they have on one another. And the prediction is still usually just a mean value for many experiments, because there is a range of different states in which the system might be at that point, depending on which precise phases and wavelengths the quantum kinetic cycles actually had.

The reason that operators on the Schrödinger wavefunction do not commute is that they predict two aspects of the same quantum event, such as the wavelength and phase of the quantum kinetic cycle (as in the explanation of the Heisenberg uncertainty above). It is possible to predict a property precisely when it has already been measured once. But the wavefunction that represents the quantum system as having that precise property cannot be used to predict the complementary property of the particle precisely. For example, when a measurement of the momentum has been made, there is an operator that can be applied to the wavefunction that will predict the momentum precisely. But then the phase cannot be predicted precisely, because quantum kinetic cycles with that wavelength can have different phases. The same holds in reverse if the phase of the cycle is measured.

The “hidden variable,” on this explanation, is space and how bits of matter coincide with it, because the quantum nature of the kinetic energy of the particles is the factor that determines what happens to the particles. They need a complete quantum kinetic cycle to get from one place to another, and thus, at the end of each quantum kinetic cycle, the forces picked up during that cycle are what determines the next complete quantum kinetic cycle. The interaction is step-like, and though I may be portraying it too crudely by thinking of the quantum events as having definite beginning points and ending points, the requirement that particles travel across space by such cyclic quantum kinetic events is what needs to be added in order to see how what happens to the particle is determined.

On this ontological explanation, therefore, the quantum system is deterministic, and we can understand in principle how it is determined. But it is not possible to overcome the Heisenberg uncertainty because of the nature of the quantum kinetic cycles that constitute the motion of particles with rest mass. They exist only as a whole or not at all, and thus, they are the smallest unit that can interact with other bits of matter as a unit, which means in only one way at a time. That is, the uncertainty comes from an incompleteness about the representation of the Schrödinger wavefunction: it represents quantum kinetic cycles, but it does not reveal which of all possible combinations of wavelengths and phases is actual.

This incompleteness interpretation of the Heisenberg uncertainty solves the problem of Schrödinger’s cat. Such cases arise when the phases of the quantum cycles interfere in such a way that the system can unfold in radically different ways. For example, in one case Schrödinger’s cat is alive and well, and in the other case it is dead. On the collapse of the wavefunction view, the Schrödinger wavefunction is a complete description of the situation, implying that what exists is a superposition of all the possible outcomes, and thus, since it turns out one way or another when someone looks, which one actually happens must depend on the measurement. But if which of the radically different alternatives is actual depends on the phases of their quantum cycles at the beginning, it is determined, and the uncertainty about what happens comes from that information not being included in the wavefunction representing the system. The incompleteness is inevitable, but that does not mean that it is indeterministic.

The phenomenon of tunneling can also illustrate the uncertainty. In tunneling, a charged particle moves past a force field that is classically strong enough to contain it. It occurs, for example, when there is a potential barrier separating electrons from protons attracting them that is just large enough to overcome the attractive force between them. But different electrons have different quantum kinetic cycles, setting up different patterns of spacetime cells in the inherent motion, and depending on whether they reinforce or cancel out the waves set up by the kinetic cycles of the protons, the force of attraction will sometimes be great enough for the electron to tunnel across the barrier.

The situation can be described by a Schrödinger wavefunction, which represents it as a packet of waves, each standing for a different possible combination of positions of the particles. As the situation evolves, however, the packet splits into two different parts, one in which electrons escape and one in which they do not. Thus, the equation represents two distinct channels, which subsequently do not interact. Which member of the packet is actual depends on precise locations and kinetic cycles of the particles (both wavelengths and phases). But they behave in a way described by the Schrödinger wavefunction because they follow the wave pattern set up by their kinetic cycles (See Bohm Ch. 5).

Bell correlations. The final quantum puzzle is the violation of the “Bell inequality” by certain quantum systems. John Bell pointed out that quantum theory predicts that there are correlations between distant events that cannot be explained without supposing that there is a causal influence of some kind that travels between them faster than the velocity of light.

Bell correlations occur when symmetrical particles, with opposite spin orientations, travel apart from one another in opposite directions and the spin of each is measured far away from the other. They always have opposite spin orientations when measured by imposing a magnetic field in the same direction in space. When one is up, the other is down. But the spin orientation they have in one direction of three dimensional space should not affect the spin orientation in either of the other two independent directions of space. And thus, the measurement of the spin of one of the separated particles in one direction should not affect the spin measured in the other particle in a different direction. Nevertheless, it is possible to use the measurement of the spin orientation of one of the particles in one direction to predict better than expected what spin the other particle will have when it is measured in an independent direction. That would be impossible, if spin orientation is a property that each particle has from the moment they separate and carry with them.

The greater than expected correlations are predicted by quantum theory. The prediction is made by applying the appropriate operators to the Schrödinger wavefunction for the system, and so the measurements are usually interpreted as involving a collapse of the wavefunction. That makes it seem as though the measurement of the spin of one of the particles helps determines which orientation of spin the other particle will have.

The Bell correlation is not only a prediction of quantum mechanics, but it has been confirmed by experiments.

Bohm (1993, Ch. 7) treats Bell correlations like any other puzzling phenomenon predicted by quantum mechanics, that is, as an indication of the quantum potential. Bohm is also giving an ontological explanation, but on his theory, the quantum potential is just a “non-local” aspect of the processes themselves, as if the common pool of information were broadcast faster than the velocity of light. Indeed, Bohm takes the world as a whole to have such a non-local aspect to it.

Non-locality seems to deny substantivalism about space, and that would make it incompatible with spatiomaterialism. If space is a substance, then what separates one part of space (and what happens there) from any distant part of space (and what happens there) are parts of space between them that have an existence that is distinct from both of them. Thus, the only way that this real separation between the parts of space can be overcome is by something traveling across space as time passes. To put it negatively, immediate action at a distance would seem to deny that there really is any substance between the distant points of interaction that is enduring through time distinct from them.

The inherent motion in space is a dramatic way of representing this fact about space as a substance. It is, perhaps, conceivable that Bohm’s non-locality is compatible with spatiomaterialism, because I have been speaking of the inherent motion in a more realistic way than may be necessary. That is, instead of thinking of space as containing an inherent motion, we can think of space as having a spatio-temporal geometry. Thus, what I have described as waves laid out in space by the inherent motion could likewise be just an aspect of the essential nature of space everywhere that always exists at the moment. That is, when the quantum kinetic cycle of a rest mass coincides with space, it has a certain wavelength and phase, and that wavelength and phase give it a different relationship to other parts of space with the same wavelength that are in phase with it than it does with those that are not in phase. Thus, what I have described as a particle “broadcasting” its wavelength and phase throughout space would be just a relationship that always already exists in the spatio-temporal geometry of space. If that were how the quantum potential is mediated, as Bohm assumes, it would explain the Bell correlation in the same way as other quantum phenomena.

I doubt that any such ontological explanation is adequate, however, because in order to explain interference phenomena in the two-slit experiment, for example, the quantum potential at any point in space would have to depend not only on the wavelength and phase of the particle, but also on the geometrical structure of the wall with two-slits. The waves laid out by the inherent motion that guide the particle to one of the fringes of the interference pattern must be singled out from all the other spacetime cells by the structure of the apparatus and how it fits together with the wavelength of the particle, and that would also have to be something about each location in space that always already exists for each possible arrangement of particles and wall with two-slits. This would be to attribute an enormously complex structure to the essential nature of space at every moment of its existence, and the complexity of such an explanation makes it look rather ad hoc. It would be a much simpler ontological explanation if the quantum potential were determined by an actual wave from the moving particle in the inherent motion that interacts with the two-slit wall, but that is not action at a distance.

There is, however, another explanation of the Bell correlations which is compatible with the principle of local action. Contrary to what many philosophers and physicists assume, what is actually known about this phenomenon does not force us to believe that the principle of local action is violated. There is a way of interpreting these phenomena that is compatible with explanation of the quantum potential by waves laid out in space by the inherent motion.

The predictions from quantum mechanics have to do with measurements of spin orientation, and they cover only those cases in which both events are actually measured. As a matter of fact, however, every experiment that can test Bell’s theorem involves many, many runs in which a measurement is simply not successfully made of one or the other particle (or of both particles). It is possible, therefore, that the cases in which both measurement are made are a biased sample. That is, if we could know the spin orientations in all the cases in which two particles split, it could turn out that their spin orientations in different directions were indeed independent and there is no Bell correlation.^xxxi

Such a bias in the experiment cannot be just an accident. The many cases that must be ignored because no measurement was made must, for physical reasons, be mostly of a kind that, if included, would wipe out the improbable correlation between the distant events.

It may not seem like there can be any such factor, because the Bell correlations are predicted by quantum theory. That makes it seem that the Bell correlations are just another puzzling quantum phenomena, which manifest the same underlying mechanisms (whatever they are) as in any case of measurement. This is the assumption that is made in taking the correlation to involve the collapse of the wavefunction, except that unlike the other puzzling phenomena, it cannot be explained by the kinds of ontological causes described above, because Bell inequalities show that the collapse of the wavefunction involves action at a distance. That is, the hidden variable cannot be a local property, but must be a property that somehow holds of the whole system, including both particles, regardless how far they are apart at the time.

The prediction of the Bell correlation by quantum mechanics shows, however, only that some quantum phenomenon is involved. It may not, however, be the kind of phenomenon it is seems to be. The nature of intrinsic spin is not well understood, and it is treated as though it were completely described by the outcome of a measurement.

In the case of fermions, of particles with ½ spin, such as electrons, spin is measured by imposing a magnetic field and measuring the magnetic moment, that is, the force. The orientation of spin is simply the sign of that force, positive or negative: if the force is in one direction, it is spin up, and if it is in the other direction, it is spin down. Though that is how spin is measured, it is possible that particles have a more determinate spin orientation that is not measured in that way. An electron, for example, could have a precise orientation in three dimensional space, and though that is what determines the result of the measurement in the one direction that is singled out by the magnetic field applied, it also has other, more subtle effects on how the particle interacts.

In the case of photons, which are what has been used in the experiments that confirm the Bell correlations, spin is even more puzzling. Since the photon is a boson with a spin of 1, it should have three different possible orientations in a magnetic field, but since it moves through space with the velocity of light, one theoretically possible way of interacting is eliminated, leaving two possible orientations of spin. Opposite orientations of spin in the case of photons can be understood as opposite ways in which their electric force rotates as they move across space, one clockwise in the direction of motion and the other counterclockwise. However, it is usually measured by the polarization of the photon as it passes through a polarizer which is at rest and in which perpendicular directions, usually called vertical and horizontal, correspond to the two orientations of spin. But it is not clear why a rotation through a right angle would change whether a photon with, say, a clockwise rotation of its electric force, would pass through the polarizer.

In the case of both electrons and photons, there is enough uncertainty about the nature of spin and what is being measured that it is possible that the Bell correlations depends in some way on how spin orientation is measured. In either case, the three independent directions in which spin orientation (up or down or vertical or horizontal) can be measured are measured by an apparatus that is rotated in a two-dimensional plane perpendicular to the pathway of the particle. Thus, what may be a three-way symmetry among spins in three dimensional space is, in effect, reduced to a three-way symmetry in a two-dimensional plane. It is possible that in projecting that the three dimensional structure of spin orientations onto the two-dimensional plane of the measuring apparatus, some orientations of spin are more likely to pass by undetected than others, and they could be ones that would destroy the Bell correlation.

The selectivity may depend, furthermore, on an interaction between the actual orientation of spin in three dimensional space and the phase of its quantum kinetic cycle. Though the quantum potential that is responsible for interference and other real quantum phenomena requires a real effect propagating through space with the inherent motion, there could be an aspect of the waves set up in space by the inherent motion that makes all wavelengths with the same size and phase, wherever they exist in space, relate in a special way to the three dimensions of space. For example, the two particles have quantum kinetic cycles that are not only of the same wavelength, but also in phase with one another, and thus, if certain phases make it easier for them to interact from certain directions in three-dimensional space than others, the direction used by the detectors to test for spin orientation could result in a biased sample, making it appear that distant events are correlated. Such a factor would bias the sample in a way that makes it seem there are effect traveling faster than the velocity of light. And it would be local, because it depends only on the two particles having kinetic cycles that are in phase.

There is reason to think that some such explanation is correct, because Bell correlations occur only with measurements of spin orientation and the non-locality exhibited by the Bell correlations in measurements of spin is not an essential part of any other quantum phenomena. If it really were a result of action at a distance, it should be possible to make what happens at one location determine what happens elsewhere. But Bell correlations are not of a kind that can be used even to send signals from one place to another. In short, the Bell correlations are such a limited, subtle and questionable violation of the principle of local action that it would be foolish to use it as a reason for denying that spatiomaterialism can be used as an ontological foundation for a new way of doing philosophy, especially when that foundation works out so well in every other way.

Though much more would have to be said to show that this kind of ontological explanation of the nature of matter and space accounts for all the phenomena described by quantum mechanics, including quantum field theory and what it says about the nature of spin, this is enough to show that there is no good reason to believe that it is impossible to reduce quantum mechanics to spatiomaterialism. What is known by physics does not force us to give up the principle of local action entailed by this ontology, because neither experiment nor quantum mechanics is sufficient to demonstrate that the principle of local action does not hold. But this particular ontological theory is just a possibility introduced in order to speculate about a deeper explanation of the nature of matter and space, and what is relevant here is that, even this first approximation shows that there is no reason to believe that anything established empirically by quantum physics forces us to give up spatiomaterialism. There is at least one way that a two-substance ontology like ours can account for the quantum mysteries.

Let me emphasize, however, that it is not necessary to believe that what has been described here is completely accurate. It is only one of a family of ontological interpretations of quantum theory. What is common to the family is that the essential nature of matter involves the ability of bits of matter (of the same form) to exist independently of one another so that they can acquire spatial relations by being contained by different parts of space. There may be reasons for preferring another member of that family to this one. But this explanation of the quantum mysteries is enough to show that we do not have to give up the belief that space and matter are substances that exist continuously over time.

Cosmology. By “cosmology,” I mean the ontological explanation of those parts of the cosmos having to so with the extremes of the very small and brief and the very large and long-lasting. We have already explained ontologically the truth of the basic laws of physics governing the middle range involving ordinary material objects and their electromagnetic interactions. But as we recognized when we inferred to spatiomaterialism as the best ontological explanation of the natural world, the simplest and best form of any such ontology would hold that time, space and matter are infinite. Though we left open the possibility that a more complex ontological assumption may be required to explain certain phenomena, the ideal from of spatiomaterialism would hold that the universe is infinite.

The kind of infinity in question is twofold. Starting with the finite, there are two ways there could be an infinite series of steps, one by division into smaller and smaller finite units, and another by multiplication into larger and larger finite units. And there are three basic assumptions of spatiomaterialism to which it could apply: space, time, and matter. Let us consider where we stand on each of them.

Space. Space seems to be infinite in both ways, as we noted in Spatiomaterialism. There must be finite distances in space, for otherwise space would not have a geometrical structure at all. To hold that space has three dimensions is to hold that distances in it (and lengths of the objects coinciding with it) can be measured in three independent dimensions, say, by placing measuring rods down one after another. Each measuring rod is a unit, and since units that are parts of the same world can be counted [as established in Relations (Math)], distance measurements must obey the theorems of arithmetic, including division and multiplication. Thus, space can be infinite in two way, by an unending division of finite distances or by an unending multiplication of them.

If the division of finite distances in space is without end, space is continuous. That is what we have assumed, and we have found no reason to doubt that space is continuous.

If the multiplication of finite distances in space is without end, space is infinite in extent. That is the kind of spatiomaterialism that empirical ontologists must prefer, because it is the simplest assumption. Since the essential nature of each part of space includes its geometrical relations in three dimensions to every other part of space, an end to space in any direction would mean that every part of space has a different kind of essential nature from the rest, rather than the same kind of relationship to different particular parts of space. Not only would that complicate the nature of each part of space almost beyond recognition, but it would also be difficult, to say the least, to explain what happens at the end of space. As the ancient Greeks asked, What happens at the end of space? Does a spear thrown toward the edge of space bounce back?

Thus, we assumed that space is infinite in extent. But we acknowledged that we might have to revise that assumption, for that is the prevailing belief among bit gang cosmologists and a spatiomaterial world in which space is not infinite is possible.

Time. Time seems to be infinite in both ways as well. There are finite periods of time. There must be, because there are cyclic processes involving real change. Since such cycles are units that can be counted, the theorems of arithmetic must be true of measurements of time, including division and multiplication.

If the division of finite periods of time is without end, time is continuous. There is every reason to believe that time is continuous, because space is continuous and space has an inherent motion. If the division of time were not as unending as the division of space, there would be no explanation of motion, because objects could not occupy continuously connected parts of space as they endured through time. (And the original and still most basic employment of the calculus to represent motion in a way that overcomes Zeno’s paradox about motion would be a misrepresentation of the world.)

Furthermore, spatiomaterialism is committed to the continuousness of time, because it is entailed by the assumption of an inherent motion in space as an aspect of its essential nature. Each distance in space corresponds to a period of time, and thus, if space is continuously divisible, time must also be. (To be sure, it is not possible to measure space by the velocity of light because of the Lorentz distortions, and even if we could, it would not necessarily tell us about space itself because of the acceleration of the inherent motion in gravitational fields. But the relationship between space and time, though complicated in these ways, requires time to be continuous, if space is.)

If the multiplication (or addition) of periods of time is without end, time is infinite in extent, or what is called “eternal.” The eternity of the world is entailed by spatiomaterialism, because it assumes that existence is in time. That is, spatiomaterialism assumes that the world is constituted by substances of kinds that never come into existence nor ever go out of existence, but rather endure through time. That is what enables it to explain change as really occurring as time passes. Given its view of time and existence, spatiomaterialism cannot believe that there was a beginning to the world, because that would be to hold that something comes from nothing. Nor can spatiomaterialism hold that the world stops existing at some point, for that would be to hold that what exists can become nothing.

Matter. Given our ontological explanation of quantum mechanics, however, matter can be infinite in only one way. The existence of ordinary material objects shows that there are finite accumulations of matter, and since they are units that can be counted, theorems of arithmetic are also true of matter.

If the multiplication (or addition) of matter is without end, matter is infinite in extent, that is, the total quantity of matter in the world is infinite. There is no reason to doubt that the quantity of matter is infinite, if space is infinite, because there is no reason to believe that only a finite region of space has bits of matter coinciding with it. On the other hand, if space were not infinite, matter could not be infinite, at least not ordinary matter, because there would be no room for all of it.

We know, however, that the division of matter cannot go one without end, because the theory of quantum matter holds that each bit of matter is constituted by a series of cyclic quantum events, each with the size represented by Planck’s constant, h. The spatiomaterialist explanation of quantum mechanics is based on the assumption that quantum events have a unit-like nature in which they either exist as a whole or not at all.

To be sure, force-field matter, such as electromagnetic and gravitational fields, may be infinitely divisible. But that is because force field are just properties or conditions that are imposed on space by quantum matter, and the quantity of matter they contain is already counted in the rest masses of the material objects exerting them (except in the case of gravitational waves, which are eventually converted in quantum events as they accelerate bits of matter). Quantum matter is the basic form in which matter endures through time as a substance.

At this point, therefore, spatiomaterialism still takes space and time to be infinite in both ways and matter to be infinite in extent, though only finitely divisible. The final question in this ontological explanation of physics is, therefore, whether spatiomaterialism can keep this simple form. Do its assumptions about space have to be more complicated in order to acknowledge that space and matter are finite in extent? Can its assumption that matter is not infinitely divisible be squared with what physics knows about the basic objects? And do we have to accept that time is not eternal and admit that spatiomaterialism is just an effect of a deeper, theistic ontology in order not to give up ontology altogether? These are the cosmological questions that spatiomaterialism must answer. The issues to be addressed can be separated into two sets, one having to do with the finite divisibility of matter and the other having to do with the infinite extent of space and time.

Finite divisibility of matter. Though spatiomaterialism has assumed that matter is constituted by cyclic quantum events in order to explain the truth of quantum mechanics, it had to take for granted that electrons and the nuclei of atoms can be explained in as a form of quantum matter. This is clearly not the deepest truth about nature, since physics has found other particles like electrons that are much heavier, and some that are massless and carry not electric charge at all. And it has discovered not only that the atomic nucleus is composed of protons and neutrons, but also that such nucleons are composed of quarks, not to mention the two short range forces involved in the interactions of its basic objects.

The main question is not whether the rest masses of the basic objects of physics can be explained ontologically as forms of quantum matter. There is not much reason to doubt that it is possible to give such a spatiomaterialist ontological explanation, though some might find it reassuring to see how it works out in more detail. But there is a reason to take up the issue of the nature of the most basic objects here. It is another opportunity to show the fruitfulness of an ontological explanation of the world based on spatiomaterialism.

Physics now recognizes some 38 different kinds of basic particles (counting antiparticles, but not the three colors of each quark), and though they are a far less unruly lot than the particles recognized by physics thirty years ago, they are still an odd lot. Part of the problem is that the four basic forces of nature have not yet been fully unified. Even if we count the so-called electroweak force as the unification of the electromagnetic and weak forces, the strong force still resists assimilation as part of a single gauge theory, and as we have noted, physicists are at wits ends about how to represent gravitation as another force of the same kind. Particle physicists believe that there must be a deeper theory, but the dramatic progress of high energy physics during the 1970’s and 80’s has come to a halt in the 1990’s. And they are still pursuing the “holy grail” of physics, a single mathematical law from which the laws describing all the forces of nature can be derived.

The possibility that is not even being considered in this effort is explanatory ontology. As we shall see, by recognizing that space is a substance, it is possible to reduce all the basic particles of physics to nine or ten kinds of particles (including antiparticles). Indeed, it may even be possible to formulate spatiomaterialism in a way that reduces everything to just three basic particles — and space, of course, as the substance with which they coincide.

Infinite extent of space and time. In the direction of very large and very long-lasting, spatiomaterialism must be false, if contemporary cosmogony is correct, because it is currently assumed that the universe began with the big bang and has been expanding ever since. Indeed, the prevailing theory implies not only that the universe had a beginning in time, but also that space and matter are finite in extent. And some even interpret it as imply that the universe might simply drop out of existence at some time in the future (if it collapses because of gravitation), implying that time is also finite in the direction of the future. There are both theoretical and empirical reasons for believing that the universe began with a big bang and continues to expand, though as we shall see, spatiomaterialism can be defended against both.

On the theoretical side, Einstein showed how his general theory of relativity could be used to represent the universe as a whole, and with a relatively minor revision, that approach can be used to represent the expansion of a universe being contracted by gravitation in a mathematically precise way. That is the Einstein-de Sitter model, as it is widely accepted by cosmologists as explaining the expansion of the universe.

The empirical reasons are Hubble’s discovery of a correlation in galaxies between their red-shift and distance which suggests that galaxies are all rushing away from one another, the discovery that the proportion of hydrogen and helium in the universe is explained by their synthesis shortly after the big bang, and the discovery of a cosmic background radiation that seems to be the left over from the big bang (with wavelengths elongated by the expansion of space in the interim).

Spatiomaterialism can, however, be defended against both kinds of reasons. Its critique of Einsteinian cosmology is based on the spatiomaterialist explanation of the truth of Einstein’s general theory of relativity and its explanation of the relationship between gravitation and the other basic forces of nature. And spatiomaterialism offers another way of explaining all the empirical evidence for the big bang and the expansion of the universe. It is an approach to cosmological issues that is not even being considered these days. Not only is it a plausible defense of spatiomaterialism, but it also illustrates the fruitfulness of spatiomaterialism in opening up new ways of explaining natural phenomena.

Let me emphasize, however, that it is not necessary to defend such a cosmological theory in order to spatiomaterialism as the ontology for our new way of doing philosophy. What physics has discovered about the basic particles does not even suggest that spatiomaterialism is false, and like quantum mechanics, we could simply take it for granted that a spatiomaterialist theory can be formulated. To be sure, big bang cosmogony does contradict spatiomaterialism. But scientists generally are not confident enough of its conclusions to use them as a reason for dismissing spatiomaterialism out of hand. Popular culture seems to be confident of the big bang, and the Church has welcomed it warmly. But among scientists, cosmology is still a matter of hot dispute.

There is, however, a point in carrying this project to the extremes of the very small and brief and to the very large and prolonged, because it turns up certain advantages of recognizing that space is a substance. There are straightforward ways of elaborating spatiomaterialism into an ontological explanation of cosmological phenomena, and hopefully it will do not harm to suggest them here.

This part the spatiomaterialist ontological explanation of the world is even more speculative than its explanation of quantum mechanics. It is included here in the spirit of exploration. By offering an ontological explanation, I do not suggest that these problems can be solved in the end without the use of mathematics to calculate quantitatively precise predictions and the attempt to make the appropriate measurements. Ontology is a deeper explanation than the efficient-cause explanations of empirical science, but it is not a substitute for them. An ontology must be able to explain why those efficient-cause explanations are true in order to be adequate.

Physics is, however, so dependent on the use of mathematics for representing the world that it has given up the intuitive insights that would come from recognizing that the world is constituted by space as well as matter. In explaining the truth of the special theory of relativity, the general theory, and quantum mechanics, we have seen how ontology offers a more intuitive explanation of these phenomena, one that uses our capacity to imagine space and time to think of space and matter as substances enduring through time and, thereby, constituting the natural world. Thus, it would not be surprising at this point, if, together with the enormously powerful constraints that mathematical theories impose on what is possible, the attempt to formulate an ontological explanation illuminated possibilities in the vague darkness that lies beyond what is firmly in the grasp of experimental physicists that turn out to be true.

Though I claim that the following theories are true, I am not claiming that the following explanation is the only possible spatiomaterialist explanation of cosmological phenomena, nor even that it is the best. My only claim is that it is a spatiomaterialist ontological explanation, and it does enable us to discuss these issues in a new and illuminating way. It explores an avenue that physics will travel, when it acknowledges that ontology is explanatory and uses the empirical method to infer to the best ontological-cause explanation, not just the best efficient-cause explanation. But even before it proves itself in that more demanding arena, it is possible to get a glimpse of how how the world is whole even at the extremes of the very small and the very large.

Basic objects. Let us first extend this ontological explanation in the direction of the very small and the very brief. The place to begin is with the so-called “Standard Model” of physics and the inventory of the basic forces and particles included in it. (A history of the history of particle physics by one of the participants that I would recommend is 't Hooft (1997)).

Basic particles of physics. In order to set the scene for inventorying the basic particles of physics, I will first describe more fully a basic difference that physics recognizes between two kinds of basic objects, fermions and bosons. Gauge field theories hold that forces are mediated by bosons, the so-called gauge particle of the underlying field, and the next step will be to describe the two forces of nature in these terms. That will put us in a position to list all the kinds of basic particles currently recognized by contemporary physics.

Fermions and bosons. The most fundamental difference among basic objects in space is that between fermions and bosons. (It is basic to the Yang-Mills field theories which are currently used to explain the basic forces.) This difference is exemplified by electrons and photons. As a first approximation, fermions, such as electrons, are the material objects on which forces the work, whereas bosons, such as photons, are the forces that work on them. Though the difference is more subtle, this contrast points to the basic difference in their roles.

Fermions are basically particles that exclude one another from occupying the same quantum state, whereas bosons are particles that tend to fall into the same quantum states. To put it more precisely, fermions obey the Pauli exclusion principle, while bosons do not. They behave according to Bose-Einstein statistics, as opposed to Fermi statistics.

The difference between them is the kind of intrinsic spin they have. Spin is the quantum mechanical version of a rotating object with an electric charge. It is a measure of the magnetic moment exerted by the particle when a magnetic field is imposed on it. But there are two different kinds of spin, distinguishing fermions and bosons.

The Pauli exclusion principle holds of any particle with some multiple of ½ spin (. .-5/2, -3/2, -1/2, 1/2, 3/2, 5/2, , ,) whereas Bose-Einstein statistics hold of particles with an even number of spin (. .-2, -1, 0, 1, 2, . .). The spin indicates the number of different forces the particle might exhibit when a magnetic force is imposed on it from a certain direction. The number is equal to 2s + 1. Thus, a particle with 1/2 spin can exert one of two possible forces when placed in a magnetic field, either positive or negative (up or down), whereas a particle with spin of 1 can have one of three values, positive, negative, or zero. Among the basic particles, however, there are only three kinds: particles with ½ spin, particles with a spin of 1, and particles with a spin of 0. The other values of spin come from combining basic particles. (Actually, Yang-Mills field theory recognize only particles with a spin of ½ and 1, but it has been necessary to add particles with 0 spin in order to explain the rest masses of particles.)

Fermions have the nature that makes them most like ordinary material objects, for they exclude one another from occupying the same place at the same time. The structure of the atom, for example, depends mainly on the Pauli exclusion principle. The various electron orbitals are distinct quantum states, and since electrons are fermions, only one electron (of each kind) can occupy each orbital. (The reason that there are usually two electrons in each orbital is that there are two opposite kinds of electrons, spin up and spin down, and one of each kind can fit into each orbital.)

Bosons are the particles that mediate the forces of nature, and they are called particles of the underlying field. Whereas basic fermions are point-like in the sense that they are located at each moment at a certain point in space, bosons have a nature more like space itself, because they emerge from the underlying field to mediate its forces.

Particles susceptible to a force are said to have a “charge,” but in order to conserve the charge so that it does not disappear (or multiply) as the particles move and interact, the force field laid out in space associated with the charge generates bosons, or forces, that act on the particle in certain ways, changing its motion or even its kind. This is called “local symmetry,” but it is basically the regularities about the particle that must hold in order for the “charge” to be unchanged.

One basic difference between electrons and photons does not, however, hold generally for fermions and bosons. Electrons have a rest mass, whereas photons are massless particles. But this contrast in rest mass crosscuts the distinction between fermions and bosons. There are massless fermions and massive bosons.

Though most fermions have rest mass, there is one set of fermions that, as far as physics can tell, do not have any rest mass at all. They are called “neutrinos,” which are affected only by the weak force (see below). Theory does not require them to have a rest mass, and experiments have made it clear that the maximum mass they can have is about 12 eV.^xxxii With a spin of ½, neutrinos should have two possible orientations of spin, but in this case, having opposite orientations of spin is what distinguishes each kind of neutrino from its antineutrino. Normally, antiparticles have opposite electric charges, but neutrinos have no electric charge, and the opposite orientation of spin is equivalent to having an opposite weak charge. The neutrino has left-handed spin in the direction of its motion, and the antineutrino has right-handed spin. They are mirror images of one another. (As massless particles, the fact that each kind of neutrino has only one orientation of spin, despite having a spin of ½, could be explained in much the same way as it is explained in the photon: one orientation of spin is lost because they move at the velocity of light, because they cannot stop to turn around so that they can interact from the other direction.)

Though photons are massless, there are bosons with mass. Mass would be expected in bosons that are merely fermions locked together in a way that neutralizes (or combines) their opposite orientations of space so that they have a net spin that is an even number, such as the helium atom. But bosons that are basic particles mediating the forces of some underlying field are expected to be massless, and thus, the discovery that the bosons mediating one of the basic forces of nature have rest mass (the weak force) posed a problem that had to be overcome. Let us turn, therefore, to the basic forces of nature.

Basic forces of nature. Physics recognizes four forces in nature (gravitation, electromagnetism, the strong nuclear force, and the weak force), and attempts to knit a mathematical description of them into a single, uniform deductive system have used the mathematics of gauge field theory (Yang-Mill gauge invariance). Since bosons are the kind of particle that emerge from the underlying field to mediate those forces, they can be called gauge bosons.

Electromagnetic force. We have already seen how the electromagnetic force can be explained ontologically, and in passing, I have mentioned the gauge field theory of electromagnetic interactions.

Basically, the electric charge is represented as having an orientation in a complex field, and the electromagnetic forces affecting it are what is required for local symmetry, that is, for the charge to keep the same orientation in the complex field as the particle changes location in space.

What I have described as the force field matter of an object with rest mass is a way of referring to the electric charge of such a particle, and the gauge field theory about how it works can be explained ontologically by thinking of the force field matter of an electric charges as something that is imposed on space in a cyclic way as time passes, as if the force were sent out from the object in regular pulses. If the pulses of all negative charges throughout the universe were synchronized, it would be possible to explain what is meant by “orientation in a complex field,” for it would be the phase in that cycle. Negatively charged particles would all be pulsing at the same time, jointly setting up the force field in which they are located. The pulses would propagate at the velocity of light, since they are mediated by the inherent motion in space. And since the force field that acts on the charged object is pulsating, its charge must remain synchronized with the field, even though the particle may be changing locations in space. Gauge bosons emerge from the field to keep the charge synchronized, but they can do so only by exerting forces on the particle that can change its motion, accelerating it in one direction or another. Those forces are the electric and magnetic forces described by Maxwell’s equations, and the gauge boson is the virtual photon mentioned in explaining the quantum structure of the atom. Virtual photons carry momentum and kinetic energy between charged particles and the force-field matter the particles jointly spread out in space by their pulses. They are the spin 1 particles that mediate the electromagnetic force.

The difference between positive and negative charges could be explained on this ontological explanation as having pulses with opposite phases in that universally synchronized cycle. Particles that pulsate in phase would repel one another, whereas particles that are pulsing out of phase with one another would attract one another. This dependency of the direction of the force on the phase of the universal pulsation is the reason that there must be virtual bosons to keep charges synchronized with the universal pulsation as the charged particles move across the force field they help set up (the force-field matter that comes from all the particles).

Partial electric charges could likewise be explained as phases relative to the universal electromagnetic pulsation (or as orientation in the complex field) between the extremes of negative an positive. But in order to take account of the magnetic force, the complex field in which charges are oriented may be twofold, and the pulsation correspondingly compounded.

[The mathematics of quantum electrodynamics, and gauge field theories generally, makes it difficult to figure out how a particle will move and interact in the field. Richard Feynman discovered a relatively simple way of doing so by identifying the path of least action from all the possible paths the particle could follow (which is ontologically, the path requiring the fewest quantum cycles). He showed how it could be identified by rules for canceling out more complicated, symmetrically opposite pathways and seeing what remains. This was the foundation for his famous “Feynman diagrams,” which depict electromagnetic interactions between particles as being mediated by the exchange of photons. But the mathematics involved is suspect in the minds of many, because the calculations lead to infinite quantities, which can be eliminated only by hand, canceling out those that are opposed symmetrically, in a process called “renormalization.” There must be a deeper explanation of what is going on.

[This aspect of quantum electrodynamics and other gauge field theories can be explained ontologically, I believe, in a way that involves the waves we have assumed are sent out in the inherent motion by quantum kinetic cycles. The symmetries that Feynman uses to determine the path of least action can ultimately be explained ontologically by the constructive and destructive interference of such waves (much as I have used them to explain Bohm’s “quantum potential”). But it is more complex, because the particle is carrying an electric charge through the force field, and if the force field involves a universal pulsation which constitutes the difference between positive and negative charge, the virtual photons must be synchronized with it in order to conserve the electric charge. I suspect there is some such ontological explanation, but it would take a better grasp of the mathematics than I have.]

Strong force. The strong force is the force that accounts for the nucleus of the atom. Being is about 100,000 times stronger as the electromagnetic force, it holds protons and neutrons together despite the strong repulsive forces among the positively charged protons. The strong force does not affect electrons or neutrinos (or other particles of their kinds).

The particles involved in the strong force are called “hadrons,” both the particles affected by it and the particles whose exchange mediates it. The strong force that holds the nucleons together is mediated by the exchange of mesons (such as pions). But protons and neutrons are only a two of many kinds of “baryons” that have been discovered by accelerating particles to collide with one another at very high energies, and various kinds of mesons have also been found mediating interactions among them.

The neutron, for example, decays into a proton, an electron, and an electron antineutrino, and there are many other kinds of baryons that decay into protons or neutrinos, with similar kinds of debris. The negatively charged pi meson (pion) decays into a negative mu lepton (a heavier cousin of the electron) and an mu antineutrino. Again, there are many kinds of mesons with various decay patterns, so of which decay by way of a pion.

The attempt to explain the diversity in the kinds of baryons and mesons has led to the recognition that hadrons are all composed of simpler objects, called “quarks.” Baryons are constituted by triplets of quarks, and that mesons are constituted by quark-antiquark pairs. There are some six different kinds of quarks, each with an antiquark, though only the two lowest energy quarks (u and d quarks) are found in the nucleons of ordinary matter. Half the quarks have a negative electric charge of 1/3, and half have a positive electric charge of 2/3 (with their respective antiquarks having electric charges with the opposite sign).

Interactions among quarks are mediated by the "color" force. That is, quarks have a “color charge” which makes them susceptible to the color force, and quarks interact with one another by exchanging gluons, the gauge particles of the color force. Gluons are, therefore, bosons with an intrinsic spin of 1. They are massless particles, like the photon. But unlike the photon, gluons are themselves subject to the color force, that is, they exert color forces on one another as well as on quarks. Photons, by contrast, do not interact at all, except for their tendency as bosons to fall in step with one another.

The color force has an unusual strength that keeps quarks confined in triplets to baryons. When quarks are very near one another, the color force is not very strong. But when the distance is increased, the color force increases along with it. And if the distance increases enough for the potential energy (or force-field matter) to constitute a quark and antiquark pair, matter takes that form. The quark of the new quark-antiquark pair replaces the quark that was being moved out of the baryon, and the antiquark combines with the original quark from the baryon to constitute a meson, which quickly decays.

In order for three different quarks of the same kind to help constitute a single baryon, there must be three different “colors” of each kind of quark. And according to the symmetry of the theory, eight kinds of gluons are needed to mediate all the forces that hold among three different kinds of quarks in constituting baryons.

Weak force. The weak force has long been recognized because of the need for some force to explain the radioactive decay of natural substances, such as radium. Natural substances send out particles with rest mass from time to time which can be detected, and since that suggested that they were somehow coming apart, a force was needed to explain how it could happen.

The weak force was soon also used to explain the decay of hadrons (baryons and mesons) into more common particles, such as neutrons, protons, electrons, and neutrinos, which were observed in high energy collisions of particles in accelerators. Indeed, there are also higher energy particles like the electron, such as the muon and tau particle, which decay into the electron and an antineutrino (or if they are positively charged, decay into a positively charged electron, or positron, and neutrino), and those decay patterns were also attributed to the weak force.

In order to explain these decay patterns on the model of gauge field theory, it was recognized that every kind of particle carries a “weak charge,” which makes it susceptible to the weak force. The weak force is mediated by a kind of particle, which was originally called the “intermediate vector boson,” but is not referred to as the “weak boson” or “weakon.” As the gauge particle of the weak force, the weakon is a boson with spin 1, and in order for electric charge to be conserved in decay by the weak force, there had to be two different kinds of weakons, one with a positive and one with a negative charge (W^- and W⁺⁾.

It is called the weak force, because it is so much more difficult to make particles interact in this way than by the strong force (or even that the electromagnetic force, which is about 100 times weaker than the strong force). (The weak force is about 10^-6 times the strength of the strong force, whereas the electric force is 10^-2 times the strong force.) According to recognized principles, the weakon could still actually be a force comparable in strength to the photon, if the weakness of the weakon were due to having a considerable mass. But the assumption that the weakon had such a mass spoiled the gauge theory: the weakon could no longer represented by Yang-Mills mathematics.

In one of the most famous discoveries of the past few decades, Weinberg and Salam independently discovered a way to give the weakon a mass without spoiling its role as the particle of a gauge theory. This was to postulate the so-called Higgs boson and to assume that such particles exist everywhere in space. The Higgs boson has a spin of 0, lacking any orientation at all in a magnetic field. But to postulate their existence everywhere in space was to postulate the existence of a new field that has minimum energy when it is exerting a force everywhere in space. That force could be used to explain why a boson, such as the weakon, that is otherwise massless has a mass.

Weinberg recognized that this explanation of the mass of the weakon implied that, in addition to the negatively charged and positively charged weakons, there is a weakon that does not carry an electric charge at all (Z⁰). Interactions involving the Z⁰ would not change the electric charges of the particles, but only their motion, as in an elastic collision, and when evidence for such “neutral currents” was found, it was recognized that Weinberg had discovered a theory that explained both electromagnetism (how charges interact by way of virtual photons) and the weak force (how particles generally interact by way of virtual weakons). It is sometimes called the “electroweak force.” (The color force, however, resists assimilation to that theory. Though it is possible to construct the appropriate equations describing gluons as the gauge particle mediating interactions among quarks (and gluons), it has not been possible to figure out what the equations imply.)

Gravitation. The success of gauge field theories in representing the other forces of nature has led to attempts to represent gravitation as force that is likewise mediated by the exchange of particles from an underlying field. The “charge” on which the gravitational force works is mass, and the gauge particle that mediates the gravitational force is called the “graviton.” However, in order to serve this function, it must be a boson with a spin of 2, and the attempt to integrate this force with the other three forces of nature what has led to superstring theory and the belief that there are as many as ten dimensions to space.

Though the mathematics of superstring theory is supposedly elegant, the need to recognize additional dimensions of space, if nothing else, makes it suspect. And it can be avoided, as we have seen, by recognizing that space is a basically different kind of substance from matter. Assuming that there is an inherent motion in space by which bits of matter coincide with parts of space (and that is possible, as we have seen, by the spatiomaterialist explanation of the truth of Einstein’s special theory of relativity), gravitation can be explained as an acceleration of an inherent motion in space. That is the spatiomaterialist explanation of Einstein’s general theory of relativity.

This is a radical departure from contemporary physics, because without recognizing that space is a substance, it has no other way to explain gravitation than as just another field that holds among particles. That is what leads to the belief that gravitation is mediated by gravitons and poses what is the most formidable problem for contemporary physics: connecting gravitation with the other forces of nature.

Substantivalism about space makes it possible, however, to explain basic particles in a way that may be similar to superstring theory, but without the extra dimensions.

Catalogue of basic particles. Let us catalogue the basic objects that are currently recognized by physics, and then we shall see how we might account for all of them quite simply, given our ontology. The objects that are currently taken to be basic include both bosons and fermions.

The bosons are the particles mediating the forces. According to current gauge theories, there are bosons for each of the four forces, including the graviton to mediate the gravitational forces. (See diagram of Basic Particles of Physics.)

Current explanations of the weak force requires the postulation a Higgs boson, with a spin of 0, to give weakons (and other particles) their rest masses.

Three weakons mediate the weak force: W⁺, W^-, and Z^0, each with a spin of 1.

The photon is the gauge boson that mediates the electromagnetic force. It also has a spin of 1.

Eight gluons mediate the color force, each with a spin of 1.

The graviton is the boson that is supposed to mediate gravitational forces, but it can be set aside, since I have already explained gravitation without the need for any such particle.

Fermions are particles that obey the Pauli exclusion principle and have a point-like location in space. There are two broad classes, leptons and hadrons. The hadrons are distinguished by their susceptibility to the strong force, while leptons are immune. Electrons are the most famous members of the lepton group. Their masses are well defined, and their name, meaning “light ones,” comes from being so much lighter particles than hadrons (and even than quarks). But some physicists suspect that neutrinos may not be quite massless. There are six leptons in all, and each has an antiparticle.

The first family of leptons includes the electron and the electron neutrino. The electron has a charge of –1 and a mass of 0.5 MeV/c², whereas the electron neutrino has no charge and there is not much reason to believe it has any mass at all. The antiparticle of the electron is the positive electron, or positron, with a charge of +1, and the antiparticle of the electron neutrino is the electron antineutrino, with neither charge nor rest mass.

The second lepton family is composed of the muon and the muon neutrino. The muon has a negative charge and a mass of about 106 MeV/c²,whereas the muon neutrino has no charge and no rest mass. Again, both members of this family of leptons have an antiparticle, the positively charged muon and the muon antineutrino, without any charge or rest mass.

The third lepton family is composed of the tau particle, with a negative charge and a mass of 1784 MeV/c² and the tau neutrino. Both have antiparticles with properties similar to the first two families of leptons.

Hadrons are the objects affected by the strong force, and they are made of quarks, as we have seen. (Baryons have three quarks each, whereas mesons are made up of a quark and antiquark.) Let us inventory the quarks, since hadrons have already been reduced to them. Most commentators are struck by how the quarks also fall into three families, with two particles each, both with antiparticles.

The first family of quarks includes the d and u quarks, and an antiparticle for each. The d quark has a charge of -1/3, while the u quark has a charge of +2/3, setting the pattern for all three families. The masses of quarks are not well defined, because they cannot be released from confinement in baryons or mesons, but the d and u quarks do not appear to be over 100MeV/c² (and may be considerably less). Their antiparticles are antiquarks, with opposite electric charges, that is, anti-d, with +1/3 and anti-u, with –2/3.

The second family includes the s quark and the c quark, and their antiparticles. The s quark, with a charge of –1/3, resembles the d quark, but it has a mass of about 200 MeV/c². The c quark likewise resembles the u quark, except it has a mass of about 2000 MeV/c². Their antiquarks have the same masses, but opposite electric charges.

The third family includes the b and t quarks. The b quark resembles the d and s quarks, with a charge of –1/3, while the t quark, with a charge of +2/3, resembles the u and c quarks. Again the main difference is in mass. The b quark has a mass of about 5000 MeV/c², while the t quark has a mass of about 175000 MeV/c². Their antiquarks have opposite electric charges.

The accompanying diagram listing all the basic particles recognized by physics suggests the deep symmetry that is believed to hold between the quarks and leptons. Each has three families; two members have different electric charges; all particles have antiparticles, and all are subject to the weak force. Together with the bosons required for the three forces of nature, including gravitation, there is a total of 38 particles. (But there are only 37 to explain, since gravitation has already been explained by the nature of space as a substance.)

A spatiomaterialist theory of basic particles. The basic particles of physics are described by mathematical theories, which have been accepted as the best efficient-cause explanation of precise, surprising measurements, and they constrain what can be said about basic particles in many subtle ways. What I will present here is, by contrast, a mostly geometrical story about the basic particles, or rather, the beginnings of a geometrical theory. It comes from using spatiomaterialism and its explanation of other parts of physics to constrain further our beliefs about the basic particles. They must be constituted by bits of matter that coincide with space in some way or another, and since space has a three dimensional geometrical structure with an inherent motion connecting all the parts of space in time, these most basic forms of matter must have a spatio-temporal structure of some kind. What is presented here is one way that could be true. There may be other ways it could be true. And the one presented here is merely the model for a set of more specific theories that may be elaborated in different ways. My purpose is to show how adding the ontological constraints of spatiomaterialism to the mathematical constraints of the standard model opens up the possibility of a geometrical model of the basic particles.

It is, once again, an ontological explanation of why current theories about the basic particles are true, and its advantage over purely mathematical theories is that it reduces the number of basic assumptions that need to be made. To be sure, spatiomaterialism makes a big assumption that contemporary physics does not make — that space is a substance enduring through time, indeed, one with an inherent motion. But that will enable us to reduce the 37 particles recognized as basic by contemporary physics to, at most, only ten particles. Or even fewer, it might be argued, though that issue can be put off until we discover whether such ontologically based speculation is useful.

The ten basic particles we shall postulate are the photon, the three weakons, W^-, W⁺, and Z⁰, three neutrinos, electron, muon and tau, and their three antineutrinos. In one way or another, each involves a new assumption about the nature of matter, space and how they are related.

But it is conceivable that the photon can be explained as another form of weakon, and the six neutrinos may be just properties of space, that is, aspects of its relationship to weakon. Hence, a spatiomaterialist world may be made of nothing but space and three kinds of weakons.

This explanation of the nature of the basic particles is based on the assumptions we have already made about the nature of matter in order to explain the truth of the basic laws of classical physics, relativity theory, and quantum mechanics. Quantum matter is ultimately constituted by quantum events, which are basic and can coincide with space in various ways, and since they are cyclic, they constitute bits of matter that endure through time. The total energy or mass of a bit of quantum matter is simply the number of quantum cycles per second that constitute its existence. Since the photon is the simplest and plainest form of quantum event that we considered, let me recall what has been said about it.

An independently existing photon is a complete cycle of electric and magnetic forces. Those forces interact in a way that enables them to be repeated indefinitely. But since each cycle is a quantum event with the size of Planck’s constant, h, it either occurs as a whole or not at all. The total energy, or matter, in a photon depends on the number of cycles per second, as required by the physical law, E = hf. But the photon coincides with space in a way that makes it move with the inherent motion in some direction of space. Thus, it also has a wavelength,  which is inversely proportional to its momentum, as required by the equation, p = h/

The photon has an intrinsic spin of 1, which implies that there are three different ways it could be oriented in a magnetic field. Two faces have a magnetic moment, positive or negative, corresponding to the two ways that light can be polarized. (If you follow the photon through space, the electric force rotates around to the right or left in space, which determines it circular polarization, but the difference between these properties is quantum mechanically equivalent to photons being polarized in mutually perpendicular directions as they pass through a filter.) And the third way that a spin 1 boson can interact in a magnetic field involves having no magnetic moment at all, as if there were a face in which the two possible orientations of spin were perfectly balanced. But the photon apparently loses the ability to interact from that “zero face,” as I will call it, because it is moving through space with the inherent motion.

Though the photon has energy, it has no rest mass. It might make it seem that its energy must come from its motion across space, like a form of kinetic energy. But that is not quite right, if its motion is due to the inherent motion in space. We are assuming that its energy comes from the cycles of quantum actions that are carried out by the exertion of electric and magnetic forces.

The photon is the gauge boson of the electromagnetic field, and on our ontological interpretation of gauge field theories, that means that electric and magnetic forces arise from space to act on a particle with an electric charge when it moves across space. At rest, the charged particle is a pulsating force in the surrounding space, which is synchronized with the pulsations of particles with the same charge throughout the universe (and 180⁰ out of phase with the pulsations of particles with the opposite charge). Since a magnetic force is also involved, it is a complex pulsation, perhaps, with internal cycles in two different planes. The electric and magnetic forces that arise from space to keep its pulsations in synch as the charged particle moves across space are the electric and magnetic forces, which were described by Maxwell. They are the same forces that can be coupled and exist independently as photons (for example, as a result of charged objects oscillating back and forth, as in antennas).

The photon introduces most of the properties that basic objects have, and in order to explain the other basic particles, we must postulate the existence of two other varieties of particles, weakons and neutrinos. All the other particles, both charged leptons and quarks, will be explained as combinations of neutrinos and weakons. The interaction between them is the weak force, on this ontological theory.

Weakons. The nature of weakons can be described in much the same terms that were used to describe the photon above. Weakons are also spin 1 bosons, for they are the gauge particles of the weak force. Given or theory about the nature of quantum matter, we assume that weakons are constituted by cycles of quantum events, and thus, what makes them different from photons is presumably coinciding with space in a different way.

Rest mass. One basic difference between photons and weakons is that weakons have a rest mass, whereas photons are massless. Indeed, weakons have a sizable rest mass, about 80,000 MeV/c² for the charged weakons and over 90,000 MeV/c² for the neutral weakon. That is nearly one hundred times the rest mass of the proton.

Rest mass is the property that made it impossible to explain weakons as the gauge particle of the weak field on the model of photons in the electromagnetic field, since gauge bosons are massless, according to Yang-Mills field theory. What makes Yang-Mills field theory so attractive is that particles interact the same way regardless of scale. They are, in other words, “gauge invariant.” But if one simply assumes that gauge particles have a rest mass, then the particles are no longer invariant under a gauge transformation. When the relevant particles are described on a much smaller scale, as if we were looking at them through a microscope, their mass decreases to the vanishing point. Mass in not gauge invariant.

In order to give the gauge particle of the weak field a rest mass, therefore, physicists postulate another kind of particle, the Higgs boson, which is the gauge boson of yet another field. Unlike the weakon and the photon, which have a spin of 1, the Higgs boson has a spin of 0, meaning that it does not line up at all in the magnetic field. But it gives weakons a mass, only if Higgs bosons are located everywhere in space. Thus, it is assumed that the Higgs field is in a condition of least energy when there are Higgs particles everywhere. But the Higgs boson is a force with a certain strength (which enables the weakon to resist acceleration so that it tends to stay at rest), and so that is to say that the Higgs field has least energy when its force is strongest everywhere. This is paradoxical, because the energy associated with every other force of nature increases with the strength of the force.

Notice, however, that although this description of what gives the weakon a rest mass is paradoxical only when it is assumed that it is a description of matter. It is not paradoxical at all as a description of space. Space has no energy (it is not matter), but since it is a substance, it can exert a force. If the weakon’s relationship to space is what gives it a rest mass, it is not surprising that the force is exerted everywhere. Nor is it surprising that that is the condition of least energy, because it does not involve any energy at all. Thus, since we have already postulated the existence of space as a substance for other reasons, we can explain the rest mass of weakons without postulating Higgs bosons. We can take talk of Higgs particles to be a way of referring to space.

The function of the Higgs mechanism can be served by recognizing that quantum cycle have another way of coinciding with space. Instead of being picked up by the inherent motion and laying out their cycles as a certain wavelength in space, the quantum cycles of weakons have a purely rotational motion, and so they can be at rest in space. We assume that when quantum cycles coincide with space at rest, their matter has the form of rest mass, that is, the matter resists acceleration by a force. Weakons can, of course, be accelerated, and their rest mass determines, as we have seen, the scale of the quantum kinetic cycles that move these particles across space as time passes. But that role of rest mass comes from their relationship to space, not to Higgs bosons.

Like photons, weakons are bosons with an intrinsic spin of 1. That means that there are three different ways that a weakon and interact in a magnetic field. That means, as we shall assume, that each and every weakon has all three ways of interacting, and which way they interact depends on how they are oriented in the field. Taken geometrically, each way of interacting in a magnetic field can be pictured as a different face of the particle.

Two of the faces correspond to spin up and spin down, that is, having a positive or negative moment in the magnetic field. Each such face can be represented as a direction of rotation along an axis parallel to the direction of its motion, yielding two possibilities, left-handed spin and right-handed spin, as depicted in the accompanying diagram. These two faces are all that a particle with ½ spin has, and so as a first approximation, it could be represented as rotational quantum cycles of some kind which could be oriented in opposite directions relative to the magnetic field.

A spin 1 particle has a third face by which it can be oriented in a magnetic field in which it has no magnetic moment at all. But in the case of the weakon, we cannot hold that this zero face is lost by moving through space with the inherent motion of space, because weakons can be at rest. Instead, we have to admit that the weakon can interact in a way in which its two faces, with opposite orientations of spin, are somehow perfectly balanced. That suggests that we think of the weakon, not as a rotation which can interact only from either side of its axis, but as a rotating cylinder. If it is oriented so that one end is interacting with the magnetic field, it is rotating in one direction, and if it is turned around so that it interacts from with its opposite side, it is rotating in the opposite direction with a magnetic moment of the opposite sign. But if the cylinder interacts with the magnetic field from its side, it has no net rotation in the magnetic field, and its other faces are balanced against one another. That is how its zero face will be represented geometrically.

Electric charge. There are three kinds of weakons. Two have electric charges, with signs opposite to one another, and the third weakon is neutral. These are different kinds of weakons, not faces of each weakon. But given out assumption about the nature of the electromagnetic field, their charges can be explained as opposite ways of relating to the universal, electromagnetic pulsation, which is mediated by the inherent motion.

The electric charge is what is conserved by virtual photons, as the gauge bosons of the electromagnetic field. Since we are assuming that the forces of an electric charge are exerted in pulses that are perfectly synchronized with similar pulsations by other particles with the same charge wherever they are located in the universe, we can explain why like charges repel. And since opposite charges are 180⁰ out of phase, particles with opposite charge should attract one another. (We have also assumed that the pulsations have an additional complexity that accounts for the magnetic forces.)

These electromagnetic pulsations are independent of the rotational quantum cycles we have been describing in order to explain the three faces of spin orientation. Their intrinsic spin lines the particles up in a certain way in the magnetic field, but the direction of the electric and magnetic forces they feel depends on the gauge bosons that arise from the electromagnetic field in a way that keeps their pulsations synchronized as they move across space.

[We shall simply assume that weakons can have electric charges (and that they can exist without them), as a basic property of weakons. But there may be a simpler ontological explanation. Since weakons and photons are both constituted by quantum cycles, it is conceivable that the charged weakon is simply a photon at rest, or to take the weakon as basic, that the photon is simply a weakon that is moving across space. Though the weakon may have an electric charge when it is at rest, its zero face (without any magnetic moment) may be engaged with the inherent motion so that moves it across space at the velocity of light. In that case, it loses is rest mass and its electric charge is disengaged from the universal pulsation and becomes an electric force that is exerted in time with the rotations of its intrinsic spin, marking out the wavelengths of light. But when this particle is at rest, its cycles of electric forces are exerted from a point in space, and that geometrical configuration could be the radial field of the electric charge of the weakon, whose pulsations are synchronized with the pulsations of like particles everywhere. This would simplify the ontological explanation of basic particles even further, but I will leave it here as just a possibility.]

Weak charge. The weakon is the gauge particle of the weak force, and though it can act on other weakons, it needs fermions on which to act, and that is the role of neutrinos.

Neutrinos. The other kind of basic particle we must postulate is the neutrino, though as I suggested, it might be just an aspect of space in its interaction with weakons. The neutrino is a fermion, an opposite kind of particle from bosons, because it excludes other particles of the same kind from occupying the same quantum state (including location in space). Its spin of ½ means that it should have two possible orientation by which it can interact in a magnetic field, one face with a positive magnetic moment and another face with a negative magnetic moment.

Fermions can be represented geometrically as a rotational motion of some kind. From one side, a fermion would be rotating in one direction, whereas from the other side, it would be rotating in the opposite direction. There are, however, various kinds of rotation that could constitute a fermion, on this ontological theory, and let me emphasize that, though the frequency of the rotation or circular motion may vary, the magnetic moment is quantized. That is, the strength of the magnetic moment is a fixed quantity that does not depend on how fast it is rotating. That is just how basic particles coincide with space.

Varieties of neutrinos. Neutrinos differ from one another in two ways, by size and spin.

There are three sizes of neutrinos: the electron neutrino, which is the biggest, the muon neutrino, which is smaller, and the tau neutrino, which is the smallest of all three. It is not impossible that there are even smaller neutrinos, and I will suggest how they would be incorporated in this theory later. Furthermore, we shall assume that the spin of the neutrino is more like a motion around a circular pathway than it is the simple rotation of an object, and thus, the size of each kind of neutrino is the size of its circular pathway.

The spin of neutrinos are seen as problematic, because they violate the principle that fermions have two possible orientations by which they can interact in a magnetic field. Neutrinos have only a left-handed spin, that is, they rotate counterclockwise along an axis parallel to the direction of their motion. There are no neutrinos with a right-handed spin. Or at least, the weak force interacts only with left-handed neutrinos. (This is a violation of a symmetry recognized in particles, called “parity,” in which it is required that it also be possible for their structures and interactions to occur as if reflected in a mirror.)

The antineutrino, the antiparticle of the neutrino, however, does have a right-handed spin; that is, it rotates clockwise in the direction of its motion. Thus, for each neutrino, there is an antineutrino of the same size, but with the opposite orientation of spin. What is problematic about the spin of the neutrino is, therefore, that the distinction between being the same particle with the opposite orientation of spin and being the antiparticle breaks down in the case of the neutrino. That may be problematic mathematically, but it is not an ontological problem.

On this theory, neutrinos are special because they are elements that constitute other particles and, thereby, explain their properties, and it would not be surprising if the simplest particles do not have all the properties of the particles they explain. Thus, we will assume that neutrinos, as fermions, have two faces by which they can interact in a magnetic field, but that the opposite orientation of spin is also the antiparticle. Neutrinos have a left-handed spin along an axis parallel to the direction of their motion, whereas those with a right-handed spin are antineutrinos.

The reason the difference in orientation of spin gets confused with the difference between particle and antiparticle is that “antiparticles” is defined in terms of opposite electric charge, or “charge conjugation,” and we shall see how their opposite orientations in spin give neutrinos and antineutrinos different relationships to electric charges.

Relationship to space. Though I am counting neutrinos as basic particles, they will be explained ontologically in a way that may be come down to reducing them to an aspect of space. That is possible, because space is a substance, and its circular motion could be just an additional aspect of the inherent motion. Let us assume, accordingly, that there is at every point in space at least three kinds of motion that travel around in circles. Each goes both ways, and they are found in every plane of three dimensional space. There is a largest size for such circular pathways, which determines the longest period for a complete circuit, and circular pathways with shorter radii have shorter periods, with more complete circuits per second.

The idea is that there exists both a neutrino and antineutrino of all three kinds at every point in space. These circular motions are another aspect of space, like the inherent motion and presumably connected with the inherent motion in some way. Although these pairs of circular pathways do not have any linear motion through space (except for the motion of the inherent motion itself in a gravitational field), they do not have rest mass in space, because they are just parts of space itself.

We assume that there is an angular momentum associated with each circular motion, which would give it a moment of force in a magnetic field (explaining its intrinsic spin). That is to say that these circular pathways are oriented relative to the magnetic field. But since neutrino and antineutrino exist together, their angular momentums cancel out. They are neutralized, because they are circular motions in opposite directions. Thus, these circular pathways in space do not usually have any effect on what happens. Photons pass right through them, as do particles with rest mass, as if there was only space at that location.

This is to explain the neutrino ontologically in an opposite way from weakons. Unlike weakons, which have a rest mass that can be explained ontologically by the quantum cycles per second, neutrinos have no rest mass. At least, nothing in the theory requires them to have a rest, and experiments show that it cannot have more mass than about 12 eV/c². Thus, they may not even be constituted by quantum cycles, like forms of quantum matter. They could be simply aspects of space, because as we assumed, the magnetic field in which they are oriented is just an aspect of space (a form of force-field matter).

Interaction with weakons. Though neutrinos do not have an electric charge, they do have a weak charge. That is, they interact with weakons. But weakons exist only as pairs with opposite orientations of spin, and thus, we shall assume that the weakon can act on neutrinos by extracting one of these circular pathways from space and using it to travel around in circles. The weakon and the circular pathways are both oriented in the magnetic field, and when the weakon latches onto a such pathway with a circular motion in one direction, and it releases the pathway with opposite circular motion.

Since the released neutrino has no rest mass, it moves away from its former partner at the velocity of light. That is what physics assumes, though we shall explain its motion as due to the inherent motion in space. It engages with the inherent motion and thereby acquires the velocity of light. The released neutrino is just a bit of angular momentum that propagates through space, and it will not interact with anything, unless it runs into a weakon.

Weakons act on neutrino-antineutrino pairs where they are located, but how they act on such a pair depends on the charge of the weakon. A negatively charged weakon extracts a circular pathway with a left-handed circular motion relative to the direction of the magnetic field, and thus, it releases an antineutrino, that is, a neutrino with a right-handed circular motion. Correspondingly, a positively charged weakon extracts a circular pathway with a right-handed circular motion, and since that is an antineutrino, what it releases is a neutrino, which runs off with the inherent motion. The 180⁰ difference in the phases of pulsations of the positive and negative charges of weakons corresponds, therefore, to the right-handed and left-handed spins of neutrinos.

Charged leptons. This interaction between charged weakons and neutrinos affords an ontological explanation of charged leptons. The member of the neutrino pair that is retained by the weakon is used as a pathway to guide its own motion, transforming the weakon into a charged lepton, such as a tau particle, a muon, or an electron. Let us see how the properties of a charged lepton can be explained by this combination.

Electric charge. The weakon that interacts with the neutrino-antineutrino pair has an electric charge, and since electric charge is conserved, the charge is inherited by the lepton created by this weakon-neutrino interaction.

Negatively charged weakons extract neutrinos from space to use as their new pathway, and thus, negatively charged leptons contain a neutrino and they release an antineutrino. Positively charged weakons, on the other hand, extract an antineutrino for themselves and release the neutrino.

[It would be possible to formulate a theory like this by holding that the weakon simply acquires a new kind angular momentum from space and explaining the antineutrino as simply a form of angular momentum that remains in space as its way of conserving momentum. That might be a simpler theory, which emphasizes that neutrinos are just aspects of space, but it would leave out how space supplies the angular momentum that the lepton acquires as the weakon changes to a fermion. Thus, I will continue to describe the near basic particles as being constituted in part by neutrinos, if only to keep track of what space is contributing to their structures.]

The neutral weakon, Z⁰, does not interact with neutrino-antineutrino pairs at all. It mediates purely elastic collisions among particles with a weak charge. The electromagnetic pulsation of the electric charge is presumably what engages with space to extract neutrinos from them (suggesting that the circular motion of the neutrino and antineutrino is synchronized with the universal pulsation of negative and positive charges, respectively).

Rest mass. Let us assume that the weakon interacts with the neutrino from its neutral face, that is, from the side of the cylindrical boson. Such a geometrical relationship is possible, since both particles are assumed to be lined up with the magnetic field. We have assumed that the cylinder is rotating, presumably with each rotation being a quantum cycle, so that the frequency of its quantum cycles explains its rest mass. It has a large rest mass, but if we assume that, when it interacts with a neutrino, its own rotation becomes a circular motion along the neutrino pathway, we can explain why the charged lepton has less rest mass than the weakon.

Since each circuit around such a circular pathway would take longer than one of the simple rotations that constitute the rest mass of the weakon, there are fewer quantum cycles per second in the new lepton, giving the composite particle a lower rest mass. But matter is conserved. The quantum cycles that previously constituted the rest mass of the weakon do not drop out of existence, but rather are converted into quantum kinetic cycles, which give the new particle with a smaller rest mass a velocity relative to the inherent motion. (Momentum is conserved, because the antineutrino that takes off some direction in space with the inherent motion has an equal and opposite momentum.)

There are, however, at least three different sizes of circular pathways in space, and the smaller the circular pathway, the shorter the period and the greater the rest mass. Since a weakon has an enormous mass, it would usually become a tau particle or a muon before it became an electron. When a negatively charged weakon extracts a tau neutrino from space, for example, it releases a tau antineutrino. But since the muon and electron have longer pathways, requiring fewer quantum cycles per second, the tau particle can decay further. What remains of the negative weakon in the tau particle will release its tau neutrino, extract, say, a muon neutrino from space and release a muon antineutrino (with surplus matter converted to kinetic energy). Likewise, the muon would decay into an electron by releasing its muon neutrino, extracting an electron neutrino from space, and releasing the electron antineutrino to run off with the inherent motion. The electron is the last step, because it is the largest circular pathway possible in space, requiring the fewest quantum cycles per second. These are the decay patterns of weakons and charged leptons that have been found by physics, though they are explained here ontologically, by the size of the circular pathways provided by the neutrinos.

Spin. Intrinsic spin angular momentum is also conserved in the creation of a charged lepton, though in a curious way that might explain a couple of otherwise puzzling fact about leptons. The neutrino has no rest mass of its own, but when it is used as a pathway by a weakon, the composite particle acquires rest mass, which enables the lepton to be at rest in space. Thus, though free neutrinos lose one of their faces to the inherent motion, the captured neutrino can give the lepton it helps constitute a spin of 1/2 , with two faces from which it can interact in a magnetic field. With a weakon on its circular pathway, it has a rest mass and can turn around. Thus, it can be oriented in either way in a magnetic field. In one case, it will have a left-handed spin along an axis parallel to its motion in the magnetic field, and in the other case it will have a right-handed spin.

If the spin of the charged lepton comes from the neutrino, however, what happens to the other two faces of spin of the weakon? We have explained what happened to its neutral face. That is the face that the weakon uses to travel around the circular pathway (much as the photon uses its neutral face to travel along with the inherent motion). But the weakon had two other faces, one that give it a positive moment in a magnetic field and another that would give it a negative moment. These are represented by the two ends of the cylindrical structure of the spin one boson. The question is what happens to them.

Geometrically, the simplest explanation is that each of the weakon’s two non-zero faces coincides with one face of the neutrino in constituting the charged lepton. The circular pathway gives the charged lepton two opposite ways of being oriented in a magnetic field, because one of the non-zero faces of the weakon coincides with one face of the neutrino, and the other non-zero face coincides with the other one face of the neutrino.

To be sure, we have assumed that following the neutrino pathway requires the weakon to have fewer quantum cycles pre second, lowering its rest mass. It is as if the rotation of the cylindrical weakon were slowed down so that the weakon could follow the circular pathway provided by the neutrino. But the decrease in quantum cycles per second does not mean that its spin angular momentum is changed, because we are assuming that spin angular momentum is quantized. That is, the magnetic moment due to intrinsic spin is an all or nothing property: either the particle has it or not. Thus, the particle would have that same quantum property regardless of the frequency of the quantum rest mass cycles constituting it.

It may seem redundant or even gratuitous to suppose that the two non-zero faces of the weakon coincide with the two faces of the lepton. But it would explain one or two otherwise puzzling facts about leptons.

First, we know from Dirac’s equations that charged leptons, such as the electron, cannot be turned over completely by rotating them 360⁰, as one would expect, but requires two full turns. Since a 180⁰ rotation would make the face with the opposite orientation of spin in front, one would expect that two 180⁰ rotations would turn it back to its original state. Though a 180⁰ does give it the opposite orientation of spin, the equations imply that the electron has returned completely to its original size until it has been turned over twice, that is, 720⁰. That otherwise curious feature of the charged lepton would be explained ontologically on this theory, because turning it over completely would involve turning over not only the two opposite faces that the charged lepton derives from the neutrino’s circular pathway, but also the two opposite, non-zero faces that it derives from the weakon that is using that circular pathway.

Second, this ontological explanation of the charged lepton might explain another puzzling property. The electron has a spin of ½, as if its spin were only one-half of a quantum of action, and yet the magnetic moment that it exhibits in a magnetic field is more like what it would have, if it were a complete quantum of action, that is, about twice the expected strength. That could be explained, perhaps, by the way in which the spin of the charged lepton derives from the non-zero faces of the weakon. With a spin of 1, the weakon has a stronger moment in a magnetic field, when it has one at all, and that could be the source of the magnetic force of the charged lepton. This would be to interpret the “½” as just a device for cataloguing basic objects by the number of faces they can show for interaction in a magnetic field. (That is, according to quantum mechanics, the strength of the magnetic moment is the square root of the product of the spin and the spin-plus-one, or (s(s + 1))^1/2, and that means that the non-zero faces of the weakon have a magnetic moment equal to the square root of two times Planck’s constant, whereas the spin ½ particles has a magnetic moment equal to the square root of three divided by two times Planck’s constant.)

Decay patterns. As we have seen, this ontological explanation explains the decay patterns of the negatively charged weakon into the tau particle, muons and electron. It remains only to point out that it also explains the decay patterns of the positively charged weakon, and why decay stops there.

The positively charged weakon, W⁺, interacts in a magnetic field with the neutrino-antineutrino pairs in space, but it latches onto the circular pathway with a right-handed spin in the magnetic field, or the antineutrino, and it releases the neutrino, with a left-handed spin. Otherwise, the decay pattern is the same as described above, because the tau neutrino is the smallest, followed by the muon neutrino and, finally, the electron neutrino. The rest masses of the resulting positively charged leptons is inversely related to the sizes of their neutrino pathways.

The electron (or positron) is a stable particle, because it carries an electric charge, which cannot come apart, and there are no larger pathways in space than those provided by the electron neutrino (or antineutrino). We must take the conservation of electric charge to be a fact about how matter coincides with space, an aspect of the electromagnetic field whose gauge bosons exert forces that keep its pulsations in phase with other charged particles throughout the universe, on this interpretation of gauge field theories.

Quarks. Quarks cannot be explained in the same way as charged leptons, because weakons do not decay into quarks. Indeed, quarks are never found in isolation from one another. Hence, baryons, at least, must have existed from the beginning of the universe (or forever). But quarks can still be given a genuine ontological explanation in terms of the simpler particles of which they are composed, for their constitution could explain their properties and decay patterns. Though that would mean that quarks are not basic particles, the special configuration of more basic particles constituting them must have existed from the beginning, and that would be an ontological explanation of them. That is what is proposed here.

By contrast, attempts by physicists to explain quarks by a more basic structure focus on formulating a mathematical law from which both the electroweak force and the strong (i.e., color) force can be derived. This is the attempt to discover what is called the “grand unified theory,” or GUT, and though it is successful in some ways, it implies that there is a magnetic monopole and that the proton can decay. Neither phenomenon has been observed, and on this ontological theory, neither is possible. (Instead, the magnetic field is an aspect of space connected with the inherent motion by which particles are lined up according to their spin orientation to interact with one another, the protons may have a geometrical structure in space that literally cannot be undone.)

Quantum matter. The main idea of this theory of quantum matter is that bits of matter are constituted by cycles of quantum events in such a way that the quantity of matter in any object is equal to the total number of its quantum cycles per second. Such a nature is plain enough in the photon, whose motion across space with the inherent motion marks out its wavelength. And it has revealing implications in the case of the quantum kinetic cycles, which constitute the kinetic energy of particles with rest mass. But this nature is not so clear in the case of the particles with rest mass themselves, because their quantum cycles must somehow be contained by space in a way that does not involve motion relative to the inherent motion in space.

Weakons are a most elementary from of quantum matter, and so we have assumed that the weakon manages this trick by simply rotating like a cylinder, though, of course, with a fixed and unchanging number of quantum cycles per second (about 10²⁴ cycles per second, given its rest mass of 80,000 MeV/c² and a photon with an energy on the order of a few electron volts having a frequency of about 10¹⁵).

We have seen how charged leptons could be constituted by quantum cycles in which the weakon’s unit of action completes a circuit provided by a neutrino’s circular pathway. Each circuit takes so much longer than a simple rotation around it own axis that it reduces the total number of quantum cycles required each second to constitute the continued existence of the particle.

Quarks can also be explained as being constituted by a pathway for quantum cycles of the kind that derive from weakons. But the pathway must be more complex than leptons. The simplest way to explain why quarks cannot exist apart from one another is to hold that the pathway followed by their constituent quantum cycles depends on a combination of quarks. This is plausible, because physics has discovered that three quarks are required to make up a baryon, the only stable hadron, and each meson, the particle that mediates the strong force between them, is made up of a quark and an antiquark. As it happens, there is a way to explain these particles, their properties and decay patterns along the lines of the foregoing ontological explanation of charged leptons.

Twisted circular pathways. The key to the ontological explanation of quarks is, once again, the interaction between weakons and neutrinos. This is to interpret the weak force, not merely as the cause of decay patterns, but as the force that is responsible for their constitution. The weak force gives particles a nature by binding weakons to neutrinos. I have been describing this bond as a weakon moving along a pathway provided by a neutrino, and that is still the best way to represent it geometrically in the case of quarks. But even a single quark involves a more complex interaction between weakons and neutrinos than is found in charged leptons.

We must assume that the weak force can interact with two neutrinos. Such interactions are possible only when the neutrinos are of different sizes and one is a neutrino, while the other is an antineutrino. Moreover, it is an ordered interaction in which the two neutrinos play different roles. One neutrino is dominant, and the other neutrino is partially hidden. Such an interaction is what constitutes a single quark.

The interaction in a quark can be pictured in terms of a pathway provided for the weakon by the two neutrinos. What happens as the weakon moves along that pathway is that the weakon starts off moving around a circle in one plane, just as in a charged lepton, but the effect of the other neutrino is that the weakon winds up moving circularly in an orthogonal plane. That is, during each quantum event, the weakon follows a circular motion that is also twisted so that the plane of circular motion rotates 90⁰. That is not by itself a closed pathway for the weakon, but there are two different ways that the pathway can be closed — by the combination of quarks in mesons and baryons.

First, the weakon coming out of the twisted circular pathway one quark can enter the twisted pathway of an antiquark, and since the second quark rotates the plane of circular motion back to the initial plane of the first quark, the weakon can go around again and again. The second quark is able to complete the closed pathway because it is the mirror image of the first quark. That is the basic pattern of the meson. But notice that two weakons are required to constitute a meson. The complete pathway involves both a quark and an antiquark, and a complete quantum event is required for the weakon to traverse the pathway of each twisted circle.

Second, it is also possible to put three of these twisting circles together as a closed pathway. In the first quark, the weakon follows a circular pathway which twists into a circular pathway in an orthogonal plane, and the second quark picks up the circular motion in that plane and twists it into a circular motion to the remaining plane which is orthogonal to both in three dimensional space. That is still not a closed pathway, but with a third quark that picks up the circular motion in that third plane and rotates it back to initial plane of circular motion in the first quark, the weakon can repeat the same trip over and over again. Since each twisting circle comes out in a direction perpendicular to its entrance, three of them together brings the weakon back to its starting point. This is the plan followed in baryons, composed of three quarks each. But three weakons are required to constitute such a particle, because one must be traversing each twisted circular pathways during each cycle. That is, three parallel series of quantum cycles constitute each baryon.

Weak interaction in each quark. This weak interaction in a quark between weakons and two neutrinos must, of course, be assumed as part of the nature of the weak force. It is a single quantum event, but it can be pictured in much the same way we did in the case of leptons.

Instead of interacting with the neutrinos by its zero face, the weakon could interact with both neutrinos at once, if it interacted by way of its two non-zero faces, each with an opposite orientation of spin in a magnetic field. That is, one non-zero face would try to follow the circular pathway of the neutrino, while the other non-zero face would try to follow the circular pathway provided by the antineutrino, and the combination of these two influences would result in a twisted circular pathway that rotates from one plane in three dimensional space to another.

This pattern would explain why the quark is constituted by a neutrino and an antineutrino, rather than two neutrinos (of different sizes). Since the non-zero faces of the weakon have opposite orientations of spin, the neutrinos with which they interact also have opposite orientations of spin.

A weakon interacting with a neutrino and antineutrino in this way would be contorted in a way that leaves its zero-face free, and that could become the face by which each quark exerts color forces on other quarks and passes its weakon on to the next quark. The eight different gluons might then be explained geometrically as the forces needed to line up three quarks properly (or to line a quark and antiquark) so that the weakon can complete a full circuit through them. Each quark must pick up a circular motion in one plane, twist it to another plane, and pass the circular motion onto another quark, and the gluons could be explained geometrically by their various roles in giving the three quarks the constant spatial relationship required for the weakons to make a complete their trips through the quarks. In other words, the color force would be another aspect of the weak force that is manifested when weakons interact with these neutrino-antineutrino combinations.

Notice that this account of the interaction between neutrinos and weakons parallels the explanation of leptons, for in that case, the interaction of the zero-face of the weakon with a neutrino exposed the two non-zero faces of the weakon, explaining the two non-zero faces of the charged lepton entailed by its ½ spin as a fermion.

[There may be other ways of picturing this interaction geometrically, though their explanations do not seem to be as complete. If the weakon uses its zero face, perhaps it begins in each quark by following the pathway of one neutrino, but in the presence of an antineutrino of a different size, it simply shifts to the second pathway, which twists its circular pathway. However, the quark seems to be a point-like object, and this theory does not explain its unity, since a sequential pathway would seem to require two quantum events. Furthermore, it does not explain why the interaction does not occur with two neutrinos of different sizes. Why is an antineutrino involved. (Notice that on the previous model, there is are reason for having both a neutrino and an antineutrino. Nor does it have any problem explaining why the neutrino and antineutrino are not of the same size, since a neutrino and antineutrino of the same size would annihilate one another.]

Kinds of quarks. If quarks are constituted by neutrinos and weakons in some such way, it is possible to explain all the kinds of quarks by the kinds of neutrinos of which they are composed. There are just enough differences between the composite particles to explain all the properties that distinguish one kind of quark from another, including their antiquarks.

Spin. As fermions, all the quarks have a spin of ½. We assume that the interaction between weakons and a neutrino and antineutrino of different sizes in each quark is a single quantum event. Together these more basic particles must make up a single fermion. As long as each weak interaction is a single quantum event, it is not impossible for a particle constituted this way to have a spin of ½, because the spins of the constituent neutrinos are not oriented in the same plane, where their spins would cancel one another out. Instead, the neutrinos are bound to one another in a way that we are assuming is unequal. One of the neutrinos making up the quark is dominant, as if the other neutrino were somehow hidden, and thus, the dominant neutrino’s orientation of spin can be assumed to be what gives the quark as a whole the two, opposite faces that fermions, with a spin of ½, must have.

There is one set of combinations of neutrinos with weakons that will explain all the kinds of quarks and their properties. Those combinations are indicated in the accompanying diagram (Constitution of Quarks). In each case, the first neutrino (or antineutrino) in each stack is the dominant one, tending to mask the other neutrino (or antineutrino).

Sign of electric charge. The d, s and b quarks all have an electric charge of –1/3, whereas the u, c and t quarks all have a charge of +2/3. And antiparticles always have the opposite electric charge. The sign of the charge of the quark depends on the dominant neutrino in the same way that the sign of the charged lepton is determined. We assumed that the spin of the neutrino is synchronized with the universal pulsation of negatively charged particles and that the spin of the antineutrino is synchronized with the positive pulsation. That is how we explained why neutrinos acquire a negative charge, and antineutrinos acquire a positive charge. Accordingly, the charge of the quark is negative, when its dominant member is a neutrino, and the quark’s charge is positive, when the dominant member is an antineutrino (whatever ultimately explains the “dominance” of one neutrino over another in a quark).

Size of electric charge. The electric charge of the quark is either 1/3 or 2/3, and that can be explained as a result of the combination of the two neutrinos. We are assuming that the charge is a pulse of electric force that is synchronized with the universal pulsation of such charges, and thus, since negative and positive charges are 180⁰ out of phase with one another, the fractional charges can be explained by an appropriate rotation or phase shift in the cycle of such pulsations. It is presumably because a neutrino and antineutrino have opposite phases relative to that universal pulsation that the electric charge of the quark is in between –1 and +1, and so the relative sizes of the dominant and hidden neutrino could determine the size of the quark’s charge. That is, if the dominant neutrino is bigger (requiring fewer quantum cycles per second if it were on its own), then it is a charge of 1/3. But if the dominant neutrino is smaller (requiring more quantum cycles per second on its own), the charge is 2/3.

If the conservation of electric charge is due to the electromagnetic field, it is possible for the weakon traversing one of these twisted pathways to be separated from the electric charge it has when its exists independently, and it could even be what actually keeps the weak force from acting in ways that would not conserve charge (though there is probably a deeper explanation).

Rest mass. The rest masses of quarks are not well defined, because the quantities are not entailed by theory and the quarks cannot be measured apart from the baryons or weakons. It appears, however, that a good part of the rest mass of the baryon and meson comes from the gluons by which weakons pass from one quark to another, and since that matter presumably exist as potential and kinetic energy, the quarks are probably somehow in motion as the weakons are passing through them. Experiments do, however, suggest a range of rest masses for the quarks themselves, and the differences among them can be explained according to the theory of quantum matter.

The second family of quarks is more massive than the first, and the third family is more massive than the second. Moreover, in the second and third families, the quarks with 2/3 charge are considerably more massive than the quarks with 1/3 charge. These differences can be explained on the assumption that the rest mass depends on the total number of quantum cycles per second, because neutrinos with smaller circular pathways require more quantum cycles per second. Thus, the greater mass of later families can be explained by their use of smaller neutrinos: the tau neutrino replaces the muon neutrino in the second family and the muon neutrino replaces the electron neutrino in the third family. And the greater mass of the quark with 2/3 charge in the second and third families can be explained by the smaller size of the dominant neutrino.

Decay patterns of hadrons. The decay patterns of both baryons and meson can be explained by this theory of quarks. In a weak decay, one kind of quark turns into another kind, and this can happen in two ways. Either the dominant and hidden neutrinos switch roles, or they switch roles and one of the neutrinos is replaced by a larger neutrino (requiring fewer quantum cycles).

One pattern is the decay that occurs within each family of quarks. When a neutron decays into a proton, for example, the triplet of ddu quarks becomes a triplet of duu quarks, giving off an electron and an electron antineutrino (which is thought to be mediated by the decay of the negative virtual weakon released in the process). On this theory of quarks, what happens is that a d quark becomes a u quark, and that means that their neutrinos change positions. The muon antineutrino, which was the hidden member in the d quark, becomes the dominant member of the u quark, and the electron neutrino of the d quark becomes the masked member of the u quark. T

The same pattern occurs in the decay of mesons, which mediate the strong force among hadrons. For example, the negative pion is made up of a d quark and a u antiquark, and it typically decays into a negative muon and a muon antineutrino (by way of a negative virtual weakon). One of the ways this could happen is that the u antiquark becomes a d antiquark. That means that the electron antineutrino and the muon neutrino switch roles, and since that leaves the electron neutrino facing the electron antineutrino and the muon neutrino facing the muon antineutrino, they annihilate one another, and the weakon extracts a muon neutrino from space to become a lepton leaving a muon antineutrino as debris.

The weakon is just a virtual particle in these interactions. It is the gauge boson that arises from the weak field, that is, from space, according to the gauge field theory, to preserve the weak charges of the particles. For that role, the weakon does not need to have the energy of an independently existing weakon (any more than the virtual photon that mediates the electric and magnetic forces among electrically charged particles needs to have the energy of an independently existing photon). On this explanation, however, it is the weak charges of the neutrinos that are be preserved, and their weak charges are preserved by forces that line the neutrinos up as parts of the quark. Thus, the weak force can change the dominance roles of neutrinos in a quark (as long as electric charge is conserved). And any matter left over can act like a charged weakon on space to extract a neutrino and become a charged lepton (leaving the antineutrino as debris).

The other pattern is the decay that occurs between families of quarks. The sigma minus is a baryon composed of the quark triplet, dds, and it typically decays into a neutron, with ddu, and a negative pion, which carries away the negative charge (and decays as described above). The decay of sigma minus requires an s quark to become a u quark. That involves not only a reversal of the roles of the two neutrinos in the s quark, so that the electron neutrino shifts from the dominant position in the s quark to the hidden position in the u quark, but also a replacement of the tau antineutrino in the s quark by a muon antineutrino as it takes up the dominant position in the u quark. Thus, this theory would imply that the decay of the sigma minus leaves two neutrinos in addition to the negative pion which is recognized, namely, the tau antineutrino that is released from the decay of the s quark and the muon neutrino that was also extracted from space in order to supply a muon antineutrino for the dominant position.

This other pattern also occurs in mesons. The positive kaon, for example, is a meson composed of a u quark and as s antiquark, and it typically decays into a positive muon and muon neutrino. Assuming that the neutrinos and antineutrinos must be lined up to annihilate one another, this requires the s antiquark to decay into a u antiquark, for then it can annihilate the u quark. That requires that the neutrinos in the s antiquark to switch roles and at the same time replace the tau neutrino with a muon neutrino (that is, the electron antineutrino gives up its dominant position in the s antiquark and takes up the hidden position in the u antiquark, and the tau neutrino from the hidden role in the s antiquark is replaced by the muon neutrino in taking up the dominant position in the u quark), Again there are two neutrinos as extra debris, because the s quark must not only release its tau antineutrino, but also extract a muon antineutrino in its place, releasing a muon neutrino.

All of the decays of quarks between families of quarks involve such additional neutrino debris, which are not recognized by high energy physics. But that is not an empirical reason for doubting that this theory is true, because neutrinos interact so weakly that they are almost impossible to detect. They cannot be monitored in particle accelerators. And this theory about the nature of quarks is not held by physicists.

Other families of leptons and quarks. It is possible, given this ontological explanation, that there are additional families of charged leptons and quarks. It would require a smaller neutrino and antineutrino. Call it “x”.

Charged leptons could be constituted by them and charged weakons in the same way as the electron, muon and tau particle (and their antiparticle). Their smaller size would require more quantum cycles per second, and that may be the reason they have not been observed, if they exist at all.

Given the role of neutrinos in constituting quarks, such a smaller neutrino would mean that there could be three more families of quarks. Consider the families of quarks with negative 1/3 charge, the d, s, and b quarks. Following their pattern, there could be such a quark composed of an electron neutrino and the x antineutrino, a muon and x antineutrino, and one with a tau particle and an x antineutrino. Similarly for the other members of each current family, there would be three new kinds of quarks, which could constitute baryons and mesons in the same way as currently recognized quarks.

The rules for constituting charged leptons and quarks make it possible to describe yet further families, if there are yet smaller neutrinos.

Permanence of the proton. Contrary to theories currently circulating about the deeper structure of the basic particles of physics, this ontological explanation of their constitution by weakons and neutrinos implies that the proton never decays. That is the other side of the assumption that baryons must have been part of the universe from the beginning. Though their constitution can be explained, they cannot be taken apart.

The structure of the baryon has been explained by holding that quarks have a structure that rotates a circular pathway in one plane of three dimensional space to another plane. Thus, three quarks rotate circular pathways through all three independent planes of three dimensional space in order to provide a complete pathway for weakons. This suggest that the pathway of weakons in the proton is a knot in three dimensional space that cannot be untied. (This model was suggested by P. W. Atkins, 1981., p. 86.) There are two such knots, and since they are mirror images of one another, they would correspond to the difference between baryons and antibaryons.

If, therefore, quarks can be explained by neutrinos and weakons in some such way, then given what has been said about the charged leptons, all the ordinary objects in space are explained ontologically. Physics recognizes 38 different basic particles, and we have seen how spatiomaterialism might make it possible to postulate only 10. It can explain the structure of ordinary material objects by starting with nothing but the photon, three kinds of weakons, and six kinds of neutrinos (three neutrinos and three antineutrinos). And as we have seen, the photon may be simply another form of the charged weakon, while the neutrinos may be just aspects of space that have to do with how space interacts with weakons. It may be possible to explain everything in the world by postulating nothing but space and three kinds of weakons. All the rest could be just how they work together to constitute the natural world.

Whatever the total number of basic particles that must be postulated, this ontological explanation of the basic objects of physics avoids having to believe that everywhere in the vacuum there are particles of every kind and their antiparticles. It is true that an energetic enough photon to create any particle and its antiparticle “out of the vacuum,” as they say. But it is not necessary to believe that all the various kinds of particles recognized by physics are contained everywhere in the vacuum, because if the vacuum is substantival space and it provides the neutrino and antineutrino pairs, all the different kinds of particles can be created together with their antiparticles from them and weakons, wherever there is enough energy.

To be sure, this ontological theory is speculative, and much more would have to be said to defend this theory of basic objects in detail. But the project of ontological philosophy would not be sunk, if this explanation of the basic particles of physics is not correct, because it is not necessary to give such an ontological in order to believe that the world is constituted by space and matter as substances enduring through time. I have included it, because it shows the power of spatiomaterialism to reorient our ways of thinking about physics and to open up new, more promising avenues of thought.

This covers all the basic issue of physics concerning the extreme of the very small and the brief, leaving only the extreme of the very large and long-lasting. In the same speculative spirit, let me suggest what this ontological explanation of the truth of the laws of contemporary implies about the beginning of the beginning, large scale structure, and end of the universe.

Cosmogony. Contemporary cosmology may seem to pose a more serious challenge to spatiomaterialism than current theories about the basic particles. The prevailing belief is that the universe began with a big bang and has been expanding ever since, and if that is true, spatiomaterialism false. Indeed, if that is true, it is not possible to explain the natural world ontologically. There can be no such explanation in a world that begins with the big bang. (For a recent account of modern cosmological theories, see Hawley, 1998.)

Big bang cosmogony. According to the big bang theory, space and matter came into existence at some finite time in the past. (One group holds that it was about 20 billion years ago, and another group holds that it was closer to 10 billion years ago). Before that, there was nothing. No space. No matter. Not even time. At that first moment in time, matter is supposed to exist in a highly energetic state, something like a radiation field with very high energy photons (called gamma rays), and the pressure of this radiation is supposed to cause the expansion. The big bang might be likened to an explosion, except there was, of course, no space for it to expand into. Rather space came into existence with the expansion. That is when time began. Indeed, the theory assume that what exists besides energy is spacetime, not space, and thus, that spacetime was at the beginning tightly curved. The intense radiation field would include all the forces of nature, including the Higgs field, and the energy of those fields, being equivalent to mass, is supposed to have given rise to all the kind of basic particles. The big bang and the subsequent expansion of space is just the increase from zero in the separation of basic objects in spacetime, and since it is the expansion of spacetime itself, and not an event in spacetime, the expansion can be faster than the speed of light in space.

As spacetime itself expanded, the temperature fell. At some point (between 10 and 100 billion degrees Kelvin), the temperature fell far enough for nucleons that had been used into the simplest nuclei to be stable. They were the nuclei of helium (with two protons and two neutrons each), deuterium (an isotope of hydrogen, with both a proton and a neutron), and a few other simple nuclei (such as helium-3 and lithium).

As space expanded further, there was a time about 100,000 years after the big bang when electrons coupled with protons and other nuclei to form atoms. As a result, photons could travel long distances through space without interacting with charged particles.

Subsequent expansion of space led somehow to the formation of galaxies of stars. Indeed, what formed were not only galaxies, but also clusters of galaxies and superclusters of galaxies. It is not at clear how this would happen, or even how stars would form, because when matter is distributed evenly throughout space, there are no net gravitational forces. Presumably, there was an uneven distribution of matter in space, but its origin is still obscure.

The expansion of the universe continues to this day, though it is assumed that the expansion is being slowed down by the gravitational attraction among bits of matter throughout the universe. One of the unresolved issues is whether there is enough matter in the universe to bring its expansion to a halt at the end of time, as most cosmologists would like to believe. A greater quantity of matter would stop the expansion in a finite period of time, causing a contraction which would draw all the matter in the universe (and presumably spacetime) itself back towards a gigantic collapse. But it now appears that the amount of matter (per unit volume) detected in the universe is only about 5 to 10% of what would be needed to stop the expansion, which would force cosmologists to believe that the universe will expand forever.

There is a variant of the big bang theory, the so-called “inflationary” view, due to Alan Guth, which holds that there was a period of very rapid, accelerating expansion very early on (10^-33 seconds after the big bang). In one billionth the time it takes light to cross the diameter of an atomic nucleus, there was a huge expansion, increasing distances in space on the order of 10⁵⁰ times. This would transform submicroscopic distances into cosmic distances, and the reason for this late addition to the big bang theory is that it would explain why the temperature of the universe is the same no matter how far we look in any direction from earth. Without this early inflation, the big bang would have results in a very lumpy universe. But it implies that the universe is much larger than the visible universe, though still finite.

Incompatibility of spatiomaterialism with big bang cosmogony. The big bang theory is incompatible with spatiomaterialism for two reasons, one because it contradicts its assumption about the infinity of time and the other because it contradicts its assumption about the nature of space. .

Time. Part of what makes spatiomaterialism the best ontological explanation of the world is its assumption that existence itself is in time. That assumption about the nature of existence and time entails a certain interpretation of ontological explanation, for an ontological explanation of the world explains everything in the world and everything about the world by showing how it is constituted by substances, and to hold that existence is in time is to hold that the substances used as ontological causes endure through time. If substances never come into existence nor ever go out of existence, any world constituted by them will be temporally infinite in extent.

This is admittedly not the only way of taking ontology to be explanatory. We have acknowledged that it is possible to hold that time is just an aspect of what exists. That is what Einsteinians who take spacetime to be a substances assume about the ultimate nature of the world. Spatiotemporalism, as I called the Einsteinian ontology, is compatible with the belief that the universe had a beginning in time, for it implies merely that there is a limit to the temporal extent of spacetime as a substance that is not itself in time. That makes it possible for cosmologists to accept the big bang explanation of the origin of the world.

The same difference between substantivalism about space and substantivalism about spacetime arises concerning the end of the world. It is possible, according to the big bang theory that the universe might stop expanding and collapse back on itself, and some cosmologists hold that such an outcome would mean that time comes to an end. That would make time finite in the direction of the future as well as toward the past. Such a belief is compatible with Einsteinian ontology, because it would merely mean that the temporal dimension of spacetime as a substance comes to an end in both directions.

There is, however, no way to reconcile spatiomaterialism with either a beginning or an end to the universe it time, because in either case, it would be to give up its view about the nature of existence and time and, thereby, the kind of ontological explanation it gives. To be sure, it is possible for ontologists to hold that existence is in time and to believe the universe had a beginning. That is the view that theists hold. The big bang could be just the way in which God created the world, and the need for such an explanation of the big bang explains why the Pope authorized discussion of the big bang theory so early in its career. But theism gives up naturalism, which is the first of our basic assumption. Any God who could create the natural world would have to be outside space and time and, thus, not something that naturalism can accept.

Space. The other reason that spatiomaterialism cannot accept the big bang explanation of the origin and development of the universe is what it believes about space, and two aspects of its assumptions are at stake. One is its theoretical preference for believing that space is infinite, and the other is its basic assumption that space is a substance.

Infinity. Ontologists would prefer to believe that space is infinite in extent, as well as in its divisibility, because that is the simplest theory. The essential nature of each part of space can be defined as having three-dimensional geometrical relations to every other part of space, for each part would have such relations to a different, ordered set of other parts of space. But if space is finite, each part must have a different essential nature, because each part will have a different spatial relation to the edge of space. And that is not to mention the problem in explaining how space could have an end.

If space is infinite in extent, it is hard to see how space could expand, because there would be, so to speak, no room for more space. All the places in space would already exist. How could ontologists make any sense of the notion?

Cosmologists assume that they can take space to be finite in extent without encountering any problems about the end of space by holding that spacetime throughout the universe is curved. If spacetime contains enough matter, then Einstein’s general theory of relativity implies that a spacetime universe will curve back on itself. If we use two-dimensional space to represent three-dimensional space, then this possibility is supposed to be modeled by the geometry of the surface of a sphere (or Riemannian geometry). But that is not a possible form of spatiomaterialism, because spatiomaterialism replaces the belief in curved spacetime with the belief in the acceleration of the inherent motion in absolute, three dimensional space. Apart from Einstein’s general theory of relativity, there is no reason to believe that space is curved. Indeed, there is no reason to believe that curved space is even possible, if space is a substance. The ability to construct a formal axiom system for curved space does not show that it is ontologically possible.

Substantivalism. Though it is possible for space to be finite in extend in a spatiomaterial world, it is not possible for space to expand. To be sure, if space were finite, the lack of room for the expansion of space would not be a problem. But there would still be an insuperable ontological objection to assuming that it expands, because if space is a substance, the expansion of space would be just another way for something to come from nothing. The measure of space is the distance between parts of space in three dimensions, and if distances were actually increasing, there would have to be more spatial substance separating the points.

Since the big bang theory contradicts spatiomaterialism, it is relevant for ontological philosophy to consider the reasons for believing in the big bang, for they may provide reasons for doubting that spatiomaterialism can be used to do philosophy in this new way. There are two kinds of reasons for believing in big bang cosmogony and the subsequent expansion of the universe, one theoretical and the other empirical, and as we shall see, neither is a good reason for doubting that this is a spatiomaterial world.

Theoretical foundation of big bang cosmogony. The theory behind big bang cosmogony is Einstein’s general theory of relativity. In 1917, shortly after completing his general theory of relativity and before Hubble had discovered evidence of the expansion of the universe, Einstein himself turned his attention to cosmology. Einstein used the basic equation of his general theory of relativity to represent the entire universe, assuming, in effect, that the universe contains a finite quantity of mass and is finite in extent. A finite universe was not implausible to Einstein, because he believed in spacetime, rather than space enduring through time, and a finite spacetime universe can contain enough mass and energy for spacetime to curve back on itself, giving the universe as a whole a spherical geometry. There would be no edges of space to explain, because traveling far enough in any direction would bring one back to where one started.

Einstein soon discovered, however, that even in a universe with spherical geometry, gravitation, being a universal attractive force, would quickly lead to the collapse of the universe. The tendency toward gravitational collapse is even greater than in the Newtonian counterpart of Einstein’s way of representing the universe (which takes the universe to be a finite sphere of material objects in infinite space all attracting one another). On its own, Einstein’s universe would crash in on itself in about the time required for light to cross the universe.

In order to keep his equation from predicting the collapse of the universe, Einstein introduced the so-called “cosmological constant.” It was a perfectly legitimate move, because it was a constant of integration. That is, his general relativity equation had to be integrated in order to represent the universe, and Einstein initially set the constant of integration as zero.

The left side of Einstein’s equation in the general theory is a differential equation that represents the metric of curved spacetime, while the right side of his equation represents the presence of mass and energy in spacetime. To set the constant of integration on the right side equal to zero was to assume, in effect, that the force of gravitation falls to zero at great distances. That is what led to the problem of collapse of the universe.

It was also possible to set the constant of integration at something other than zero. That would represent a repulsive force between material objects at great distances from one another. It would be a very small force at short range, such as the solar system, but the repulsive force would increase with distance. Hence, it would be the dominant force at large scales, and his general relativity equation would no longer predict the collapse of the universe. This was the origin of the cosmological constant. It suggested that there is a form of negative energy associated with the vacuum, and it could make the universe static by canceling out the gravitational attraction at great distances.

The cosmological constant was destined, however,, however, to be rejected, because it implied that the universe is unstable. Though it could be used to represent a static state in which gravitation and long-range repulsion are equal, it was inevitably a precarious balance. The problem is that gravitation falls off with the square of distance, while the repulsive force represented by the cosmological constant increases linearly with distance. Thus, a slight contraction in the universe would make the gravitational force stronger than the repulsive force could resist and the universe would collapse. On the other hand, a slight expansion of the universe would make the repulsive force stronger than gravitation, and the universe would expand faster and faster. In either case, it was not likely to remain the same size.

When Edwin Hubble’s evidence for the expansion of the universe became known in 1929, it seemed that Einstein’s mistake was the attempt to represent the universe as static. If the universe is expanding, the size of the universe must be a dynamic phenomenon. Since his equations had told him, in effect, that the universe is not static, Einstein retracted his cosmological constant. He called it his “biggest blunder,” which big bang cosmologists rarely fail to mention, taking comfort in his agreement.

The equation from Einstein’s general theory of relativity was adapted for big bang cosmogony, because it could be used to represent a universe in which the initial pressure and outward momentum of the expansion is countered by the universal gravitational attraction. The “Einstein-de Sitter model of the universe” is one such theory. It holds that gravitation will bring the expansion of the universe to a halt at the end of eternity. Preference for this view has posed a problem for cosmologists, because all indications are that there is far less matter in the universe than such a limit to its expansion would require.

Spatiomaterialists critique. Ontological philosophy has a different way of interpreting Einsteinian cosmology which is based on its ontological explanation of the truth of Einstein’s general theory of relativity. Spatiomaterialism assumes that space is an infinite, three dimensional substance enduring through time, and it explains why Einstein’s general relativity equation yields true predictions of gravitational phenomena by holding that the accumulation of matter at any location in space causes an inbound acceleration of the inherent motion in the surrounding space. On this view, space is assumed to be infinite, and the so-called called the “curvature of spacetime” turns out to be just an acceleration of the inherent motion of space (that is, an acceleration of the ether, as an aspect of space). If that effect of matter accumulation of space is what makes Einstein’s equation true, then there much to criticize in its use as the theoretical underpinning for big bang cosmology.

The most basic objection to Einsteinian cosmogony is the use of Einstein’s question to represent the entire universe. That is to assume that the universe contains only a finite amount of mass and energy (that is, matter) and that spacetime is finite. But thus far in this ontological argument, we have still found no reason to believe that space is finite in extent or that the total quantity of matter is finite.

This is not to deny that Einstein’s general relativity equation can be used to represent a sizable chunk of the universe. Indeed, the truth of that representation is what was explained ontologically in the General theory of relativity. But when we recognize that it represents only a region of space and the matter contained by that region, we can see that Einstein’s introduction of a cosmological constant was not a mistake at all, but merely a way of representing the infinity of the space and matter outside that region.

Einstein introduced the cosmological constant as a constant of integration in the integration of his general relativity equation. But he introduced it on the right-hand side of that equation. Since that side represents the mass and energy contained in the region, the cosmological constant that was needed to make the universe static seems to represent a repulsive force which is counteracting gravitational attraction.

However, the constant of integration could have been introduced on the left hand side of Einstein’s general relativity equation, which represents the metric of spacetime. That may seem like a mere mathematical correction to the geometry of curved spacetime. But it could be interpreted as representing the infinity of space and matter beyond the region covered by the equation. If the universe is infinite, rest of the universe is, in effect, tugging at the edges of the finite region of spacetime represented by the equation, keeping its overall curvature flat. The cosmological constant does not represent a negative force that increases with distance, but simply a constant of integration that must be included in order to take into account the rest of the infinite universe.

Thus, ontological philosophy would lead us to see Einstein’s greatest blunder, not as introducing the cosmological constant, but as giving it up. For that concession comes from failing to recognize that what is described by his general theory is just a gravitational force that works through space in a world in which space is an infinite substance enduring through time, that is, in which space and time are absolute. Einstein’s mistake was to believe in spacetime.

Thus, we conclude that the truth of Einstein’s general theory of relativity gives us no reason to think that the universe might be expanding and, thus, no reason to believe that it began with a big bang.

Empirical foundation of big bang cosmogony. Though Einstein’s general theory of relativity is the main theoretical reason for believing in a big bang, it is probably not the most important reason. The most persuasive reasons are empirical. It seems to be the best explanation of three phenomena: the apparent explanation of the universe, the proportion of helium in the universe, and the background radiation. However, in a spatiomaterial world, as we shall see, there is another possible explanation of those same phenomena, and it is far more plausible.

Hubble’s law. In 1929, Hubble published the result of his work at the Mount Wilson gathering evidence about the spectra of distant galaxies. He reported that galaxies are moving away from earth, and moving away faster the farther away they already are. That is Hubble’s law.

Hubble found a red-shift in the electromagnetic radiation from distant galaxies, that is, a shift of radiation from known sources toward longer wavelengths, and as far as he could measure (about 10 million light years), the red-shift increased directly with the galaxy’s distance. Such a shift could be explained as a Doppler effect. It is well established that the wavelength of a signal sent from an object moving away is elongated. Assuming that the red-shift he had observed is a Doppler effect, Hubble argued that the galaxies he had observed were moving away from earth, and his data indicated that the farther galaxies were away from earth, the faster they were moving. Hubble’s law states that the recession velocity of a galaxy increases directly with its distance, and the constant of proportionality is Hubble’s constant.

Hubble’s own calculation of his constant is now though to have been off by a factor of two, though to this day, there is still considerable uncertainty about what it is. Current measurements seem to cluster around two different values. (One group finds that galaxies have about 15 kilometers per second of additional velocity for every million years of additional distance from earth, while another group finds them to have about 25 kilometers per second of additional velocity for every million years of additional distance from earth.)

The correlation between the distance to a galaxy and the velocity its recession suggests that the whole universe is expanding, because that is how it would appear not only from earth, but everywhere, if the universe were expanding. Though strictly speaking, the red-shift of distant galaxies would not be a Doppler effect, because their recession velocity does not come from moving through space, but rather from the expansion of space itself, it is assumed to come to the same thing quantitatively. (The wavelength of a photon is supposed to increase with the expansion of the space it is crossing.)

Hubble’s law makes it possible to calculate the age of universe, because if galaxies are all receding from one another as that law describes, there must have been some time in the past at which they were all located together at the same point. Current estimates tend to cluster on either an age of about 20 billion years or 10 billion years, depending on which value of the Hubble constant one accepts. There is considerable room for error. First, it is necessary to separate out the “peculiar motion” of galaxies which is caused by local gravitational effect (and that is a significant factor, since nearby galaxies are the ones mainly used to measure Hubble’s constant). And if the expansion of the universe has been slowing down because of the gravitational attraction between galaxies, as cosmologists assume, then the estimate of the age of the universe should be considerably lower (by as much as one-third).

Nucleosynthesis. The measured expansion of the universe supports the idea that the universe began with a big bang, but that idea was first proposed by George Gamow in 1947. The evidence Gamow offered for such a beginning is the prediction of the proportion of helium and other light elements in the universe, which has been confirmed.

Gamow thought of the initial state of the universe as being nothing but an intense radiation with a very high temperature. He assumed that the objects with rest mass would be created by high energy photons. (Since most of the rest mass in the universe is now composed of baryons, that would not explain what happened to all the antibaryons that must have been created at the same time.) And Gamow assumed that the pressure of radiation at such a high temperature was responsible for the expansion the universe, though without any space outside into which it could expand, it had to create its own space.

Particles would be created, and as the expansion continued, the temperature would fall. Gamow recognized that at some point the density of nucleons and the energy of their interaction would be enough for nucleons fused into small nuclei to be stable (between 10 and 100 billion degrees Kelvin). He explained the proportion of helium (with two protons and two neutrons) that is found in the universe (about 25 to 28 percent by weight). Similar reasons can be given for the proportion of matter in the form of deuterium (one proton and one neutron), helium-3 (two protons and one neutron), and some lithium and boron.

Since there is no other plausible explanation of their relative abundance in the universe, this is good empirical evidence of a period in the past during which the temperature of the universe was once much higher than it is now and that is has been falling since then.

Background radiation. In 1966, Arno Penzias and Robert W. Wilson, discovered radiation coming from all directions in space, day and night, every season of the year in the microwave region of the electromagnetic spectrum. It was the wavelength that one would expect of an object with a temperature of 2.7 degrees above absolute zero. They recognized that the radiation must have a cosmic source, and they argued that it must have been caused by the big bang and the subsequent expansion of the universe.

The radiation must come from a period long after the nucleosynthesis discovered by Gamow, because for a long period of time, the electromagnetic radiation would have been sufficiently energetic to break any bonds that electrons might form with the nuclei bouncing around at the time. About 100,000 years after the big bang itself the universe would have expanded enough for the temperature to fall to a level that would allow atoms to be stable. Neutralizing the charges of electrons and nuclei in that way allowed photons to pass unhindered for great distances. The period at which the universe became transparent would explain the origin of the cosmic background radiation.

These empirical reasons for believing in the big bang are independent of general relativity. Even though spatiomaterialism can reject Einsteinian cosmology because of the assumptions it makes, these observations are still evidence for the big bang. But since they are just observations, they support the belief that the universe has been expanding ever since a big bang only if that is the best explanation of them. Thus, the empirical foundation for contemporary cosmogony can be undermined by offering a better explanation of those observations. There is at least one way that spatiomaterialism can do just that.

Spatiomaterialist cosmogony. The spatiomaterialist alternative to received cosmogony will be presented here in two stages. First, I will show that spatiomaterialism is not falsified by the evidence for the big bang because is has another way of explaining it, a way that make it a better theory, at least in the eyes of ontologists. Then, I will show that there is a variation on it that is an even better explanation of all the relevant evidence, because it also explains certain observations that are currently acknowledged to be puzzling and problematic. I call the first stage of this explanation “the big shrink” and the second stage the theory of “local big shrinks.”

The big shrink. It is possible to explain all the observations offered in support of the big bang theory without supposing that the universe is expanding, because they can be explained at least as well by the shrinking of particles with rest mass in size. Spatiomaterialism assumes that space and matter are infinite in extent and that they have existed from eternity. But let us assume for now that the universe as we know it did begin with a singular event, which is currently called the “big bang.” But instead of assuming that it was like an explosion, let us assume it was more like an implosion. Instead of a big bang, it could have been a big shrink.

This theory assumes that until that point in the history of the universe, space was filled with matter. All the particles with rest mass were so big that they coincided with every part of space. Since according to our theory of the basic particles, the proton never decays, we should think of space as being densely packed with baryons, or triplets of quarks, all existing side-by-side everywhere. There need not even be any electrons, if these baryons were all neutrons. There is nothing inconceivable about infinite space and matter existing in that condition from eternity.

Possibility of big shrink. What is called the “big bang” could have been what happened when all that rest mass matter started shrinking. Assume that the shrinking happened simultaneously everywhere in space. Set aside for now why it occurred when it did. Just suppose that it happened. Our theory about the nature of the basic particles explains how it would be possible.

Such a shrinkage of particles with rest mass is possible, on our theory of the basic objects, because baryons are constituted by both space and matter. If quarks are weakons traveling on twisted circular pathways provided by neutrinos, the condition of matter at the beginning could be explained by the huge size of those neutrinos. The shrinkage of rest mass matter in size could then be explained by the neutrinos shrinking in size. The quarks (and, thus, the baryons) would become smaller, and since there is only a finite amount of matter in any finite region of space, distances between baryons would begin to grow. Thus, the “big shrink,” as I will call it, would not require space to expand.

The strong forces between baryons, mediated by mesons, could have held neutrons together from eternity. But as baryons began to shrink, spaces between them would begin to open up, and at least at the boundaries where empty space appeared, particles and small clumps would break off and start moving and interacting with one another. The strong force is actually a repulsive force at small distance between independent hadrons, tending to keep them apart, but the temperature might be high enough in places for them to fuse again into masses. The weak force would make neutrons decay into protons, leaving electrons to interact independently, and if the temperatures were high enough, they would interact like a plasma. But let me set aside for now the description of how they move and interact in order to focus on the effects of the big shrink on photons and the basic forces of nature.

Photons would be generated in the usual way by the interaction of charged objects. But photons would be unaffected by the shrinkage of rest mass matter, because they are not constituted by neutrinos. They are quantum cycles that coincide with space in a way that moves them along at the velocity of light, though at first they would not be able to travel very far before they were scattered by charged objects.

Nor would the electromagnetic force be affected directly by the shrinking of neutrinos. The electromagnetic field is imposed on space, as we have seen, by electric charges, and they would do so in the same way (which we have assumed involves a universal pulsation in which a 180⁰ phase shift distinguishes negative from positive). Since space is not changed, this reflection of electric charges in space would be the same. However, the particles carrying the electric charges would be much larger, and thus, the electric and magnetic forces would be much weaker relative to the weak force. That is, virtual photons by which the electromagnetic force acts on particles with rest mass would be the same size, but the charged particles would be much bigger and, thus, less affected by their point like charges.

The short range forces would dominate interactions. The weak force is also mediated by gauge bosons, and the main role of virtual weakons is to exert forces that keep the quantum cycles of weakons traveling along their neutrino pathways and to keep the neutrinos lined up as twisted circles in quarks, though they also mediate all the decay patterns of high energy particles. The color force would work the same way, given our theory of the basic particles, because gluons are just how the weak force keeps the quarks lined up either in triplets or quark-antiquark pairs (when the weakons are contorted by traveling twisted circles). Hence, the strong force would work the same way as it does now, except that the mesons would be much larger and its reach would much greater. Since there is a neutral weakon, Z⁰, the weak force could also mediate elastic collisions among particles as well as keeping the basic objects together.

The gravitational force would also work basically the same way with swollen rest mass matter, because on our theory, it is just the effect of accumulations of matter on the inherent motion in space. But there would be one important difference. The particles with rest mass would be much bigger and have much less rest mass. The quantity of rest mass depends on the number of quantum cycles per second involved in their constitution, and with larger neutrinos, the weakons would have farther to travel. Baryons and leptons would, therefore, have fewer quantum cycles per second, or less rest mass. That would affect the sizes of the quantum kinetic cycles by which particles with rest mass move across space, because according to this ontological explanation of quantum mechanics, the wavelengths of the quantum kinetic cycles are scaled according to the mass of the object (that is, constitute momentum, not just velocity). The smaller rest masses of particles together with their swollen sizes would mean, however, that the gravitational force has considerably less effect on what happens.

Compatibility of spatiomaterialism. Unlike the big bang, the big shrink is compatible with spatiomaterialism. It is not necessary to deny that space is infinite nor to believe that space is expanding. And given the spatiomaterialist ontological explanation of the basic particles, we can conceive how the big shrink would work. There would be no change in Planck’s constant, only a change in the size of neutrinos. But as the shrinking of neutrinos continued, the quantum cycles constituting particles with rest mass would speed up. The increase in their rest masses would mean an increase in gravitational force-field matter, because the gravitational force is in proportion to mass and the distances in space across which the force is acting will be increasing. That is, the force-field matter of the gravitational field would increase with the total quantity of quantum matter. But that seems to be a violation of the conservation of matter.

Such an increase in the total quantity of matter in the universe is not, however, unthinkable at this point. It does not pose the same problem for spatiomaterialism as the expansion of space would, because it is possible to conceive how it would happen, even in an infinite world.

To be sure, it does violate the conservation of matter. But we merely used the principle of the conservation of mass and energy as working hypothesis by which to figure out what spatiomaterialism had to assume about the forms of matter in order to explain the natural processes described by classical physics. Having done that, we are now in a position to derive new conclusions about the world from spatiomaterialism. If the universe began with a big shrink, then the total quantity of matter has been increasing ever since. That is just the nature of a spatiomaterial world with the big shrink.

However, at the second stage of this theory, we will see how matter can be conserved, even though its total quantity increases throughout the big shrink.

Explanation of relevant phenomena. As the shrinking of rest mass matter continued after the beginning, physical processes would take place that could explain the phenomena cited as evidence for the big bang. At first, the strong (and weak) force would dominate, holding large clumps of neutrons together as they separated from one another. They would be cool, but energetic interaction would occur only at their boundaries. Assuming that the shrinking were fast enough, the continued shrinking of particles with rest mass would eventually break up the clumps of neutron into smaller clumps and independent baryons along with other particles. But since huge groups of baryons would already be separated by huge distances, the increasing strength of the gravitational force would draw the still swollen matter into collisions with one another where the temperature would be high (relative to their size).

Nucleosynthesis. As some point in the shrinking of matter, the temperature would reach a point at which larger clusters of neutrons would be broken up by the kinetic energy of their interaction and only small nuclei would be stable. Since it would depend on the temperature of their interaction, such a process could give rise to the same proportion of helium and other small nuclei that Gamow predicted.

Background radiation. There would also be point during the big shrink when electrons and nuclei through out the universe would become coupled in atoms, making it possible for photons to travel long distances without interacting with charged particles. The wavelengths of those photons would mirror the swollen sizes and lowered masses of the charged particles that were interacting, and since those elongated photons would not shrink further, that would explain the cosmic background radiation. We are parts of galaxies in which rest mass matter is much smaller as a result of the continued shrinking, and thus, the photons generated when nuclei and electrons were much larger would have a much longer wavelength than photons generated by similar processes on earth.

Hubble’s law. The big shrink would explain why Hubble’s law appears to be true. At some point during the big shrink stars would from, and assuming that the shrinking has continued throughout the universe to this day, the radiation generated by those bigger and slower processes would have a longer wave length. In fact, there would be a correlation between the red shift observed in galaxies and their distances from earth, because light from more distant galaxies would have spent more time traveling before being intercepted by us, and it would be measured as longer by us, since the rest mass matter constituting us would have shrunk more since it was emitted than from galaxies that lie nearer to earth. To be sure, the red shift would not indicate the expansion of space nor the velocity of their recession, but rather how much matter had shrunk since the time the light was emitted. That would require a reinterpretation of Hubble’s constant. However, there would still be a correlation between the red shift and distance, which is the observation in which Hubble based his law about recession velocities. And it would be possible to use the red shift to measure the relative distances of faint galaxies.

It is not impossible, therefore, to explain the three main observations used as evidence for big bang cosmology in another way — one that is compatible with spatiomaterialism. And since the big shrink theory does not have to hold that something comes from nothing, it is prima facie a better theory, if it possible — at least in the eyes of naturalists, who believe that the natural world is constituted by substances that exist independently of themselves.

The possibility of big shrink, instead of a big bang, makes it possible, therefore, to believe that the universe is infinite in every way, except for the finite divisibility of matter. Both space and time are infinite in both senses, being infinitely divisible, or continuous, as well as infinite in extent. Time is eternal not only in the direction of the future, but also toward the past, for it is not necessary to believe that substance comes into existence, as entailed by the big bang theory, though there was a time when the big shrink began. And since space is infinite in extent, the total quantity of matter in the universe can also be infinite, even though there is a finite quantity in any finite region of space.

To be sure, the big shrink does imply that the total quantity of quantum matter in any closed region of space is increasing. But that extra matter does not come from nothing. It comes from the matter that exists at the time and the shrinking of neutrinos. Since neutrinos are just an aspect of space having to do with its interaction with weakons, neutrino size could be just a changing property of space.

The increase in the total quantity of quantum matter in any closed region is conceivable because matter is finitely divisible. The existence of elementary units of matter is the only way in which the universe does not have a twofold infinite in its basic aspects: time, space and matter. And there is, as we shall see, a way that the total quantity of matter in sufficiently large regions of space can be conserved even though quantum matter increases during the big shrink.

There is, however, still a problem about big shrink cosmology, because it does not explain why the big shrink happened when it did. Even if the substances constituting the universe always existed, the big bang still implies there was a change at some moment when rest masses suddenly started shrinking. Why did it happen then?

Local big shrinks. Not only can spatiomaterialism offer a better explanation of the observational evidence used to support the big bang theory than the big bang theory, but like so many times before in this ontological argument, it opens up the possibility of a explanation which heretofore has not even been considered. In this case, the fruitfulness of spatiomaterialism as a way of explaining the natural world is shown by its solution to the problem about when this remarkable event occurs. That is the second stage of the spatiomaterialist ontological explanation of the origin of the universe, the “theory of local big shrinks.” What is more, however, it solves other cosmological puzzles posed by current astronomical observations. Thus, unless this approach is on the wrong track, some such theory as they will make a credible claim to being the best explanation of astronomical phenomena, according to the empirical method of science.

It is not necessary to explain why the big shrink occurred when it did in order to believe that substance has always existed, because its is possible to hold that the big shrink is a local event, rather than a global event. A big shrink could occur repeatedly as time passes, but in different places at different times. That is the theory of local big shrinks. It holds that the universe has always existed pretty much as it appears now.

The theory of local big shrinks is, therefore, a “steady state” theory of the universe. Such a theory was advanced in 1948 by Herman Bondi, Thomas Gold, and independently by its most famous defender, Fred Hoyle. Their steady state theory accepted that the universe was expanding, and it held that matter comes into existence as hydrogen atoms (or, later, so called Planck particles). This was the result of a so-called “creation field,” which is one way of interpreting Einstein’s cosmological constant. A creation field requires new physical processes, but so does the big bang theory. Thus, it was once considered a viable alternative to the big bang theory.

The steady state theory has, however, fallen into to disfavor. It could not explain the cosmic background radiation, when it was discovered. And since it assumes that the universe appears the same way at every moment in its history, it cannot explain the evidence that the universe was previously in a radically different condition. For example, quasars are extremely intense sources of radiation, but since they tend to have an extremely high red shift, they must be far away (according to Hubble’s law), and thus, most cosmologists take quasars to be characteristic of a much earlier era in the history of the universe.

The local big shrink theory is, however, different from the traditional steady state theory. It does not agree that the universe is expanding, but explains that appearance by the shrinking of rest mass matter. And as we shall see, it can explain the background radiation. Indeed, it can explain all the phenomena covered by the big bang theory, including quasars.

The scale of the local big shrink on this theory is roughly that of a supercluster of galaxies. It has recently been recognized that the large scale structure of the universe includes not only stars configured as galaxies, but also clusters of galaxies, and clusters of clusters, or superclusters of galaxies. Indeed, it now seems that there are vast empty regions of space between such clusters of galaxies that look something like soap bubbles because of how they are bounded by galaxies. Let us assume, therefore, that from time to time in such empty regions, very swollen matter comes to exist and starts to shrink as described above. Let me also emphasize some aspects of this process and also refine the assumptions we are making about the big shrink.

We assume that particles with rest mass start off packed together in a swollen condition coinciding with a huge region of space. Assuming it was made of baryons held together by the strong force, it would be like a giant neutron star. Since this matter would be surrounded by empty space, there would be a gravitational attraction that tends to pull all the particles towards the center of mass. It might seem, therefore, that a local big shrink could not develop as described above, because the gravitational force would accumulate enough to cause a giant black hole. But that is not inevitable, for two reasons.

First, the condition of matter at the beginning makes the gravitational force weaker in its effect. The weakons are traveling the pathways of much larger neutrinos in baryons and charged leptons, and thus, those particles are constituted by fewer quantum cycles per second than the same kinds of particles on earth. On our theory, that means that they are not only larger, but that they also have less rest mass. Hence, the gravitational field that they impose on space will be much weaker than it comes to be later on.

Second, let us assume that the shrinking is initially much more rapid than it is later. In fact, we will assume that the shrinking slows down asymptotically to a limit that is not much smaller than matter constituting earth. Though at first, the electromagnetic force is weaker and interactions among basic particles are dominated by the strong force (and the weak force), the rate of shrinkage could be fast enough for spaces to open up between huge clumps of baryons that are still held together by the strong force. These huge clumps of matter would still attract one another by gravitation on the largest scale, but if the shrinking were fast enough, they would remain isolated from one another, and the main role of gravitation on a smaller scale would be to help the strong force hold the remaining clumps of matters together.

The same process of division could occur more than once. As particles with rest mass shrank further, baryons would still tend to stick together because of the strong force, and thus, the clumps would subdivide into smaller clumps, opening up huge distances between them as they continued to shrink. And those sub-clumps of matter might do so again. Such a process could explain the large scale structure of a supercluster of galaxies, that is, the huge distances between clusters of galaxies, between local groups of them, and ultimately between single galaxies.

The rapidity of the initial shrinking means that this phase of the local big shrink would be completed in much shorter period of time than assumed by the big bang theory, because the local big shrink occurs in a much smaller region and it does not require galaxies to spend a lot of time moving away from one another. Instead, the galaxies would “precipitate out” from the original mass of swollen particles as they shrink in size.

Eventually, however, the shrinking of the basic particles would weaken the strong force relative to the electromagnetic force, and the strong force, together with gravity, would no longer be able to hold matter together in huge clumps. In addition to the kinetic energy of the collision among masses of baryons, the repulsive electromagnetic forces between protons would help separate them, and the short range repulsive force between baryons that are not bound together by the strong force would keep them separate. Thus, baryons would break up into smaller and smaller clusters and eventually into individual baryons.

As the shrinking continued, the temperature would fall, because the distances separating baryons and bunches of baryons would increase. Gravitation would be pulling them into regions of dense collisions, but they would still be too swollen and light to form stars. This is the point at which the “nucleosynthesis” that explains the proportion of helium and other simple nuclei in the universe would take place. Large groups of baryons would be unstable at that temperature, but simple nuclei would be stable and remain stable as the temperature fell.

Not long after that, electrons would couple with nuclei to form atoms, and since photons would be able to travel much longer distances, more photons would escape into the space beyond these more or less isolated clusters of matter, and there would be a vast increase in the radiation from them. That would account for the cosmic background radiation, because matter would still be swollen enough for the photons released to have longer wavelengths. The size of the particles would make it appear that it is a 2.7⁰ Kelvin blackbody radiation, though actually it would be a much higher temperature relative to swollen rest mass particles. To be sure, photons with even longer wavelengths would have been emitted by clusters of matter prior to that, when matter was even more swollen. But that radiation would not be nearly as intense, because photons could come only from the edges, as the radiation from stars. When the region became transparent, however, photons could also escape from throughout the clusters of matter, and that is what is observable.

By this point, the “precipitation” from the shrinkage of matter would already have isolated galaxies from one another and, presumably, made the distribution of matter in each galaxy somewhat uneven. But since particles with rest mass have been shrinking in size and increasing in rest mass, the total mass accumulated in these local regions would increase and gravitation would begin to play the dominant role in what happens.

To be sure, from the beginning, gravitation would have been attracting clusters of matter toward one another, and that attraction would also increase as rest mass increased. But since, initially, gravitation was not strong enough to keep up with the effects of shrinking, clumps of matter would separate off from one another leaving vast distances between them that gravitation could not overcome quickly enough. Thus, gravitation would wind up exerting much the kind of attraction among galaxies that is observed now.

Within each galaxy that precipitated out during that earlier process, however, the continued shrinking of matter would increase the effective gravitational force, because fermions would be smaller and have greater rest masses than ever. Gravitation would play two roles at this stage, pulling matter throughout the galaxy towards its center and turning regions of relatively denser accumulation of matter within each galaxy into stars.

The gravitational attraction at the scale of an entire, separate galaxy would create enormous pressures at the center, where matter would accumulate, and with smaller, heavier particles, it would be enough in most galaxies to create giant black holes which would gobble up all the extra matter that had accumulated at the center. They would give off, at least for a while, enormous quantities of energy as matter tried to spiral into them, and their magnetic fields might even spew out prodigious quantities of particles in certain directions at enormously high velocities. And the gravitational field centered on such a black hole would organize the motion of matter throughout the galaxy.

On a more local scale, gravitation would cause the formation of stars of various sizes. Regions of highest density would tend to be the first to form stars, and those giant stars would explode rather quickly as supernovae, spewing heavy nuclei throughout the regions around them. Smaller would form from smaller variations in density, and since most of them would form later, the planets that formed out the matter spiraling into them would be rich in atoms with heavy nuclei.

[Perhaps, some aspect of the process of galactic development by “precipitation” from the local big shrink would even account for the observations that now lead to the belief that there must be a great deal of dark matter that exists in an unusual form.]

The formation of a black hole and stars would give galaxies the appearance they now have, for matter would be much smaller and heavier, radiating photons with much shorter wavelengths. Visible light would make galaxies observable from great distances, and their spectra could be examined by astronomers. Assuming that the shrinking of matter had not quite reached its asymptotic limit when it was emitted, a red shift is precisely what we would expect to observe from earth, where the shrinking has gone on longer. On the other hand, assuming that earth is very close to the asymptotic limit where matter stops shrinking, it would also explain why there are no galaxies with a blue shift, as one would expect, if the shrinking went on.

The theory of local big shrinks would imply, nevertheless, that Hubble’s law is false. Since local big shrinks would be occurring at different times at different locations throughout the universe, there would be no general correlation between the red shift of a galaxy and its distance from earth, as Hubble concluded from his observations. But that does not necessarily falsify the theory of many local big shrinks.

The reason it escapes falsification is the difficulty in measuring the distances to faint galaxies. Hubble was able to measure galaxies only up to about ten million light years away, and even current attempts to extend the range of independent measurement of distance beyond that do not yield reliable, independent readings of distances to galaxies beyond our supercluster of galaxies. The most reliable measurement of distance depends Cepheid variable stars, whose intrinsic brightness is known, but it does not reach beyond our own Virgo cluster of galaxies, that is, about 50 to 75 million light years away. And though supernovae and sheer brightness of galaxies can be used beyond that limit, the reliability of those standards has not been established.

The correlation between red shift and distance within our supercluster of galaxies is what would be expected, according to the theory of local big shrinks, since it assumes that all those galaxies were generated at roughly the same time by the same local big shrink. The red shift of a distant galaxy within our supercluster would be explained by the length of time that light has been traveling since it was emitted, since both our galaxy would have been shrinking further during that entire period. Thus, the red-shift of a galaxy would be a good indicator of the relative distances to galaxies within our supercluster.

Disagreements about Hubble’s constant tend to cluster around two different values, one yielding about 20 billion years as the age of the universe and the other yielding about 10 billion years. That disagreement may be due, in part, to the attempt of one group of astronomers to measure the Hubble constant by more distant galaxies, some of which are beyond our supercluster, where it is much more difficult to measure distance.

Thus, it is possible to reject Hubble’s law as a misinterpretation of data from relative nearby galaxies in terms of the big bang theory and its assumed expansion of the universe. But recognizing its falsity would revolutionize out view of the universe, because red-shift would no longer be a reliable way of estimating the distance to faint galaxies.

Not only can the theory of local big shrinks explain all the phenomena on which big bang cosmogony is based, but there are observations that can be explained only by the theory of local big shrinks. For example, there is accumulating evidence of stars whose lifetimes are longer than the lower estimates of the age of the universe based on Hubble’s constant. But the most spectacular fallout is that it explains the observation of quasars.

Quasars are extremely red-shifted light sources that seem far too intense to be located as far away as they seem to be according to Hubble’s law. Its radiation is typically much more intense than the rest of the galaxy of which is a part. The radiation seems to come from something like a star, because its strength can vary too quickly for an entire galaxy to be its source. And it is widely assumed that the only currently plausible such an enormous quantity of energy is a giant black hole which is drawing large quantities of matter beyond the event horizon (at the Schwartzschild radius). But since they have much greater red shifts than is measured in galaxies from our supercluster, they are assumed to have existed very early after the big bang. Relatively few have less than an enormous red shift of z = 2, that is, with wavelengths twice as long as those generate by similar processes on earth, and some, with red-shifts approaching z = 5, seem to come from sources that existed as long as 12 billion hears ago. Twelve billion light years is an enormous distance in space, and it is quite astonishing that we are receiving light from a source that far away, because it means that the universe must be completely transparent throughout a sphere with that radius.

However, all these observations are precisely what would be expected on the local big shrink theory. As we have seen, it is likely that black holes would form early in the history of isolated galaxies because of the accumulating gravitational forces at the centers of those clusters of matter. Their formation early in the history of galactic development would explain their relatively greater red-shifts, because at that point in their development, particles would still be quite swollen. Assuming that the sizes of the particles varies with the wavelengths of the photons that their interactions give off, it would mean that matter at that stage is from two to five times the size it is on earth. The intensity of the radiation could be completely explained by its origin in a black hole, because quasars could be located so much closer to earth that would be required by Hubble’s law (though those with high red-shift must be located beyond our supercluster of galaxies). And this theory does not require us to believe that the universe is so transparent that photons can travel without being intercepted for 12 billion light years in every direction from earth.

Thus, quasars cannot be used as evidence against the theory of local big shrinks. It is much more likely that they are not how the universe looked early on after the big bang, but simply how it would look anywhere in the universe where the local big shrink had reached the stage at which galaxies were separate and black holes began to form at their centers.

But there is still one ontological objection to the theory of local big shrinks. Even if the universe as a whole is eternal and infinite, this theory seems to imply that matter is coming into existence, which contradicts the assumption of the conservation of matter (though not the more basic ontological principle that something cannot come from nothing). Where would the matter for the big shrink come from?

Again, however, spatiomaterialism seems to have an answer — an answer that also has to do with black holes. The one puzzling feature about black holes is what happens to the matter that falls into them. If there is a singularity at the center of the black hole, as seems required by the infinite force there, the matter seems to just disappear forever from the universe. The size of the Schwartzschild radius is the only indication of how much matter has disappeared into it.

However, that loss would not be permanent, if black holes were the source of the matter that shows up in local big shrinks. The laws of physics do not cover conditions as extreme as those that hold for the singularity in the center of the black hole, and thus, it is possible that matter is transformed into an aspect of space, that is, into a condition of space that could be the source of the matter that shows up as local big shrinks. This condition would hold only when enough matter had been gobbled up by black holes in the galaxies surrounding some vast empty region. But it is possible that when space has absorbed enough matter through those black holes, it gives birth to a big shrink in the nearest vast region of empty space between superclusters of galaxies.

There may be no need, therefore, to believe that the matter that comes to exist at the beginning of the local big shrink or the matter that comes to exist as particles with rest mass shrink and become more massive is coming into existence our of nothing. Instead of the “creation field” of earlier steady-state theories, what is needed is only a transformation field, in which matter absorbed by space from black holes re-emerges as a local big shrinks.

That is a process that could go on forever. Matter would be recycled, and the universe need never run out of room, for gravitational attraction would always be shrinking existing superclusters of galaxies away from some huge region of empty space or another. But it could mean that all galaxies are ultimately destined to be consumed by black holes.

No doubt, this theory of local big shrinks needs further refinement before it will be fully reconciled with what is known about physical processes. But it illustrates what could be true, if this is a spatiomaterial world and physics is explained ontologically.

Conclusion about local regularities. What has been established by Cosmology, and more broadly, by this ontological explanation of contemporary physics?

It is clearly not a necessary truth of ontological philosophy. This spatiomaterialist ontological explanation of the basic particles of physics and the origin of the universe is, like its explanation of quantum mechanics, more speculative than that. It is obviously incomplete, for there are many quantitative details to be filled in. And it would be surprising if it is not mistaken in some ways, especially the theory of the big shrink. What I have said above will have to be changed, not merely expanded.

Even what has been said about Einstein’s special and general theories of relativity is not a necessary truth. It is also just an ontological explanation of the truth of relativity theory. But I do claim that it is closer to the truth that contemporary physics. That is what needed to be shown to pay off the mortgage on spatiomaterialism and use it as the foundation for ontological philosophy. But I do not mean to make such a strong claim for what has been said about quantum mechanics, the basic objects, and cosmogony. They are more speculative, and I suspect that there still much gold to be mined in the hills of the theory of local big shrinks.

What I believe has been show in these past two chapters, on Quantum mechanics and Cosmology, is that some such theory is probably true. It is possible to give an ontological explanation of the truth of quantum mechanics, high energy physics, and big bang cosmology based on spatiomaterialism. That shows, at least, that spatiomaterialism cannot be rejected by claiming that it contradicts what has been discovered empirically in any of the fields of physics. But it also shows the fruitfulness of spatiomaterialism in physics.

The widely acknowledged problems about the theories in these fields of physics make them a rather flimsy foundation for denying a theory of empirical ontology. Though the big bang theory, for example, is warmly embraced by popular culture, where mystery and faith live comfortably with relativism, it is held with much less confidence by physicists, if only because they are, as naturalists, more inclined to believe that that the natural world is constituted by substances that exist independently of themselves. Though it is not an explicit principle of science, it simply does not make much sense to hold that something can come from nothing. Puzzles in the other fields likewise make scientists more skeptical than dogmatic. Few scientists would claim that physics has already discovered the deepest truth about the nature of what exists.

By saying that spatiomaterialism is fruitful in physics, I mean that it opens up new ways of explaining the observations made by physics. But to show that there is no reason to doubt that some ontological explanation along the lines of those given here is also to show that some such theory is probably true, because any such theory would explain more of the phenomena and explains it better than physics does at present.

What explain the power of spatiomaterialism to cast new light on physics is the difference between ontological-cause explanations and efficient-cause explanations with which we began in the Foundation of ontological philosophy. Instead of trying only to discover the laws by which it is possible to predict and control what happens, empirical ontology tries to discover the substances that would explain why those laws are true. In addition to efficient causes, it seeks ontological causes.

In these chapters on contemporary physics, we have seen what ontology can add, when it infers independently of empirical science to spatiomaterialism as the best ontological explanation of the natural world. Whereas physics relies on mathematics to represent the quantitatively precise relationship among properties by which it can predict the outcomes of measurements, ontological philosophy relies on our spatial and temporal imagination to represent geometrically the substances whose aspects are those properties.

The kind of mathematical representations used by physics are based on Cartesian coordinates, and that means that everything can be reduced to algebra, that is, basically, arithmetic. As we saw in Relations, the explanations of the truth of arithmetic and geometry are independent on one another. One comes down to counting units, while the other comes down to representing spatial relations spatially (or, more accurately, as we shall see, spatio-temporally), and both can be shown to correspond to aspects of a spatiomaterial world.

The power of ontological philosophy to illuminate contemporary physics comes from how spatiomaterialism adds spatial and temporal imagination to the more abstract mathematical imagination that is the workhorse of physics. Keep in mind that ontological-cause explanations do not replace efficient-cause explanations, but rather explain their truth. That provides a deeper explanation of the world, because it adds constraints that are understood through spatial and temporal imagination to constraints that are understood through mathematical manipulations. The puzzles in physics arise from the limitations inherent in its mathematical representations, mainly its attempt describe physics with nothing but the algebraic representations introduced by Descartes, and spatiomaterialism sheds light on physics, because it shows how it is possible to use spatial and temporal imagination to impose additional constraints on our beliefs about the world. And that is what I believe has been shown in these past four chapters. It points the way to new physics, a physics that is ontological. Some such ontological explanation of physics is possible.

In order to refute this argument, in other words, what is required is a proof that no such theory is possible. It is not enough to point to details that have not been explained. Nor even to point out ways that it is mistaken. I would be surprised if there were no mistakes in these theories. But goal in formulating them has not been to avoid small errors, but to show a larger truth. I believe I have done that. And to show that I have not, it is necessary to show that no spatiomaterialist ontological explanation of the truth of physics can be given. Having answered the challenge that contemporary physics might be thought to pose for the belief that this is a spatiomaterial world (and solved, in the process many of its unsolved problems), that is the challenge I make to physicists.

This concludes the ontological explanation of local regularities, but that is not all that is regular about change in a spatiomaterial world. We have been focusing, as physics usually does, on regularities about the motion and interaction of bits of matter that can be described relative to those bits of matter. We have seen the role that space plays in their explanation. But since the bits of matter all coincide with parts of space, space plays another role in making change regular, namely, how the wholeness of space makes the change that occurs in whole regions of space regular. That is what will be taken up at this point, and the conclusions to be drawn from that part of the argument are necessary truths of ontological philosophy. What will be said global regularizes does not depend on the truth of this ontological explanation of the truth of physics, because except for the implications of quantum mechanics for chemistry, it does not depend on contemporary physics at all. However, just as in the explanation of contemporary physics, the power of spatiomaterialism to cast light on what has been discovered empirically by these less general branches of science comes from how it adds a constraint to its conclusions that is understood through spatial and temporal imagination. And what is more, those conclusion will include an explanation of the nature of the faculty of imagination that makes it possible.

Global regularities about change. Global regularities are regularities about change in a spatiomaterial world that hold of whole regions of space.

Change, as an aspect of the substances constituting the world, involves something more than just properties and relations. It also depends on the temporal aspect of (the existential aspect of) the nature of substance as substance. Having explained (in the first two chapters of the Necessary Truths of ontological philosophy about What is) how properties and relations are aspects of a world constituted by space and matter (given how they exist together), we have already found in Change how the endurance of space and matter through time as substances explains local regularities about change. In the remainder of this ontological explanation of change, we shall see how the same ontological causes also explain global regularities about change. There are four kinds of global regularities, explaining, respectively, the truth of the first law of thermodynamics, the second law of thermodynamics, the principles of mechanics, and two unrecognized laws about evolutionary change.

There is, besides local regularities, another kind of effect that space has as an ontological cause. The two principles about local regularities describe limits that the structure of space imposes on how bits of matter change locations relative to one another and act on one another because they coincide with parts of space. The reason that there are also necessary principles about global regularities is that the parts of space all fit together as a whole. Bits of matter must move and interact (if they can move and interact act all) in some part of the same space that contains all the bits of matter in the world, and that means that the changes they undergo are all interconnected in a regular way.

The changes that occur in one place must affect bits of matter that are located nearby before they affect what happens farther away. That is a consequence of the principles of local motion and local action. But such effects do spread out in space as time passes, affecting more and more of the world. And it is a reciprocal relationship, because what happens elsewhere in space also has effects that spread back in space towards it. The structure of space with which they coincide helps determine how each event affects what happens elsewhere. But since that structure entails a wholeness about space, the motion and interaction of the bits of matter in any region of space must all add up in space as time passes. And insofar as the bits of matter are located in a region of space that is closed or isolated from the rest of the world, the way that all their local changes add up over time in the whole region may be regular. Since such regularities would hold of whole regions of space, I will call them “global regularities.”

Space is an ontological cause of regularities about change, because space and matter together constitute the world, and change is just an aspect that those substances have because they endure through time. We have seen how space is an ontological cause of local regularities. It causes global regularities in the same way. But global regularities are different, because they depend on a further aspect of the nature of space, the wholeness that is entailed by the geometrical structure of space.

Local regularities about change in bits of matter are caused ontologically by space, because the bits of matter all coincide with parts of space and change is just an aspect of substances enduring though time. It follows from this explanation of change, as we have seen, that two principles hold necessarily about how bits of matter change, namely, the principles of local motion and local action. They hold in every possible spatiomaterial world. But space also helps cause ontologically contingent laws about how bits of matter change, as we have seen by showing that space and matter can explain ontologically the truth of the basic laws of physics (classical and contemporary).

Global regularities about change are caused ontologically by space (and matter) in the same way, by constituting the world in which the regularities are aspects of substances enduring through time. They must be caused the same way, because space and matter constitute everything in the world and everything about the world. But global regularities are a different aspect of the change that takes place, because they depend specifically on the wholeness of space.

Local regularities are aspects of change that are picked out by referring to particular bits of matter and describing how they move relative to one another and how they interact with one another. But global regularities are aspects of change that are picked out by referring to space itself and describing how all the bits of matter in some region of space move and interact relative to it. Because of the wholeness of space, the local changes must all “add up” in the region of space as time passes, and what they add up to are global regularities about change over time.

It may not seem possible to describe motion and interaction relative to space itself, because velocity relative to space (absolute velocity) is not measurable. But that aspect of the relationship of bits of matter to space is not relevant in causing global regularities. What is relevant is that space connects what happens to all the bits of matter so that what happens to each must affect all the others. This comes from a property of space, namely, its wholeness, and it is not affected by absolute motion.

Physics does not necessarily ignore regularities as a result of failing to recognize that space is a substance. It can studies global regularities in practice by taking some more stable material object (such as the box containing a gas of molecules) as its frame of reference (and arguing from what happens in such closed regions to what would happen everywhere or anywhere in the world).

Wholeness is an aspect of the structure of space, because it is a consequence of the essential natures of the parts of space, that is, how they are related to one another geometrically in three dimensions. The wholeness is the fact that all the parts of space fit together in a uniquely simple way.

The aspect of the nature of space that is relevant in causing local regularities, both necessary and contingent, is the geometrical structure itself, that is, the relations among parts that are described by the various theorems of geometry (and trigonometry). That aspect of the space that contains the bits of matter determines, for example, where the inertial motion of a material object takes it, how fast, and which other bits of matter it will interact with as a result. It might be called the “local aspect of space.”

The global aspect of space is its wholeness, or the fact that all the parts of space fit together in the uniform, simple way they do. It means that parts of space in different regions fit together as parts of their more limited wholes in the same way. And the property of wholeness is a cause of global regularities, because it implies that the changes that occur to the bits of matter that coincide with different parts of space must all add up as time passes. How they add up in space also depends on the local regularities and basic laws of physics (which are explained ontologically by the nature of matter and the local aspect of space). But that they all add up as time passes depends on its wholeness. And we shall see how local changes add up in space over time to global regularities.

Space is, therefore, together with matter, the ontological cause of another kind of regularity about change, besides local regularities. That means that there is an ontological necessity about global regularities, because ontological philosophy takes every proposition that follows from its ontological foundation to be a necessary truth. But unlike the two principles about local regularities, the following global regularities (except for the simplest) have only a conditional ontological necessity, because they also depend on matter and space having the specific natures they have in our spatiomaterial world, that is, on the basic laws discovered by physics. Hence, global regularities are only conditionally necessary truths. Their truth is ontologically necessary only in a spatiomaterial world like our own.

In a spatiomaterial world with different physical laws, there might not be any interesting global regularities, because bits of matter do not move and interact at all or they move and interact in different ways. However, as we shall see, the physical laws in the actual world seem to be of just the right kinds to make the most of the wholeness of space in generating global regularities. Many regularities that are not even currently recognized to hold turn of our world out to be ontologically necessary in spatiomaterial worlds like our own.

To be sure, in order to use spatiomaterialism as an ontological foundation for proving necessary truths about the world we had to take out several mortgages. But they are being paid off, and in any case, global regularities do not involve any of the extreme phenomena on which Einsteinian relativity is based.

Two of these mortgages have been paid off. We kept our promise to explain the nature of consciousness in Properties. And the debt that arose from the apparent incompatibility of spatiomaterialism with Einsteinian relativity was paid off by explaining ontologically why Einstein’s theories are true. Indeed, we have seen that all of the basic laws of classical and contemporary physics can be explained as regularities that hold of substances that endure through time as a spatiomaterial world. (See Contingent laws).

Having just completed those explanations, it is relevant to mention, furthermore, that far from casting doubt on spatiomaterialism, contemporary physics provides additional empirical evidence that spatiomaterialism is true. The recognition of space as a substance would solve several mysteries that currently puzzle physics, such as the nature of spacetime, curved spacetime, the relationship between gravitation and quantum mechanics, and even the Bell Inequality entailed by quantum mechanics. And science has further reason to accept this ontological explanation of physics, because it offers a new approach to cosmology which may help solve the prevailing mysteries about the origin of the large scale structure of the universe.

In fact, given our interpretation of contemporary physics, the existence of space as a substance can even be shown by an inference to the best efficient-cause explanation, because substantival space is the efficient cause of the Lorentz distortions (which explain the phenomena of special relativity) and its interaction with centers of mass is the efficient cause of the acceleration of the ether (which explains gravitation). That is, scientific realists about contemporary physics would have to admit that space is a substance, if they believed that nothing exists but the present moment, for the existence of space would be known by its effects on the behavior of matter.

Global regularities are not very sensitive to the extreme phenomena that divide contemporary from classical physics. They are basically unaffected by Einsteinian relativity, as long was we can take gravitation for granted and can assume that the universe has a large scale structure that includes planetary systems like ours. Most global regularities do depend on matter being of the kind found in our spatiomaterial world and, thus, on quantum mechanics. But none of the puzzling phenomena of quantum mechanics are particularly relevant. Global regularities depend mainly on the wholeness of space, that is, how, by containing all the bits of matter, space gives the world itself (as well is regions within it) a determinate wholeness.

There are four kinds of global regularities. Each is recognized in a way by empirical science, as a principle, law or “mechanism” of some kind. But since empirical science does not recognize the validity of ontological explanations, it does not recognize space as an ontological cause of them, and thus, it does not have an explanation of why these regularities hold. Nor does it always fully recognize what the regularities involve. Furthermore, although global regularities depend on the basic laws of physics, they do not follow from those laws alone, and thus, empirical science does not recognize that they are necessary, even when the basic laws of physics are assumed.

The crucial role in explaining each of the kinds of global regularities ontologically is played by space, and more specifically, by the wholeness of space (or, if you will, the “global aspect” of space). Though the wholeness of space makes the world itself whole, it also makes every region of space whole. Thus, global regularities can be seen in regions of space that are somehow closed or isolated from the effects of what happens outside. Since the global regularities are ontological effects of the wholeness of space (and what coincides with it), they arise from inside the region.

The reason there are four different kinds of global regularities is that different aspects of what exists according to spatiomaterialism can be combined with the wholeness of space to generate regularities about the change that occurs in whole regions of space as time passes.

Spatial global regularities. The first kind of global regularity has a single instance, namely, the conservation of matter. It will be called the “spatial global regularity,” because it makes no assumptions at all about the nature of matter except that it is many different substances that each coincide with some part of space or other. Thus, the spatial global regularity can be said to be generated by “spatial causation,” for it is how the wholeness of space makes any kind of matter add up over time. When we take into account the various forms of matter that we distinguished in order to explain the truth of the basic laws of physics ontologically, spatial causation will also explain ontologically the truth of the first law of thermodynamics, the principle of the conservation of energy.

Material global regularities. The second kind of global regularities will be called “material global regularities,” because in addition to the wholeness of space, these regularities depend on matter obeying the basic laws of physics. Alternatively, material global regularities will be said to be generated ontologically by “material causation,” for they are simply how the wholeness of space requires motion and interaction to add up over time when the bits of matter obey the basic laws of physics. That will explain ontologically why the second law of thermodynamics is true.

Structural global regularities. The third kind of global regularities will be called “structural global regularities,” because in addition to the wholeness of space and material causation, these regularities depend on the unchanging geometrical structures of the material objects contained in the region of space, or what will be called “material structures” or “structural causes.” Structural global regularities will be said to be generated ontologically by “structural causation,” because these regularities are how the wholeness of space requires motion and interaction to add up over time when the bits of matter include material structures (or particular structural causes). This explains ontologically the truth of the principles of mechanics (such as the principle of the lever), and when combined with the other ontological effects of material causation, it will explain the sense in which machines can “do work” and certain dispositional properties.

Reproductive global regularities. The fourth kind of global regularities will be called “reproductive global regularities,” because in addition to the wholeness of space, material causation, and structural causation, these regularities depend on how complex material structures go through reproductive cycles, that is, how they go through cycles of structural global regularities that include the reproduction of the structural cause itself as well as non-reproductive work. Thus, reproductive global regularities will be said to be generated ontologically by “reproductive causation,” because these regularities are simply how the wholeness of space requires motion and interaction to add up over time when the bits of matter include complex material structures going through cycles of reproduction. This will explain ontologically the truth of Darwin’s mechanism of evolution, or what might be called the principles of evolution, which includes much more than is currently recognized.

The order of these kinds of global regularities is necessary, because each adds a new ontological cause that works together with ontological causes of all the previous global regularities. That is, we start by assuming that the world is constituted by space and matter (with all the bits of matter coinciding with some part of space or other), and we consider how the wholeness of space constrains what happens to the bits of matter. When no further assumptions are made about the nature of matter, these assumption entail the simplest global regularity (spatial causation). The second global regularity adds that matter with the specific nature described by the basic laws of physics, including the forms of matter that were distinguished. The third adds material structures to the region. And the fourth adds the temporal structure of complex material structures going through reproductive cycles.

The first global regularity is entailed by the basic assumptions of spatiomaterialism themselves, and each of the other three is the result of adding an ontological cause, that is, assuming something further about the nature of what coincides with space in the region: about the specific nature of matter, about its spatial structure, and about its temporal structure.

Thus, considering the ontological causes added to the basic assumptions of spatiomaterialism, material global regularities may be said to be due to “material causation,” structural global regularities may be said to be due to “structuro-material causation,” and reproductive global regularities may be said to be a result of “temporo-structuro-material causation.” Those names bring out the necessary order of the global regularities in a spatiomaterial world.

In the following four sections, these kinds of global regularities will be shown to follow from spatiomaterialism and the kind of matter that explains the truth of classical and contemporary physics ontologically. If nature had a different essential nature, some of the global regularities might not hold. (For example, there would be no structural causes unless matter could make up material objects with geometrical structures that do not change as they move and interact.) But given that matter takes the various forms we used to explain the basic laws of physics, the global regularities are simply how the wholeness of space makes the change in what coincides with space add up as time passes. The ontological effect of spatial causation includes the first law of thermodynamics, or the principle of the conservation of energy. When material causation is added to spatial causation, the ontological effect is the second law of thermodynamics, or the law of entropy. When structural causation is combined with spatial and material causation, we have an explanation of how machines do work. Finally, when reproductive causation is added to spatial, material and structural causation, the ontological effect is evolutionary change.

The ontological explanation of evolution as a global regularity has, as we shall see, implications about what is to be found in nature that goes far beyond what is recognized by evolutionary biology and contemporary Darwinists. But it depends on all the other global regularities, and so we will begin with the simplest and work our way up.

Spatial global regularities. The basic spatial global regularity is that matter is conserved. The total quantity of matter in any closed or isolated region of space does not change. But under certain circumstances, it entails a less general spatial global regularity, the conservation of energy.

“Spatial global regularity” is an appropriate name, because nothing is assumed about the nature of matter except what is entailed by spatiomaterialism (besides space, the existence of many particular substances, each coinciding with some part of space or other.) This global regularity is the purest ontological effect of the wholeness of space.

The regularities caused ontologically by space are not just global. The structure of space also helps cause necessary principles and contingent laws about local regularities (or the basic laws of physics, classical and contemporary). Since bits of matter have spatial relations to one another because they coincide with parts of space, the way those spatial relations change as a result of motion is partly determined by the structure of space. This might be called the local aspect of space.

The global aspect of space, on the other hand, is its wholeness, or the fact that all the parts of space fit together as a single system of locations that are all related to one another geometrically. The wholeness of space is an ontological cause of regularities about change in entire regions of space, because it requires that all the local changes that occur in any region fit together in space as time passes.

When combined with the assumption that matter has a nature that makes the basic laws of physics true, the spatial global regularity (that matter is conserved in a closed or isolated system) entails that energy is conserved in any closed system. That is an ontological explanation of the first law of thermodynamics in a spatiomaterial world like ours.

Conservation principles are called “principles”, because they are supposed to be too basic to be explained by anything else. But conservation principles can be explained ontologically, though in the case of the conservation of matter, the global regularity is so obvious that it may seem to be trivial.

The conservation of matter. Spatiomaterialism holds that matter and space are substances enduring through time. Since matter is a substance, it neither comes into existence nor goes out of existence over time. That is how matter itself is an ontological cause of the conservation of matter. The total quantity of matter cannot change, because matter is a substance. But space is also a ontological cause of this regularity, because matter is contained by space and it is by coinciding with parts of space that bits of matter have spatial relations to one another. Space is what gives particular substances the relationship that makes it possible for them to add up, that is, to be added together and have a total, as we saw in Relations, where the truth of mathematics was explained ontologically.

The relevance of space as a cause of conservation principles is implicit in the way they are formulated. They hold that some quantity does not change in closed or isolated regions of space. But this reference to a region of space indicates a further ontological effect of space. The reason the total quantity of matter does not change in any closed or isolated region of space is that that is how change of any kind adds up in space as time passes when the bits of matter conform to the principle of local motion.

The principle of local motion holds that the only way that bits of matter can change location is by motion, and since it was derived from spatiomaterialism, it is an ontologically necessary principle. But if it holds of all possible change, then the total quantity of matter in a closed region of space cannot change, because to be closed or isolated means that there is a two-dimensional surface surrounding the matter across which no matter is moving That is how bits of matter must “add up” over time because they coincide with space as a substance enduring through time. “Adding up” is an ontological consequence of the wholeness of the space that contains them.

Change in bits of matter adds up in space in the same way that the bits of matter themselves add up in space, except that change takes their endurance through time into consideration. The bits of matter endure though time, but since whatever happens, they cannot change location except by motion, the total matter cannot change in any closed or isolated region of space.

Though it may be obvious and simple, the lack of change in the total quantity of matter in a closed region of space is a regularity about change over time. It is a global regularity, because it has to do with the properties of whole regions of space. The regularity is not just what is assumed by postulating matter as a substance, but rather is explained ontologically by spatiomaterialism, because it is an aspect of the world enduring through time that depends on both space and matter and how they exist together as a world. Thus, the conservation of matter is an ontologically necessary regularity. If the total matter in a closed or isolated region did change, spatiomaterialism would be false. Matter is conserved, therefore, in every possible spatiomaterial world.

The conservation of energy. The first law of thermodynamics is the principle of the conservation of energy. It is a consequence of this spatial global regularity, if we take into account the forms of matter we have assumed in order to explain the basic laws of classical physics ontologically.

This implication will hardly be a surprise, since we used the principle of the conservation of mass and energy as a guide to ensure the completeness of our inventory of the forms of matter that had to be postulated in order to explain the basic laws of classical physics. But since that was just a working hypothesis for distinguishing the various forms of matter, it is relevant, now that we have shown that the forms of matter we assumed can indeed explain the truth of the basic laws of physics, to consider how those forms of matter make the principle of the conservation of energy true. The ontological explanation is not as simple as it may seem.

It may seem that the principle of the conservation of energy is an immediate consequence of the conservation of matter, because it is usually assumed that mass and energy are conserved separately as long as no nuclear reactions, converting rest mass to energy, occur in the region. The total quantity of matter that exists as energy in the region cannot change, because when the total rest mass does not change, matter does not exist in any other forms and matter does not come into existence or go out of existence.

However, the principle of the conservation of energy is not so simple ontologically, because given our ontological explanation of the nature of potential energy, there is a conversion between rest mass and kinetic energy (or other forms of actual energy) whenever potential energy is being consumed or created, which happens in most ordinary physical processes.

Material objects exert forces that can accelerate material objects, and our theory is that those forces are a form of matter that helps make up the material objects and whose quantity is counted in their rest masses. When potential energy has given the objects kinetic energy, for example, the objects have not only changed their relative positions, but the force field itself has changed. The change in the force field means that less matter is required to constitute it, and that is the source of the kinetic energy, which on our theory is also a form of matter. Thus, it is a conversion of some of the matter counted as rest mass into matter that is counted as kinetic energy. The opposite conversion occurs when kinetic energy becomes potential energy, and the same principle holds for conversions between potential energy and photons (and other forms of matter). Thus, the conversion between potential energy and kinetic energy does not violate the principle of the conservation of mass and energy.

Even though, in these processes, matter is being converted between a form that is counted as rest mass and a form that is counted as kinetic energy, the total quantity of energy does not change. The reason is that potential energy is counted as zero when it is maximum and that any potential energy that is consumed as kinetic energy (or photons) is counted as a bit negative energy in the region. There can be no such thing as negative matter, since matter is a substance. But counting potential energy as negative energy keeps the energy accounts balanced.

Negative potential energy is explained ontologically as a decrease in the rest masses of the material objects. The “rest mass” of a material object is defined, according to our ontological explanation of physics, as its mass when it is at rest in absolute space and the only force field in its neighborhood is the one that it imposes by itself (that is, separate from other material objects).

Thus, when it is (falsely) assumed that the rest masses of the objects involved are unchanged, counting potential energy as negative energy keeps the total quantity of mass and energy the same. The actual loss of mass from the total quantity of rest mass in the region is so small (according to Einstein’s equation, E = mc²) that the change in potential energy is not easily detected as a change in rest mass. Thus, counting potential energy as a negative quantity makes it seem that energy is conserved separately from rest mass in these processes.

But in fact, rest mass is not conserved. An object’s mass changes as its potential energy is actualized. Only the total of mass and energy are conserved even in most ordinary processes (where an object’s mass apart from its kinetic matter is accurately determined by subtracting the potential energy it has given up from its rest mass).

Thus, whereas the conservation of matter is an ontologically necessary global regularity, the conservation of energy is ontologically necessary only on the condition that matter has a nature that makes the basic laws of physics true, and thus, this shows it to be ontologically necessary only in spatiomaterial worlds like our own.

Material Global Regularities. The second law of thermodynamics, like the first, is stated as a regularity about the change in a total quantity that holds of closed region of space: the total entropy cannot decrease, though it may increase and usually does until it is maximum. It is also possible to explain the second law of thermodynamics ontologically, given that matter obeys the basic laws of physics. Once again, it an ontological effect that space has on the world because space, like matter, is a substance enduring through time and it contains all the bits of matter. Unlike the explanation of the conservation of matter, however, the explanation of the law of entropy depends not only on the principle of local motion, but also on matter having the more specific nature described by the laws of physics, whose truth was explained in Contingent laws. The reason is that there are geometrical aspects about the various forms of matter involved, and thus, not only does the wholeness of space require that all their local changes add up over time, but the structure of space requires the motion and interaction of the bits of matter to add up in a certain way geometrically.

The first and second laws of thermodynamics. The spatial and material global regularities made their appearance in physics as the first and second laws of thermodynamics. These laws were originally formulated to describe certain phenomena that were discovered in the development of steam engines. Physicists knew that steam engines could extract mechanical work from heat energy, but when they recognized that the total energy in a closed system does not change (the first law of thermodynamics), they had to admit that only some of the energy in such a system could be used to do mechanical work, for a closed system could change in ways that make it unable to do work. They knew that what makes it possible to extract mechanical work from the energy contained in such a system is a flow of heat from high temperature regions to regions with a lower temperature. The energy that is available to do work was called “free energy” (or “usable mechanical energy”). Thus, they recognized that, although the total energy in a closed system does not change, the free energy does. The free energy can decline and usually does. A quantity was introduced as a measure of the portion of the total energy in the system that could not be used to do mechanical work. They called it “entropy”. Thus, in these terms, the second law of thermodynamics holds that the entropy in any closed system never decreases. It may increase, and usually does, stopping only when it becomes maximum. But it never decreases. What decreases as entropy increases is free energy. The notion that there is a form of energy that declines, even though energy is conserved, was puzzling. And though it was discovered by thinking about steam engines, the second law of thermodynamics was eventually recognized to hold for systems of all kinds. The law of entropy increase is universally true, holding everywhere (except possibly for the origin of the universe in a big bang or the alternative to the big bang to be proposed in Cosmology).

The free energy available in a system has something to do with “order”, but it has never been very clear what order is in general or how it makes energy free.^xxxiii In the case of steam engines and heat engines generally it is clear what the relevant order is. It comes down to the temperature differences between parts of a system and the quantities of heat each contains, for the flow of heat between them is what makes it possible to extract mechanical energy. But when the law of entropy is generalized to cover systems of all kinds, it is less clear what the nature of the order is.

It is, however, possible to explain order of all kinds in an intuitively clear way, if we take the wholeness of space into account as an ontological cause of global regularities, along with matter as contained by space. Energy is, in our terms, a form of matter, the same stuff that accounts for the rest mass of material objects, though there are several, basically different forms of energy—kinetic energy and the energy due to forces, both potential and actual (especially, photons). What makes energy free is, as we shall see, a geometrical aspect of these forms of matter and how they are contained in a region of space, for there are regularities about how such geometrical properties change over time. Showing that these global regularities follow from spatiomaterialism is, therefore, an ontological explanation of why the first and second laws of thermodynamics are true. It will require not only the material global regularities, but also the structural global regularities (to be discussed next). However, not only will that prove their ontological necessity, but it will also make clear what these regularities are all about in their full generality, including the way in which free energy depends on order.

Two global regularities are involved in making the second law of thermodynamics true according to this ontological explanation. The first is the tendency of potential energy to become kinetic energy or photons (or the tendency toward kinetic energy), and the other is the tendency of dynamic processes to become random (or the tendency toward randomness). Both are ways in which the specific nature of matter works together with space as an ontological cause to constitute a global regularity. But they work together, because the first is usually the source of the situations in which the second global regularity is exhibited. Let us consider each in turn and then see how they are combined.

The tendency toward kinetic energy. The first global regularity included in the second law of thermodynamics is the tendency of potential energy to become kinetic energy (and photons). The very name, “potential” energy, suggests this tendency, because potential energy is actualized by becoming kinetic energy (and/or photons). Though it is also possible for kinetic energy to become potential energy, the tendency is toward kinetic energy, because potential energy that has become actualized is less likely to restore itself. In order to see why, we need only contrast the natures of potential energy and kinetic energy. The same kind of contrast also shows that potential energy tends to be lost to other kinds of energy, such as photons, but to keep it simple, let us focus on kinetic energy for now.

When potential energy becomes kinetic energy, the kinetic energy comes from the forces that material objects exert on one another. According to our ontological explanation of the basic laws of physics, potential energy is actually a form of matter that constitutes the force fields themselves (and whose quantity is already counted in the rest masses of the objects exerting the forces). A force is called a field because its (potential) effects are distributed in the space around the object imposing the force, with a geometrical structure centered on the location of the object. That force field is explained ontologically by a form of matter that coincides with all those parts of space at once, and thus, the matter has a geometrical structure. The matter making up the force is spread out continuously in space, varying with the strength of the force it exerts. That geometrical structure means that there is a wholeness about the energy when is still potential, because each part contributes to the total potential energy (and, thus, to the total rest mass of the material object exerting the force) by having a definite location relative to every other part.

Kinetic energy, by contrast, is a form of matter that is not only attached to the material object, but also located at its center of mass. Kinetic matter, as we are calling it, has a location that enables it to connect the material object to space in a way that makes the object move across space in some direction at a certain speed. But that means that kinetic energy (or kinetic matter) lacks any inherent geometrical structure, except for the location of the object and its direction in the region where it exists.

Given that potential energy has an inherent geometrical structure and that kinetic energy does not, we can see why there is a tendency of potential energy to become kinetic energy in the motion and interaction of material objects by considering what is involved in the conversion between them. In order to convert potential energy into kinetic energy, more than one material object must be involved, because kinetic energy is actualized as material objects are accelerated by the forces they exert on one another. Such acceleration can occur only when the objects are spatially related so that the forces they exert on one another are able to accelerate them, and when they are a source of much energy, they are rather special. Objects at rest, for example, can acquire kinetic energy from attractive forces only when they are separated by a distance that can be closed by their acceleration (and they can acquire kinetic energy from repulsive forces only when they are located near one another and can move away). When objects are accelerated, however, the objects change their locations in space, and that changes the capacity of the force to accelerate them, because it decreases the special kind of spatial relationship needed to accelerate them. The potential energy has been consumed, and in its place the objects have some kinetic energy. The kinetic energy actually comes from the matter constituting the force field, and that is possible because the force field itself has changed in a way that requires less matter to constitute it. Thus, what has happened is that some of the matter that had an inherent geometrical structure has been extracted and has become matter that is located with the objects’ centers of mass. The matter’s loss of inherent geometrical structure is what is responsible for the temporally asymmetric tendency, for that makes it a form of matter that can be divided up among many other material objects as they interact. In particular, according to Newton’s laws of motion, when an object with high kinetic energy interacts slower moving objects, some of its kinetic energy is carried away by the other objects, being divided up among them.. It is not very likely that other objects will ever move in just the right ways to restore the special spatial relation that accelerated the object in the first place.

For example, if an object falls toward a planet because of the gravitational forces they exert on one another, it loses its potential energy as it approaches the planet and it gains kinetic energy. But as it collides with other material objects, either on its way down or when it runs into the earth, it gives up kinetic energy, and though it may rebound, much of its kinetic energy will be lost to other objects (and to overcoming the forces that may be involved in its fragmentation or deformation). The system will never restore the object’s potential energy.

To be sure, the conversion can work the opposite way. When objects exerting forces on one another have accelerated one another and lost potential energy, they have also acquired kinetic energy, and that can restore potential energy. Objects with kinetic energy restore potential energy when their retreat from one another is slowed by attractive forces (and when their approach to one another is slowed by repulsive forces). Indeed, a system involving only two material objects may simply go on converting energy between kinetic and potential forms indefinitely, such as a planet in an elliptical orbit around its star.

The reason there is a tendency toward kinetic energy is that other material objects are usually involved. According to Newton’s laws of motion, when objects with kinetic energy interact with one another, they exchange kinetic energy in a way that tends to equalize the kinetic energy among them. Thus, objects with unusually large amounts of kinetic energy see their kinetic energy divided up into smaller bits of kinetic energy that subsequently move around separately from one another. Kinetic energy is no longer moving objects in the right locations in the right directions at the right times to restore the unusually large potential energy from which it derived.

For example, even in a pendulum, which continually converts potential energy to kinetic energy and back again as it rises and falls in the gravitational field, this tendency to kinetic energy cannot be avoided. The bob also loses kinetic energy as it collides with particles of air and as it stretches and relaxes its tether, and it never restores all the potential energy and eventually comes to a stop.

There are, of course, processes in which kinetic energy and potential energy are continually being converted into one another, such as those involved in elastic collisions or a plasma of charged particles, but the potential energy in those processes is not a source of free energy, but just part of a random interaction that is the subject of the other global regularity, as we shall see.

The wholeness of the space containing the objects and their two forms of energy is what requires all the motion and interaction of bits of matter in the region to add up over time. That is how space causes all the global regularities. But in the case of the tendency to kinetic energy, space plays an additional role, which depends on its geometrical structure. There is a geometrical structure inherent in potential energy, and since it is superimposed on the uniform structure of space, there is a geometrical aspect to how the motion and interaction of the material objects adds up over time. A region with a large amount of potential energy must have a rather special geometrical structure, because potential energy exists in the forces that objects exert and it can be converted to kinetic energy only when objects have kinds of relative locations in the force fields they impose that can accelerate them. There is a tendency to kinetic energy, because when it becomes kinetic energy, is a form of matter that is located with the center of the material object’s rest mass, thereby losing that kind of its geometrical structure inherent in potential energy. It moves across space with the material object and can be transferred to other objects by collisions, which tends, as we shall see, toward randomness. Thus, the geometrical structure inherent in potential energy tends to be erased from the region.

In other words, when potential energy becomes kinetic, matter that did exist as part of the whole force field surrounding the material objects comes to be kinetic matter located with their centers of mass, and that makes it possible for the matter to be divided up further by collisions with other material objects. Once the matter is divided up, it is unlikely that the objects will have just the right speeds in the right directions at just the right locations and just the right times to put the objects back in the same spatial relation that gave them potential energy in the first place. Indeed, it is unlikely they will put any object in any similar significant source of potential energy, for that would require assembling separate bits of matter as a form of matter (a force being exerted) whose inherent geometrical structure is testimony to its unity as a single bit of matter.

The examples used here are based on gravitation,^xxxiv but it should be noted that the same holds for electromagnetism and short range forces. When protons are combined randomly with electrons, their long-range attractive forces bind them together as hydrogen atoms, and though the potential energy may take the form of photons, instead of or as well as kinetic energy, the photons also lose their energy as they are scattered by other objects with electric charges and the geometrical structure inherent in potential energy is still broken up into many smaller bits.

Much the same happens in the case of short-range forces, though the spatial relations required to actualize potential energy are different. In nuclear fusion reactions, for example, nuclei must collide with enough energy to overcome an initial repulsion by the strong force, for otherwise the short-range attractive force does not reach far enough to bind them together.

Likewise, atoms (or groups of atoms) that exert attractive forces on one another may be separated too far by the molecular structures of which they are parts for their forces binds them together, until the local temperature is high enough for collisions to put them momentarily within the effective range. This is what happens when a match is used to start combustion.

Likewise in fission reactions, the potential energy of repulsion between clusters of positive charges in a heavy nucleus becomes kinetic when they fly apart, but first the nucleus must be made unstable by the absorption of a neutron.

In these cases the geometrical structure inherent in potential energy is more internal to the material objects, but that structure is still part of the geometrical structure of matter in the region, for there must be conditions in the region that will release it.

The tendency toward randomness. What tends to become random is the motion and interaction of bits of matter in a closed or isolated region, or what may also be called “dynamic processes.” In the dynamic processes used to think about this phenomenon, material objects are assumed to have repulsive forces by which elastic collisions keep them from occupying the same places at the same time.

In elastic collisions, material objects keep moving and interacting, because no kinetic energy is lost or absorbed by their parts when they interact. Force fields and conversions to potential energy are actually involved in these interactions, but they can be ignored here, because there is no net change and we want to consider what happens to their kinetic energy and other properties of the kinetic matter attached to material objects.

The traditional model for the tendency to randomness is the motion and collisions of billiard balls in a box. Once again, it is being contained by space that requires their motion and interaction to add up over time, and all that is needed to see why there is a tendency to randomness is to consider how motion and interaction in accordance with Newton’s laws of motion add up in space over time. There is, once again, a geometrical structure about the region that gets wiped out.

In a spatiomaterial world, everything happens by the motion and interaction of bits of matter, and in this case, it is extremely simple, because the bits of matter are all material objects with rest mass and kinetic energy (that is, the kinetic matter attached to material objects). There is no geometrical structure about the material objects in the region except their locations, speeds and direction of motion. These three properties are the initial conditions that would have to be described along with Newton’s laws of nature, according to the D-N model of explanation, in order to predict and explain what happens. They are all part of the efficient cause that determines what happens in the region. But it is not necessary, or even relevant, to derive mathematically what happens in detail in particular cases. If we consider the material objects relative to the space that contains them, we can see why their motion and interaction becomes randomized before long, if they aren’t already, because it is due to a geometrical aspect that we can understand, when we see them against the background of space.

The wholeness of space is what requires the motion and interaction of the bits of matter located in the region to add up as time passes, but the structure of the space within the region is what determines how the local changes add up. The objects have locations, speeds and directions at any moment that determine a geometrical structure relative to space, and when they move and interact according to Newton’s laws of motion, local changes add up in space over time in a way that erases that geometrical structure by evening out the spatial distribution of all three of the kinds of efficient causes that are relevant.

This tendency can be seen in each of the kinds of relevant efficient causes. That is, (1) the rest masses of material objects become spread out evenly throughout the region of space, (2) their kinetic energies become evenly distributed in space, and (3) their directions of momentum also tend toward an even spatial distribution.

(1)   If there are more material objects moving and interacting in one part of the region of space than in another, as when a gas of molecules is released in a vacuum, they will spread themselves out, because, other things being equal, objects at any boundary between highly and lowly populated regions are more likely to be turned back by collisions on one side than on the other. Hence, material objects will tend to move toward the less populated region until they are all evenly distributed in space.

(The diffusion of the molecules of one gas or liquid that is released into another works similarly, because when the objects colliding have different rest masses, the directions of the motion of less massive objects tend to change more, until the more massive objects are evenly distributed among them.

(2) Randomness may still not prevail, however, when rest masses are evenly distributed in space, because objects in some areas may be moving faster than those in other areas, for example, when there are hot spots or cold spots in the region. However, such spatial unevenness in their kinetic energy is also evened out, because elastic collisions of slow-moving with fast-moving rest masses tend to speed up the former and slow down the latter. That is the only what that both kinetic energy and momentum can be conserved. Kinetic energy tends to be divided up among the colliding objects. Thus, at the boundary between regions of different temperature, symmetrical elastic collisions will be so located and oriented in space that kinetic energy is communicated to the less energetic regions (that is, by conduction of heat).

(3) Motion and interaction may still not be random, even when rest masses and their kinetic energies are distributed evenly in space, because their speeds may be mostly in the same direction, as in a wind. But any such unevenness in the distribution of direction of motion among the objects also tends to be evened out, because when kinetic energies are evenly distributed within and outside the wind (their temperatures are the same), the wind tends to be invaded by objects moving perpendicularly to it. Objects making up the wind have more of their kinetic energy tied up in moving in the direction of the wind than objects outside the wind, and thus, objects approaching the wind perpendicularly are less likely to be turned back by collisions than those traveling in other directions (that is, the pressure exerted sideways by molecules of the wind will be less than elsewhere in the region, called the Bernoulli effect). As molecules invade the wind, they collide with molecules making up the wind, which tends to make their directions more perpendicular to the wind, and such reactions are more likely until the directions of momentum of all the objects in the region are evenly distributed.

The result is that the rest masses of the objects, their kinetic energies, and their directions of motion all tend to become evenly distributed in the region. That is the tendency toward randomness, and this distribution can be described statistically. But since heat is just the kinetic energy of the molecules in these simple cases, it is a tendency of kinetic energy to become evenly distributed heat, equalizing the temperature everywhere.

This tendency continues to hold when we take various complications into account. For example, collisions among real molecules are not necessarily elastic, because they can absorb some of the kinetic energy being exchanged. But as the kinetic energy is evened out among the objects, so is the energy absorbed by their parts.

And though material objects also emit and absorb photons, the spatial distributions of the locations, directions, and energies of the photons in the region also tends to be evened out by their interactions with the material objects, assuming that photons are reflected back and the region is closed. There are no kinds of interactions that can prevent the randomness.

The tendency toward randomness is that aspect of the law of entropy that is described as heat flowing from regions of high temperature to regions lower temperature, like water from high altitudes to lower altitudes. And since kinetic energy is a form of matter, according to this ontological explanation, it can even seen as vindicating the belief that heat is a “caloric fluid” that exists in addition to the rest masses of the objects involved. It is a form of matter that flows from hot regions to cold.

There is nothing very original about this explanation of the tendency to randomness. These effects are obvious to anyone who thinks about concrete examples of this tendency. What is new is recognizing that the tendency depends not only on the nature of matter (that is, the basic laws of physics), but also on the nature of the space with parts of which all the bits of matter coincide.

Our ontological foundation entitles us to take space into account as an ontological cause in explaining regularities about change. The wholeness of space is what requires the motion and interaction of all the objects to add up over time, as in all global regularities. But how they add up over time also depends on the structure of space, for it is only against the background of space that the causally relevant factors determine a geometrical structure.

It is the lack of evenness in the spatial distribution of one or more of the relevant efficient causes (their locations, kinetic energies, or directions of momentum) that makes the state non-random. And in each case, a geometrical structure about the non-random state is what causes the tendency toward randomness. It is the structure of space that determines where their motions will lead them and which objects they will interact with next. And we have seen how the unevenness in the distribution of the causally relevant factors puts certain objects are in asymmetrical situations which will eventually even out the spatial distribution of these factors. Thus, the temporal asymmetry of the second law of thermodynamics is a result, not only of the basic laws of physics, but also of how the motion and elastic collisions of material objects obeying those laws add up over time because they are contained by space.

Thus, when we take space into account, there is no mystery about why there is a temporal direction to change in which the kinetic energy of objects in non-random states winds up as heat evenly distributed in the region. The geometrical structure involved in any unevenness about the distribution of the three relevant factors is what causes those aspects of matter to become evened out in space, that is, more like the structure of space containing them.

The second law of thermodynamics. This ontological explanation of the second law of thermodynamics reveals that two different global regularities are involved: a tendency of potential energy to become kinetic energy (and/or photons) and a tendency of kinetic energy (and/or photons) to become evenly distributed heat. In both cases, there is a geometrical structure about the region that tends to be wiped out by how objects move and interact. One is the geometrical structure that the region has because it contains the geometrical structures inherent in the potential energy of forces (which can become kinetic energy). The other is the nonrandom distribution of causally relevant factors in the region (which tends toward the randomness of evenly distributed heat). Both kinds of geometrical structures tend to go out of existence, as we have seen, because that is how the motion and interaction of the bits of matter adds up over time because of the uniform structure of the space containing them. In one case, when the energy of position becomes energy of motion, matter with an inherent geometrical structure is replaced by a form of matter that can be broken up into different pieces. And in the other case, when any of the causally relevant factors is unevenly distributed, that is a geometrical structure in the region that tends to wipe itself out over time, with kinetic energy winding up as heat evenly distributed in the region. When geometrical structures of either kind go out of existence, only very special situations can bring them back into existence. And these two tendencies are connected, because the tendency to kinetic energy supplies nonrandom dynamic processes that tend to become random. Together, they make up a temporally asymmetrical change in the region as a whole.

Given how both global regularities involve the disappearance of a special kind of geometrical structure in the region as time passes, it may be useful to suggest that the law of entropy increase can be seen as a kind of four dimensional geometrical structure in the region as a whole. In its most complete expression, the geometrical structure inherent in potential energy becomes the geometrical structure inherent in nonrandom distributions of causally relevant factors, which in turn becomes the lack of any salient geometrical structure inherent in the randomness of evenly distributed heat. At the later edge of this four dimensional structure, the bits of matter have the kind of geometrical structure that is most like the structure of the space containing it. It is as if matter in the region were coming to mirror the uniform structure of space.

This explanation of the second law of thermodynamics solves a puzzle about the reduction of the second law of thermodynamics to physics. The law of entropy seems to resist reduction to the laws of physics, because it describes a regularity about change that is asymmetrical in time, whereas the laws of physics describing how the material objects interact are all time-symmetrical. The temporal asymmetry of the law of entropy comes, however, not from the laws of physics by themselves, but from the forms of matter they describe having geometrical aspects that are casually relevant in how local changes adds up in space over time. Both tendencies involved in the explanation of the law of entropy are a result of how geometrical structures about the matter involved are efficient cause of their own extinction. That solves the problem. (See Change: Epistemological philosophy of causation: Second law of thermodynamics.)

The thermodynamic flow of matter. If we look at the second law of thermodynamics in terms of matter, the two tendencies can also be seen as a “thermodynamic flow of matter” from potential energy to evenly distributed heat. This is a flow of matter in a certain “direction” through a series of forms of matter. The matter starts off as part of the rest masses of the material objects involved, for matter in that form is what constitutes the forces that the objects exert on one another. When the objects have spatial relations in which their forces can accelerate one another, it is potential energy. And when potential energy is actualized, the matter takes the form of kinetic matter, which lacks any inherent geometrical structure, since it is a form matter that is located at the material object’s center of mass. And since interactions among material objects tend to equalize their kinetic energy (and other causally relevant factors), kinetic matter tends to become randomized as heat and evenly distributed in space as heat. Since matter flows through these forms in only one direction, however, matter winds up as evenly distributed heat, that is, with higher entropy in the region.

This thermodynamic flow can also involve potential energy becoming photons, but they are merely another route to evenly distributed heat. The photons interact with the material objects and become randomized for much the same reasons.

This is to characterize the global regularities described by the second law of thermodynamics as if the processes followed a direct path to evenly distributed heat of increasing entropy. But the thermodynamic flow of matter may include twists and turns in which some of the kinetic energy becomes potential energy in other forms only to be released again as kinetic energy before finally turning into heat that is then evenly distributed in space. As we shall see, such transformations between potential and kinetic energy are how machines use this kind of matter, as free energy, to do work. Similarly, though nonrandom distributions of the three causally relevant factors becomes evenly distributed heat, it may be used as free energy to do work, as in heat engines, which may create potential energy and give some objects high kinetic energy, before it becomes evenly distributed heat. These complications will be considered when we take up structural causation.

The transformation of free energy into entropy. To sum this up in more familiar terms, at the most general level, according to the second law of thermodynamics, what is happening in any closed or isolated region of space is the transformation of free energy into entropy. Free energy is all the energy in the region that has not yet become evenly distributed heat, where heat is simply randomness in the motion and interaction of the simplest physical objects that can move relative to one another. And entropy is, technically, a measure of how much of the total energy in the region exists in the form of evenly distributed heat. The second law of thermodynamics, or law of entropy, holds that in a closed or isolated system, entropy can increase, but it cannot decrease. That is, all the other physical forms of energy (that is, forms of matter) are ineluctably becoming evenly distributed heat.

This is the supposedly bleak image of a world made up of matter in motion which sees the universe as condemned to a “heat death.” This image has traditionally been used to discredit materialism, or at least discourage belief in it. But if we consider what it means more concretely at the scale of planetary systems, the transformation of free energy into entropy is, as we shall see, the fountain of everything valuable in the world. Free energy is what makes it possible for structural causes to do work, as we shall see next.

To talk of “free energy” is to classify energy by its capacity to be used by machines to do work, but concretely, such free energy takes many different physical forms. On the scale of a planetary system, the richest and most constant source of free energy is the star, because such a huge accumulation of mass has a gravitational field that contains an enormous amount of potential energy. The energy stored in its force field is the source of all the free energy that will eventually become evenly distributed heat (except for energy from radioactive decay). Its gravitational field constantly accelerates bits of matter toward its center. Even inside the star itself, the inward acceleration of more distant matter causes a pressure that is balanced against the kinetic energy (and photons) constituting the random motion and interaction of more centrally located particles and their electromagnetic interactions. Indeed, the kinetic energy is great enough for the collisions of protons, neutrons and small nuclei to bring them within the short range of the strong attractive force that they can exert on one another, and as it fuses them together, the potential energy of the strong force is actualized as kinetic energy and photons, decreasing their rest masses. High energy photons (and other particles) escaping at the surface of a star radiate outward toward cold, empty space, showing the surrounding planets. Since radiation is a form of free energy (like kinetic energy before it is randomized), it can be used to do work on the planets intercepting it. Not only do photons heat the planet, but they supply energy in a form that can drive chemical interactions. There is also heat from the tidal forces that planets orbiting a star suffer as they rotate on their own axis (and from the radioactive decay of particles making up the planets). The energy eventually flows through the planets, since planets also lose heat as they radiate energy into cold empty space in the form of lower-energy photons.

The star’s radiation is, therefore, a form of energy that can be used by machines on planets to do work, or free energy. This is the setting, as we shall see, for reproductive causation to generate its spectacular global regularity. But first we must consider how this thermodynamic flow can be used to do work, and that is an effect of structural causation.

Structural global regularities. Spatial and material causation are the most direct ways that space and matter impose regularities on change in whole regions over time. But they are not the only ways, because the forms of matter that explain the truth of the basic laws of physics are not the only kinds of substances that can coincide with space. The nature of matter also makes non-basic, or derivative substances possible, and they can work together with space as ontological causes to generate global regularities.

Though everything that coincides with space is made of matter, matter is capable of being organized into more complex material substances that move around in space and interact as units with other bits of matter, and the wholeness of space also requires their motion and interaction to add up in space over time. They are more complex ontological causes, and they add up in space over time to more complex regularities about the change that takes place in entire regions.

These more complex ontological causes are “derivative substances” (or “derivative ontological causes”) because they are constituted by the basic ontological causes, matter and space. Though they can endure through time like basic substances, they can also come into existence and go out of existence as time passes.

These more complex kinds of substances include not only material objects with unchanging geometrical structures, such as ordinary composite objects, from cups to automobiles, but also a more complex, temporally structured kind of process that is based on such material structures. The first is discussed in this chapter, and the second will be taken up in Reproductive global regularities.

In both cases, however, the derivative substances are ontological causes of global regularities, because they work together with space to cause change to be regular in entire regions by their continuous existence through time as (derivative) substances that coincide with some part of space or other in the region. Though the wholeness of space is what requires motion and interaction to add up in space over time, how their motion and interaction adds up in space over time depends on their natures as (derivative) substances as well as the structure of space. And as we shall see, they add up to complex global regularities about change.

Material Structures. Since material structures are just material objects with relatively stable geometrical structures, most ordinary objects are examples of them. They have geometrical structures that do not change in relatively wide ranges of interactions because they are byproduct of certain cases of the tendency of potential energy to become kinetic (one of the two material global regularities). Thus, they continue to exist in the region even when entropy is maximum. Though as we shall see, material structures can be constructed by machines using free energy to do work, that is just a more complex example of the structural global regularities to be explained. And the existence of material structures does not depend on such machines, because there are material structures that form naturally.

The best examples of such naturally forming structures involve the electromagnetic forces described by quantum field theory. It account for the formation of atoms (from nuclei and electrons), molecules (from atoms), and crystals, rocks and other natural material objects (from molecules). But similar explanations hold for the formation of the nuclei of atoms.

Material structures come to exist naturally because of the attractive forces that simpler material objects exert on one another. The exertion of attractive forces across space is a form of potential energy that can draw material objects together and bind them into relationships with one another that are stable and do not change. The stability of such composite objects comes from the parts giving up potential energy as kinetic energy (or radiation) when they form themselves into a unit, because, once united, their bonds to one another cannot be broken, unless subsequent interactions supply enough energy in the right form to make up for the energy that was lost forming the bonds. The improbability of that happening is, as we have seen, what causes the tendency to kinetic energy. (Kinetic matter and photons lack the inherent geometrical structure of potential energy, and thus, almost anything that happens to such matter will make it impossible for it to regain its initial geometrical structure as potential energy). But the quantum nature of the interactions helps account for their stability, because that means the objects can be freed from their embrace with one another only when enough energy is supplied by a single interaction (as illustrated by the photo-electric effect). Thus, such composite objects have geometrical structures that do not change even though they are interacting with other objects (as long as the energy of those interactions is not too great).

Thought material structures may seem to override the tendency to randomness, they are just byproducts of the tendency toward kinetic energy, the other global regularity involved in the second law of thermodynamics.

Material structures may seem to override the tendency toward randomness in two ways. Instead of interacting by elastic collision, the parts of composite objects exert forces that bind them to one another, and thus, instead of being spread out evenly in space, material objects are clustered together in the same local area. And instead of winding up with momentums in every which direction, the parts of such structures all have much the same direction, like a wind with fixed parts. In other words, instead of being a gas or liquid, they are a solid state of matter, which moves and interacts as a whole.^xxxv

But instead of overriding the tendency to randomness, they exemplify the other material global regularity that is covered by the second law of thermodynamics. The existence of material structures is part of the price that is paid to have kinetic energy that can become randomized as evenly distributed heat. It is the loss of potential energy (which is actually a loss of rest mass) that binds the parts into stable geometrical structures. Their formation is part of the process of free energy becoming entropy.

Composite material objects with unchanging geometrical structures are the derivative ontological causes that will be called “material structures” or “structural causes”. But it should be noted that not all objects that form naturally as byproducts of the tendency of potential energy to become kinetic energy are material structures, and the main exceptions, not surprisingly, result from gravitation.

Stars form as a result of gravitation, but these “composite objects” do not have unchanging geometrical structures in this sense. Gravitation concentrates material objects in certain locations, and though this is a deviation from the tendency of rest masses to be distributed evenly throughout space, the forces are so great, when enough matter is concentrated at some location, that material objects continue to move and interact randomly with one another, as a plasma of nuclei and electrons (a fourth state of matter, besides solids, liquids and gases). This gives stars only the minimal geometrical structure required to speak of them as composite objects at all. They approximate a sphere, but since there are no unchanging spatial relations among particular parts that would give the whole a geometrical structure that remains stable as it interacts with other objects in space, they are not structural ontological causes. Though planets and smaller astronomical bodies do acquire unchanging geometrical structures from gravitational attraction, they also depend on the parts forming bonds based on electromagnetic forces.

If gravitational acceleration is explained by the acceleration of the ether, then the nature of the gravitational force would explain why stars are different from objects that depend on other forces. Material objects that are clustered simply because of the ether (by which they coincide with space) accelerating them towards one another do not necessarily form bonds with one another. By contrast, the interactions on which other kinds of composite objects are based involve either opposite forces of attraction and repulsion canceling one another out (as in electromagnetism) or are short range forces (as in the weak and strong forces), and they all have a quantum nature which helps makes the structures they constitute stable.

It should be noticed, however, that even some composite objects formed by forces with a quantum nature lack unchanging geometrical structures. For example, water molecules interact by weak electromagnetic forces, called “hydrogen bonds”, but when water forms into a drop, the molecules continue to move relative to one another as they interact, resembling to some extent star-like gravitational objects on a small scale.

Reversible processes. The existence of material structures depends on the specific nature of the matter that helps constitute the actual world, and when they exist, the wholeness of the space containing them causes their motion and interaction in any region to add up over time as regularities about entire regions of space. But since they have a geometrical structure, how they add up also depends on the structure of space. Though the new global regularity is rather simple by itself, it makes all the difference in the world, as we shall see, when combined with material global regularities, that is, free energy, for that is what constitutes irreversible processes.

What is regular in the case of reversible processes is not just that the geometrical structure of the material object does not change. That is a property of the composite object, rather than a property of region as a whole. But since its geometrical structure does not change over time, there is a geometrical structure about the dynamic processes in the region that does not change, and that is a global regularity. In other words, material structures contribute to the geometrical structure of the region in much the same way that potential energy does, by its inherent geometrical structure. The difference, of course, is that the material structures do not lose their geometrical structure as potential energy tends to do as it becomes kinetic.

As long as the composite object’s geometrical structure does not go out of existence, it is like a new kind of material substance, which is not mentioned by the basic laws of physics. Indeed, the reason material structures are ontological causes is that, like space and more elementary forms of matter, they exist continuously over time like substances. And since change is just an aspect of substances enduring through time, material structures cause change to be regular by helping constitute the process. As in all ontological explanations, that is how the essential natures of substances help determine the nature of what is found in the natural world. Material structures are unchanging aspects of the substances making up the region as time passes.

Material structures cause a global regularity, because as they move and interact as particular substances in space, their geometrical structures help determine, along with the structure of space and the other bits of matter in the region, how change occurs as time passes. Though everything happens by efficient causation, the motion and interaction of material structures with other bits of matter must add up over time in space. The kind of global regularity that material structures add up to is simple. It is just the existence of the material structures in the region moving and interacting with other bits of matter. And material structures with different geometrical structure impose different regularities on how geometrical structures of whole regions change over time.

Though the wholeness of the space containing all the bits of matter is what makes their motion and interaction add up over time, how the motion and interaction of material structures adds up over time depends on the structure of the space containing them.

In the first place, the uniform structure of space makes it possible for composite objects to move without changing the spatial relations among their parts. Every local area in space has a geometrical structure that can contain any specific kind of geometrical structure that composite material objects may have.

Second, when such objects do interact, space allows what happens to depend not only on the forces that the objects exert on each other (by way of the forces exerted by the parts of such geometrical structures), but also on how their geometrical structures fit together. This is a geometrical aspect about how material objects in the region interact with one another that cannot even be simulated by forces.

Material structures can, therefore, be said to structure dynamic processes. Thus, structural global regularities of are “structured dynamic processes”.

Even though structural global regularities may be little more than the existence of material structures in the region, there is no doubt that the existence of such geometrical structures in the region imposes a regularity on change in the region. It can be seen in how round pegs, but not square pegs, fit into the round holes in a board, how rings linked with one another act like a chain, or how molecules can be confined in a box.

Consider, for example, a box of gas that is part of a larger (closed) region of space. Although the molecules are not bound to the box and move around independently of it, those on the inside never get outside, while the molecules on the outside never get inside. This is because the box has a geometrical structure that, together with the structure of space, leaves no route for molecules to move from one region to the other. The gas molecules are not equally likely to be located in every part of the region, and as the box moves around in the region, the structure about the distribution of matter in the region changes in a regular way, because the otherwise randomly moving molecules always move around inside the box. The dynamic process taking place in that region has, therefore, a geometrical structure that does not change over time.

The part-whole relationship in the box-of-gas example suggests a more general point about material structures and the global regularities they and space generate: the unchanging geometrical structure of a composite object as a whole constrains the motion and interactions of its parts, and that generates (regular) behavior in the object as a whole. This is, perhaps, obvious in complex machinery, but consider a simple example, two rings linked together. The rings can move and interact independently of one another to some extent, but their locations are not random, because they can move only within limits which are imposed by the geometrical structure of the object as a whole. This further geometrical structure about what happens to the rings is a kind of global regularity about change over time that might well be called the “behavior” of the object as a whole. The behavior of chains of many such linked rings is quite useful in communicating forces from one place to another. The notion that the whole controls the part is sometimes thought to entail a holism that is incompatible with materialistic reductionism, but when we recognize that the substances constituting such objects include space as well as matter, a regular behavior on the part of the whole is just what is expected.

Structural causation introduces a complication into the ontological explanations of spatiomaterialism, because material structures are derivative ontological causes. In order to be ontological causes of the global regularity about change, they must endure through the whole period. But over longer periods of time, material structures do come into existence and go out of existence. In speaking of them as ontological causes, we are treating them like substances, which have essential natures, that is, properties that hold at each moment of their existence and help determine how contingent properties come and go over time. But since they are derivative ontological causes, we must take into account their “generation” and “corruption”, much as Aristotle did in explaining his very different kinds of substances with essential forms. They are analogous to the various, interconvertible forms of matter we distinguished in order to explain the basic laws of physics ontologically, except that we can explain the generation and corruption of material structures from simpler substances by their motion and interaction in space according to the basic laws of physics. However, the advantages of introducing this complication far outweigh the disadvantages.

Many puzzles are cleared up by recognizing that material structures are ontological causes.

It settles, for example, a question about the criterion for the identity of ordinary objects over time that arises for epistemological philosophers. Material objects are commonly classified by their geometrical structures, and some epistemological philosophers (Hirsh 1982, p. 134) rely on it so heavily that they are tempted to believe that simply having the same kind of geometrical structure at a later moment would be sufficient for its identity—even if the object were to vanish from one location at one moment and were to appear somewhere else the next. That is not a case we need to worry about, since it is not even possible according to our ontology. But the recognition of material structures as ontological causes can solve puzzles about identity posed by epistemologists who pit having the same geometrical structure against spatio-temporal continuity.

Nozick (1981, p. 29ff), for example, considers the case of Theseus’ ship, which is rebuilt, plank by plank, over a period of time. One would ordinarily claim that what results from the rebuilding is the same ship, although none of the parts is the same. But Nozick poses a further question by supposing that each of the parts of the original ship is saved and later used to reassemble the original ship. He asks, which later ship is identical to the original ship. Nozick’s answer is the “closest continuer theory”, which has intuition deciding in each case (and for each person) which is closest. But if we recognize how global regularities depend on ontological causes, it is clear which ship is identical to the original ship, because only one of them has an unchanging geometrical structure that can cause change to be regular by existing continuously over all that time as a substance. Its role as an ontological cause determines its identity over time.

The recognition of global regularities solves various problems about the irreducibility of less general laws in science to the laws of physics, as we shall see in Epistemological philosophy of causation. The general form of the problem can be seen in the case of structural global regularities. Science tends to overlook this explanatory role of material structures, because it its looking for efficient causes, not ontological causes. The only relevant factors involved in efficient-cause explanations, besides the laws of physics (and mathematical theorems), are initial and boundary conditions. A structural cause is not just an initial condition (although it can be inferred from initial conditions together with the relevant laws of physics), because it causes by its continuous existence over the whole period of time that the global regularly occurs. To be sure, boundary conditions also cause by persisting through the period of the regularity. But structural ontological causes are not boundary conditions, for they are not just a condition about the system’s limits in space (how it is related to or isolated from the rest of the world). Thus, structural ontological causes tend to fall through the cracks. That is not to say that they are ignored. It is rather they are implicit in efficient causes that are recognized. The familiar deductive-nomological model of explanation has no way to acknowledge the distinctive kind of role that material structures play as ontological causes of global regularities.

Irreversible processes. Since structural global regularities are simply the continued existence of material structures in a closed or isolated region, they seem rather trivial. But structural causation can have more dramatic effects when it is combined with material causation. Since material objects coincide with space, their unchanging geometrical structures can fit together with the geometrical structures involved in the tendency toward kinetic energy and the tendency toward randomness, since the latter also coincide with space. In both tendencies, there are geometrical structures that are wiped out by how bits of matter move and interact. The inherent geometrical structure of potential energy is lost in the tendency toward kinetic energy, and the geometrical structure of non-random distributions of causally relevant factors is lost in the tendency to randomness. Material structures can channel the flow of matter through these geometrical forms, because their geometrical structures coincide with parts of the same region of space where these tendencies are exhibited. The reason that those tendencies are called “free energy” is that material structures can thereby channel the thermodynamic flow of matter from potential energy through kinetic energy to evenly distributed heat to to bring about states of those regions that would not otherwise occur. That is how machines use free energy to do mechanical work.

What makes it possible for machines to use free energy to do work can be explained ontologically, because we have already explained how material structures are ontological causes that structure the motion and interaction of other bits of matter in the region. Ordinary machines have unchanging structures that are large enough to think of them as ordinary macro-level material objects, by contrast to the micro-level objects mentioned in describing thermodynamic processes. Let us distinguish two ways that machines do work, depending on whether the free energy comes from the tendency toward kinetic energy or from the tendency toward randomness.

Free energy from the tendency toward kinetic energy. A machine has an unchanging geometrical structure as a whole that constrains how the parts of which it is composed can move and interact with one another. Potential energy also has a geometrical structure, and when the spatial relations among the forces involved combines with the unchanging structure of a material object, the tendency of potential energy to become kinetic energy can be channeled in ways that produce useful outcomes (although it often involves complex processes in which the kinetic energy is converted into other forms of potential energy and back again to kinetic energy in order to produce the kinds of changes that are desired).

This can be seen in a wide variety of cases. For example, the potential energy of gravitation can be tapped by water wheels and other structural causes, such as cog wheels, levers, wedges, and the like, to release kinetic energy in a way that grinds corn, weaves cloth, or does other mechanical work.

Free energy from the tendency toward randomness. The nonrandom distributions of efficient causes that wipe themselves out in the tendency toward randomness are made up of objects on the micro-level, but since the nonrandom distribution itself is a geometrical structure of the region as a whole, it can fit together with macro-level material structures to do mechanical work. Distributions of three kinds of efficient causes had to be mentioned in explaining the tendency to randomness (the rest masses, kinetic energies, and momentums of molecules), and we can find examples of machines using each of them.

The most familiar example involves the uneven distribution of kinetic energy. The difference in temperature between two, spatially-separated sets of material objects is what enables the steam engine to tap the free energy that exists in the flow of kinetic energy from hot to cold. The kinetic energy released by combustion of fuel flows across the wall of a box to water, producing steam at high pressure, and its expansion against a piston in a cylinder does mechanical work, such as propelling a train along a track. Internal combustion engines are as much heat engines as steam engines, although they eliminate the step in which the flow of kinetic energy conducts heat from the combustion of fuel to the water being heated by burning the fuel in the very cylinder where the piston is pushed.

The other two causally relevant factors whose uneven spatial distributions tend to wipe themselves out can also be tapped by structural causes to do work. The free expansion of a gas is used in jet propulsion, and the uniform direction of momentums contained in a wind can be caught by a sail to pull a boat along. In the latter case, it is even clearer that the free energy comes from the flow of matter through region-wide geometrical forms that is evening out the directions of momentum, for a sail can propel a boat across wind or, better yet, against it; the free energy comes, not just from going along with the wind, but from making the molecules’ directions of momentum more random. The same principle applies in wind mills and turbines.

In either case, whenever machines use free energy to do work, the geometrical structure of some material object engages with some region-wide geometrical structures involved in the tendency toward kinetic energy or the tendency toward randomness so that the thermodynamic flow of matter toward evenly distributed heat is structured to do mechanical work. The kind of work done depends on how the material structures coincide with the geometrical structure of the potential energy or the nonrandom distribution of causally relevant factors on the macro level in the region.

In some machines, both tendencies are involved. For example, the potential energy of the forces exerted at one location are communicated in hydraulic machinery by using the tendency to randomness in liquids confined in cylinders to transfer the kinetic energy and momentum from one location to another. Electrical machinery works by the same principle, except that the potential energy is communicated by freely moving electrons confined to conductors, and the work is usually done because of the magnetic forces set up by moving electric charges.

In sum, there are two kinds of global regularities caused ontologically by material structures, reversible and irreversible processes. What makes irreversible processes different is that what is being structured is a thermodynamic flow of matter (that is, motion and interaction in the region of a kind that is changing from potential energy to kinetic energy or in which a nonrandom distribution of causally relevant factors is wiping itself out). When there is no thermodynamic flow of matter toward evenly distributed heat, entropy is already maximum, and the global regularity is just a kind of geometrical structure that holds of the whole region over a period of time because some of the material objects moving and interacting there are composite objects with geometrical structures that do not change. That kind of global regularity was illustrated in the last section by the box of gas and the interlocked rings. Any change that takes place in such a region wide process could take place in the opposite direction in time. But when a thermodynamic process is going on in the region and a material structure uses its free energy to do mechanical work, the change that occurs in the region is temporally asymmetric. The work done depends on their being matter flowing through geometrical forms from potential energy to evenly distributed heat, and since some free energy is always lost to increasing entropy in the process of using it to do mechanical work, the change taking place in a closed system cannot return to its starting point.

Since reversible structural global regularities do not depend on material global regularities (except for how material structures are a byproduct of the tendency of potential energy to become kinetic), they are not included in the following diagram of the relationships among global regularities.

The essential role of space as an ontological cause of global regularities is confirmed by irreversible process, for it is what makes it possible to combine material and structural global regularities. This can be seen in the steam engine, the concrete phenomenon that led to the discovery of the second law of thermodynamics.

The wholeness of space plays the same role in all global regularities: it makes the motion and interaction of the bits of matter in the region add up over time. But the structure of space plays a further role in generating the material and structural global regularities, because there is a geometrical aspect to how the motion and interaction adds up as time passes. The regularity caused by material causation is that two kinds of geometrical structures about the region as a whole disappear, and the regularity caused by structural causation is that the region contains material objects whose geometrical structures do not change. In both cases, these geometrical structures are superimposed on the uniform structure of the space in the region, and that is what explains how these two global regularities can be combined, for it is simply a matter of how the thermodynamic structures fit together with the material structures.

Steam engines, for example, are just material structures combined with various thermodynamic processes in the same region of space. The free energy consumed by steam engines is kinetic energy that comes from combustion, that is, the tendency of potential energy in the fuel to become the randomized kinetic energy of heat. This kinetic energy is supplied where the material objects losing some of their rest mass are located. But since that happens in a part of steam engine, material structures can channel it to do work before the tendency to randomness evens out the nonrandom distribution of this randomized kinetic energy. It makes water in the boiler heat up, and as the spatial distribution of causally relevant factors tends to even out, and the momentum of the fast-moving molecules drives a piston in a cylinder, doing mechanical work, such as lifting a weight in a gravitational field. The way that the unchanging geometrical structures of composite material objects coincide in space with the region-wide geometrical structures that are disappearing due to the thermodynamic flow of matter toward evenly distributed heat is what explains how it is possible for heat engines to tap the free energy contained in such thermodynamic processes to do work, and that confirms the role of space an ontological cause in both kinds of global regularities.

Perpetual motion machines. These examples of machines doing work illustrate how material structures can combine with the free energy contained the thermodynamic flow of matter toward evenly distributed heat to produce changes that would not otherwise occur. But since machines can do work, it might seem that they could structure it in ways that would restore the free energy they are using. By returning kinetic energy to its potential form or imposing a new nonrandom distribution of causal factors on the dynamic process, structural causes would be doing work without entropy increasing, that is, without using up free energy. If the work done restored the geometrical structure containing the free energy it uses, it would be a machine that continues doing work forever, or a perpetual motion machine.

It is not, however, possible, because any machine that structures a thermodynamic flow of matter toward evenly distributed heat is itself part of a larger process in which such a thermodynamic flow is taking place. The machine itself is not exempt from the law of entropy increase, if only because some of the free energy becomes evenly distributed heat by flowing through the machine. The machine itself is just another part of a region where the material global regularity holds.

This can be illustrated by a pendulum swinging in a gravitational field, the example used to illustrate the tendency toward kinetic energy. The material structure constrains the motion and interactions of its parts so that the gravitational potential energy that the bob has at its maximum height is released as kinetic energy, and that kinetic energy is used to do the work of restoring it to its potential form. But it cannot go on forever, because the potential energy that is given up in each swing is never fully restored. When it is kinetic, the pendulum gives up part of its energy to other objects with which it interacts (for example, as it collides with molecules in the air and causes friction in the rope suspending it), according to the tendency of potential energy to become kinetic energy describes. And the tendency toward randomness means that the thermodynamic flow of matter through region-wide geometrical forms continues until the matter becomes kinetic energy on the micro level and winds up as heat energy evenly distributed throughout the region. Thus, the pendulum slows down and eventually stops swinging altogether.

Similarly, an elastic ball cannot bounce forever, using kinetic energy to exchange gravitational potential energy for the electromagnetic potential energy embodied in the ball’s deformation, because once the energy is released as kinetic energy, it is not fully restored.

More generally, free energy can be stored in machines, either as potential energy, kinetic energy on the macro level, or as cyclic transformations between potential and kinetic energy. But when energy is kinetic, interactions with other material objects divide up the energy until the energy is randomized on the micro level and, as heat, becomes evenly distributed throughout the region. Machines produce less free energy than they consume, because some of the thermodynamic flow of matter being channeled to do work flows directly through the machine itself toward evenly distributed heat in the region.

The ultimate randomization of kinetic energy depends, as we have seen, on three factors. The material structure itself resists the randomization of two of these factors, but there is one kind of efficient cause whose randomization it cannot resist. The unchanging structure of the composite object means that the rest masses of its parts do not become evenly distributed in the region. Moreover, since they move together as a composite object, the parts all continue to have much the same directions of momentum. But the parts can have different kinetic energies (such as vibrations within the forces holding them together), and kinetic energy does tend to become evenly distributed among them, for any inequality in the distribution of kinetic energy is a geometrical structure that tends to wipe itself out. This aspect of tendency toward randomness will continue until heat is evenly distributed throughout the region and everything has the same temperature.

There are, therefore, no perfectly efficient machines. Machines use free energy to do work, but as they do, some of it is inevitably lost as heat energy, which becomes evenly distributed in the region, increasing entropy in the region. The efficiency of a machine is measured by how much of that free energy is actually made to do mechanical work as that happens.

Examples of structural global regularities from nature. Using machines designed by humans to illustrate structured thermodynamic processes should not, however, keep us from seeing how structural ontological causes are responsible for global regularities found in nature. I will describe some of them here, because these varieties of structural causation will be used to explain how reproductive causation get started in planetary systems.

The unchanging structures of atoms are, for example, structural causes of the molecules that form naturally from them. The relevant geometrical structure of the atom is the number of electrons the nucleus can bind in the outermost shell. The ways in which the geometrical structures of the atoms and the forces exerted by their parts fit together geometrically explains why their motion and interaction add up over time in the structure of space to the formation of molecules, a composite object with a higher level of part-whole complexity. The free energy for their bonds comes from the forces exerted by their parts (the positive charges of the nuclei attracting the negative charges of the electrons), and since the potential energy released by their formation becomes kinetic energy (or radiation) that eventually becomes heat evenly distributed throughout the region, it is irreversible. The formation of molecules is, therefore, a naturally occurring irreversible structural global regularity.

In a similar way, the structures of the molecules can, in turn, be structural causes of yet higher levels of part-whole complexity. The formation of crystals involves the attachment of one molecule after another to a growing, regular geometrical structure.^xxxvi It is an example of structural causation, because the growth depends on how the geometrical structures of the molecules fit together with the crystal structure created by the attachment of the last molecule and how the forces exerted by corresponding parts affect one another. It is an irreversible structural global regularity, because it depends on the free energy supplied by forces exerted by their parts (often hydrogen bonds, which are weaker than those responsible for the molecules). And the result is a new kind of material structure. The kinetic energy released becomes part of the evenly distributed heat, and the bonds of the molecules making up the crystal cannot be broken without additional free energy, that is, unless enough energy is concentrated at just the right point at the right moment to free the molecule from its bonds to the crystal.

In living objects, more complex structures of molecules have more complex effects, such as the spontaneous formation of plasma membranes in water and of complexes made up of various protein molecules from their random motion and interaction. Plasma membranes are self-assembling structures used as barriers in biological processes. They are made of phospholipids, which are long, skinny molecules that tend to line up like matches alongside one another as sheets (because of weak, Van der Waals forces between them). The sheets form double layers in water (since their hydrophobic surfaces are pushed together), and the sheets tend to close on themselves in water to form spheres.

Similarly, protein molecules are amino acid molecules linked together like a chain (by peptide bonds), and the geometrical structures (or “conformations”) they take on in water often fit together in such a way that weaker forces between corresponding parts hold them together and make them stable.

Molecules have structural effects other than merely forming higher levels of part-whole complexity in material objects. They can act more like machines. For example, their structure can give them a behavior as a whole that produces another kind of material structure, which then serves a structural cause. This occurs in protein molecules, the long chains of various kinds of amino acid molecules that are the basic micro-level machines in living organisms. Such chains can bend at their chemical bonds so that weaker forces exerted by the various amino acids bind parts of the chain to one another, giving the whole chain a further geometrical structure as a whole. (That is, the unchanging structure of the protein molecule not only constrains the motions of its links relative to one another as they move in the water and determines how the chain can bend, but it also thereby determines which kinds of amino acids will be next to one another when it bends in certain ways and, so, where weaker bonds will form among the parts.) The resulting “conformation” of the protein is usually the relevant material structure that structures thermodynamic processes in living organisms. (The DNA molecule has a similar behavior as a whole: the structure of the molecule so constrains the motions of its parts relative to one another that DNA winds up as a double helix.)

Molecules can also be material structures that produce new material structures by acting on other molecules. They are called “catalysts”. But the most dramatic examples are proteins whose conformational structure makes them “enzymes”. Such proteins hold other molecules together and distort their shapes so that new chemical bonds form among their parts, replacing the old, and thereby producing molecules that are otherwise not likely to be formed at the prevailing temperature. Such molecular machines are responsible for the replication of DNA and the synthesis of proteins.

In DNA replication, proteins in conjunction with a DNA molecule are a structural cause that catalyzes a long series of chemical changes in other molecules so that another molecule acquires its structure. The geometrical structure of the DNA and protein molecules does not change, but it temporarily binds other molecules in a way that causes bonds to form in them. Each such structural effect leaves both the original DNA molecule and the copy being formed in a slightly different state, so that a different kind of molecule will interact with it the next time and the whole series results in a copy of the original sequence. In a similar way, a series of structural effects is responsible for synthesizing strands of amino acids into proteins, this time, using an RNA molecule as the template and consuming energy from other molecules in the process. But the structural cause in this case is an enormously complex object with fifty-some different kinds of proteins and several strands of RNA (together with tRNA to supply the parts).

Enzymes bring out the appropriateness of thinking of the unchanging structures of molecules as machines. The free energy for the catalyst’s work comes from the potential energy of the forces by which the enzyme binds with the other molecules (the “substrate”), but that energy is not ultimately lost to randomness, because it is paid back from the free energy released in their forming stronger bonds as the other molecules are freed from the enzyme. Thus, the enzyme can act again. Enzymes can even construct complex molecules with weaker, energy-rich bonds by extracting free energy from energy-rich molecules available in the medium.

On a larger scale, what are called “physical properties” of bulk matter, from rigidity and elasticity to transparency, color and conductivity, are dispositions to behave in certain ways under certain circumstances. But they can all be explained as irreversible structural global regularities. The conditions under which the disposition is exhibited supply a form of free energy, and the way the material structures at the micro level within the composite object structures that thermodynamic processes explains why the physical object behaves as it does under those conditions.

The simplest case is rigidity itself, in which a force exerted on part of a composite object is communicated to other parts because of the bonds that are responsible for its unchanging geometrical structure.

This is the ontological explanation of the principle of the lever. The force exerted at the end of a lever on one side of the fulcrum moves the other end of the lever through a distance that depends on the geometrical structure, and thus, if the distance the other end must move is less, a weak force operating over a longer distance becomes a strong force operating over a shorter distance. It is simply how the material structure coincides with the free energy, in this case, the force being exerted on one end of the lever.

The collisions of billiard balls are an example of how rigidity itself is a structural cause. As the first ball hits the second and comes to a stop, the kinetic energy is absorbed, but since they are elastic, the energy is stored as potential energy in the forces among the parts of the billiard balls, and as those forces restore the shapes of the balls, their potential energy becomes kinetic energy again, making the second ball move away (conserving the total momentum of their interaction). The structural cause in the billiard balls is what is unchanging about the spatial relations of their parts as they absorb and release energy.

In malleable materials, by contrast, the structural causes lie wholly in the unchanging structures of the parts, because they are the only geometrical structures that do not change when the disposition is exhibited. Energy is absorbed locally from the forces imposed, because the molecules have shapes that allow them to switch their bonds with one another, giving the parts of the composite object new spatial relations to one another as parts of the whole. That is how the motion and interaction of the material structures add up in space, when they start out with such bonds to one another and free energy is supplied by a force being impressed.

Material objects also have other mass properties that can be explained in similar ways, such as transparency, electrical conductivity, heat conductivity. The colors that material objects appear to have when illuminated by the whole spectrum of visible photons comes from some wavelengths being absorbed, while others are reflected. The material structure responsible for this global regularity lies in various aspects of the micro-structure, which interact differently with different wavelengths of light. (But colors in this sense are, of course, physical properties, and they must be distinguished from the appearances of colors to the subject, which are qualia.)

The explanation of dispositions by material and structural ontological causation is a reduction of those regularities to spatiomaterialism, and since that demonstrates their (conditional) ontological necessity, it explains the nature of the casual connection involved in these efficient causes. In the case of dispositions, the regularities connecting causes and effects are just irreversible structural global regularities, whose ontological causes are like machines built into nature. The test conditions of the dispositions are the efficient causes, and what happens are the effects.