C
ontingent
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 19th
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.
C
ontingent
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.
F
orms
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.
T
o
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.
N
ewton’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.
M
axwell’s
laws of electromagnetism. The other basic set of laws
making up classical physics at the end of the 19th 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.
C
ontingent
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.