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<title>Quantum puzzles</title>
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<br><br>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font color="#993366"><font face="Verdana, sans-serif"><b>Q<img src="data:image/png;base64,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" name="TtsOtkCLQm_03" align="right" width="200" height="38" border="0"><img src="data:image/png;base64,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" name="HistCmt" align="right" hspace="5" width="149" height="22" border="0">uantum
puzzles.</b></font></font> Of the various quantum puzzles, the most
basic is probably wave-particle duality. The atom itself is, however,
the most important, puzzling consequence for the ordinary world. The
traditional way of summing up what is most puzzling about quantum
mechanics is the Heisenberg uncertainty principle, but recently the
most discussed is called “Bell’s inequality.” All of them are
described here as a way of introducing quantum mechanics as it is
currently understood, and after explaining the spatiomaterialist
theory of quantum matter, I will show how they can be solved. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">W<img src="data:image/png;base64,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" name="TtsOtkCLQm_04" align="right" hspace="5" width="225" height="30" border="0">ave-particle
duality. </font>According to Bohr, the basic puzzle of quantum
mechanics is the dual nature of the basic entities it describes. They
all appear to be like both particles and like waves. What classical
physics took to be waves turn out to have a particle-like nature as
well, and what classical physics took to be particles turn out to
have a wave-like nature as well. Bohr thought that both appearances
of the underlying reality are due in part to our measuring apparatus
and the classical expectations on which they are constructed. But
wave-like and particle-like natures are apparently incompatible, and
since both of these classical conceptions of reality are needed to
make all of the possible predictions, he called the basic puzzle of
quantum mechanics “complementarity.” Bohr was the originator of
the so-called &quot;Copenhagen interpretation&quot; of quantum
mechanics, which holds that the reality behind these complementary
phenomena is incomprehensible to us.</font></font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>The
particle-like nature of electromagnetic waves. </b></i>Light has long
since been thought to have wave-like nature in classical physics.
Early in the nineteenth century, Thomas Young showed that light
passing through two narrow, closely spaced holes (or slits) produces
a pattern of light and dark lines on the screen that finally
intercepts them, and he explained it by the wavelike nature of light.
The places on the screen where the waves emerging from each slit
interfere constructively are bright, while the places where they
interfere destructively are dark. When one slit is blocked, the
interference pattern disappears.</font></font></font></p>
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" name="Interference" align="bottom" width="372" height="290" border="0"></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Diffraction
phenomena also indicate the wave like nature of light. Light rays
passing through a hole that approximates its wavelength will be
spread out as it leaves the hole, with the range of the spread
varying inversely with the size of the hole. When the hole is large,
the light hitting the distant screen is like a point, but when the
hole is small, the diffraction is great. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Moreover,
as we have seen, light had been explained by Maxwell as the wavelike
coupling of the electric and magnetic forces described by his
equations. Indeed, it enabled him to predict the velocity of light.</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
particle-like nature of light was the first of the discoveries that
eventually culminated in quantum mechanics. Instead of propagating
like a wave in an elastic medium, as the classical model assumed, it
became clear that light is actually made up of distinct particles,
which are now called “photons”. This particle-like nature means
that the energy and momentum carried by light do not combine
continuously, as they do in ordinary waves, but come in separate
units, called “quanta”. The size of the quantum of light is now
represented by Planck’s constant, <i>h</i>, which is part of every
new equation used in quantum mechanics. It appears in the new
equations for the energy and momentum of light. The energy, <i>E</i>,
is given by <i>E&nbsp;=&nbsp;hf </i>(where <i>E </i>is energy, <i>f
</i>is frequency), and the momentum, <i>p</i>, is given by <i>p&nbsp;=&nbsp;h/</i>
(where <i>p </i>is momentum, and is the wavelength). </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Max Planck
first discovered the particle-like nature of light in 1900, though he
did not fully understand what he was on to. He discovered the
constant named after him by tinkering with a classical equation for
calculating the amount of energy given off at each frequency in
so-called blackbody radiation, that is, a hot body in which no
frequency of light should be favored. (It is best approximated by a
box with mirrored interior walls in which light of all possible
wavelengths for a box with certain temperature are being reflected
back and forth.) The classical equation assumed that the frequencies
of light being given off varied continuously from the lowest to the
highest, with the peak intensity depending on the temperature. That
assumption worked well enough for the low frequencies, but at high
frequencies, it led to the conclusion that the total energy given off
should be infinite. This absurdity was called the “ultraviolet
catastrophe.” Planck discovered a formula that avoided the
catastrophe and predicted the total quantity of energy given off at
each frequency by introducing a constant, <i>h</i>, into the formula
which restricted the frequencies of light. That is the source of the
equation for the energy of light: <i>E&nbsp;=&nbsp;hf.</i> (Though
its meaning is still obscure, it can, perhaps, be seen as requiring
the photons to differ from one another by that constant amount.) </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Albert
Einstein made it clearer that what Planck had discovered was the
particle-like nature of light by using Planck’s constant is his own
explanation of the photoelectric effect (in 1905, the same year that
he published his special theory of relativity). It had been known
that light being intercepted by material objects could release
electrons from the material objects, but it was found that the
release of electrons did not depend on the total energy of the light
waves (the intensity of the light), as one would expect on the wave
hypothesis. It depends on the frequency of the light. Below a certain
frequency, no electrons are released, regardless how intense the
light may be at that frequency. Whereas light with a higher frequency
would release electrons even though the intensity was much less.
Einstein showed that the release of the electrons depended on the
absorption of single photons, each of whose energy depended on
Planck’s constant: <i>E&nbsp;=&nbsp;hf.</i></font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Much later
(in 1923), Arthur Compton showed that photons also have a momentum
like particles. He shot high energy photons (x rays) at electrons and
used arguments based on the conservation of momentum and energy to
predict correctly the amount by which their energies would be changed
by such scattering. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
particle-like nature of the light does not change its wave-like
properties. Indeed, it turns out that interference effects still
occur when light is sent through the two-slit apparatus one photon at
a time. Over time, they still accumulate in fringes on the distant
wall. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>The
wave-like nature of particles with rest mass. </b></i>Material
objects are understood in classical physics as having definite
locations in space at each moment and to follow definite trajectories
as they move from one place to another. But the behavior of objects
with rest mass on the smallest scale is peculiar in the opposite way
from photons, according to quantum theory. Just as light waves have a
particle-like nature, so material objects have a wave-like nature. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">The
wave-like nature of particles with rest mass was predicted in 1923 by
de Broglie. What Einstein’s special theory of relativity implies
about the relativistic increase in mass leads to the conclusion that
the energy of a photon is equal to the product of its momentum and
the velocity of light, or <i>E&nbsp;=&nbsp;pc.</i> Since the velocity
of light is equal to the product of the frequency and wavelength, or
<i>c&nbsp;=&nbsp;f</i>it follows that the momentum of a
photon is <i>p&nbsp;=&nbsp;h/</i>De Broglie went on to
suggest that the same relationship holds of particles with kinetic
energy. He argued that particles, such as electrons, protons and
material objects with mass generally would also have a wave length
that varied inversely with their momentum in the same way. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Interference
and diffraction phenomena were the kind of empirical evidence that
was taken as showing that light has a wave-like nature, and soon
after de Broglie’s prediction, it was shown that the electrons
forced to pass through very small holes do exhibit diffraction, that
is, the smaller the hole, the more they spread out. Eventually, even
interference phenomena were demonstrated with electrons. When
electrons moving at a certain velocity are projected through narrow,
closely spaced, parallel slits at a screen (where the distance
between the slits approximates their de Broglie wave length), they
also form an interference pattern on the far wall, as if they were
waves. Even when the electrons were sent one at a time, they tended
to land on the distant screen only along certain fringes, leaving
lines between them without any hits. Thus, each particle is like a
wave. The same has been show to hold for neutrons, though in the case
of ordinary sized objects, the wavelengths are so small that
interference effects are undetectable. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">T<img src="data:image/png;base64,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" name="TtsOtkCLQm_05" align="right" hspace="5" width="225" height="30" border="0">he
structure of the hydrogen atom.</font> The laws of quantum mechanics
were discovered mainly by attempting to explain the structure of the
hydrogen atom. It had been established by Ernest Rutherford that the
atom is composed of a massive, positively charged nucleus surrounded
by far less massive electrons, and Niels Bohr hoped to explain the
chemical properties of atoms by the nature of the interactions
between the electrons and the nucleus. It was clear that atoms could
not be explained in classical terms on the model of the solar system,
since according to Maxwell’s equations, the orbital motion of an
electron would generate (as the acceleration of a negatively charged
particle) an electromagnetic wave which would drain its energy until
the electron was located at rest with the nucleus. In fact, atoms
with electrons located around it are quite stable, and when such
atoms are excited (by supplying energy to them), they give off
electromagnetic radiation at a certain set of distinctive
frequencies.</font></font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Bohr
explained the frequencies of the spectrum of hydrogen atoms (in 1913)
by assuming that electrons can have only certain orbits, each
characterized by an energy level that corresponds to the total energy
of an electron with kinetic energy in a force field with potential
energy imposed by the nucleus. (The total quantity of energy is
negative, because the kinetic energy of the particle is not great
enough to replace all the negative potential energy that would be
required to free it, and according to our assumption about the nature
of potential energy, the negative sign for potential energy indicates
that the nucleus and electron have less rest mass.) The energies of
the possible orbits were determined as a function of Planck’s
constant, and a number was assigned to each possible orbit, starting
with the lowest energy orbit and counting upwards (<i>n = 1, 2, 3, .
. </i>). Bohr showed that the spectral lines of the hydrogen atom
could be explained by the differences in the energies of these
permitted electron orbits. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">The basic
puzzle of quantum mechanics is the structure of the atom itself, that
is, what is going on that only certain energy levels are possible for
electrons bound to a nucleus by electromagnetic forces. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Given the
structure of the atom, however, there is another problem, for it does
not seem possible that electrons could be jumping from one orbital to
another. When a photon is absorbed or emitted by an atom, an electron
changes from one permitted orbital to another (so that the atom
changes from one energy state to another). But the photon has a
particle-like nature, and the particle seems to change its position
and motion in an instantaneous, step-like change, that is, without
accelerating nor even moving continuously from one state to the next.
It hard to see how the electron’s change of orbital can be
explained as the motion of a material object, since a material object
can change location only by moving across space continuously as time
passes time. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Another
puzzle has to do with the timing of the emission of photons. When an
atom or molecule is in an energy state that can decay into a lower
energy state, it is not possible, even in principle, to say exactly
when it will decay. The timing can be assigned a probability, but the
theory has nothing to explain why it happens at one moment rather
than another within that range. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Electron
jumps also seem to be involved in the phenomenon of tunneling.
“Tunneling” refers to situations in which electrons seem to jump
across barriers imposed by force fields. On classical principles,
crossing such a force field would require more energy than the
electron has. Nevertheless, some electrons do jump across. Only a few
electrons do so, and there is no way to predict which ones will jump.
But it is so regular that this phenomenon is used as a kind of
microscope for mapping the surfaces of material objects. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Erwin
Schrödinger thought that it would be possible to avoid these puzzles
about electron jumps and explain everything deterministically by
following up on de Broglie’s suggestion and explaining the behavior
of the electron in an atom as a wave. Using the model of the
classical equation for waves and taking the electron wave to be in a
potential field, Schrödinger presented an equation in 1925 that
explained the energy levels of the permitted orbitals of electrons in
the force field imposed by the nucleus of the hydrogen atom. The
time-independent Schrödinger equation (with the temporal changes
factored out so that it represents only the spatial structure of the
wave) portrays the electron bound to the nucleus of the hydrogen atom
as a standing wave, like a plucked string on a guitar. This made it
possible for Schrödinger to explain the numbers that Bohr had
assigned to the permitted orbitals of electrons as the energy states
in which the electron could be such a stable, standing wave. The
lowest energy level corresponds to the string with no nodes (that is,
half the wave length for its energy), the next one to a string with
one node, and so on. The problem of quantum jumps seemed to be
solved, because the transitions between such energy states of atoms
were explained as smooth and continuous transitions of waves. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Schrödinger
believed that his wavefunction showed that electrons were not
particles at all, but could be explained purely as waves in an
electromagnetic field. This did not explain why electrons appear to
be particles, for example, how they leave vapor trails in a Wilson
cloud chamber or interact at a certain point on the distant wall in
the two-slit interference experiment. But it is possible to explain
why electrons seem to have a determinate location by holding that
they are a &quot;superposition&quot; of waves with slightly different
wavelengths, because in regions where such wave interfere
constructively, they clump together in what are called “wave
packets.” Since the locations where such a set of waves interfere
constructively have more or less precise locations in space and seem
to move through the space occupied by the waves, the Schrödinger
wavefunction could explain the appearance that electrons move like
particles. (This was not a fully adequate explanation, however,
because such wave packets also tend to disperse over time, and yet
electrons actually turn up later at definite locations.)</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">However, it
was not possible to interpret the Schrödinger wavefunction as the
description of a classical wave. One problem was that it contained
complex numbers. There is no way to measure quantities multiplied by
the square root of minus one, and yet those complex numbers are
essential to the wavefunction, since they describe the phases of the
waves that are superimposed in the quantum system and, thereby,
determine the interference phenomena. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Furthermore,
the Schrödinger wavefunction described a wave in a space that can
have more than three dimensions (or what is called “configuration
space). When more than one particle is involved, the space occupied
by the wave described by Schrödinger’s wavefunction has three
times as many dimensions as there are particles. There is no obvious
way to relate such an equations to the actual three dimensional
world.</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">What
is now the orthodox interpretation of the Schrödinger wavefunction
was first proposed by Max Born in 1926. He took the square of the
(time-independent) wavefunction in some region of configuration space
to be a measure of the probability of finding that the particle
located in that region of configuration space (thereby predicting a
measurable property, such as location, momentum or kinetic energy).
The predictions are confirmed by measurement. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Since the
predictions are merely probabilistic predictions, however, Born took
the Schrödinger wavefunction to be a representation, not of the
world itself, but of what we can know about it. This avoided the
problems of quantum jumps and wave packets that spread out, because
what really happens is not knowable. And insofar as it is taken
realistically, it implies that what happens is not fully determined
by the state that precedes it.</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">H<img src="data:image/png;base64,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" name="TtsOtkCLQm_06" align="right" hspace="5" width="225" height="34" border="0">eisenberg
uncertainty principle. </font>An entirely different mathematical
representation of these same quantum phenomena was developed by
Werner Heisenberg. His “matrix mechanics” is basically an
algorithm for making predictions of measurements without any attempt
to explain what is going on beneath the observable surface. Though
Schrödinger showed that Heisenberg’s matrix mechanics and his own
wavefunction are mathematically equivalent, matrix mechanics makes
the limitations on what can be known about the classical properties
of the entities described by quantum mechanics clear. In arguing
against Schrödinger, he defended what has come to be known as the
Heisenberg uncertainty principle.</font></font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
matrix mechanics, there are pairs of variables called “complementary”
or “conjugate” variables, because the measurement of one affects
the measurement of the other. That is, the results of measuring one
variable and then the other would be different if they were measured
in the opposite order. The position and momentum of an electron are
complementary variables, meaning that the position and momentum of an
electron cannot both be measured with arbitrarily high precision But
the more precise one measurement is, the less precise the other is.
Using Born’s probabilistic interpretation of the wavefunction to
express the “uncertainties” in such measurement, Heisenberg
derived a general principle about complementary variables: the
product of the uncertainty about the position and the uncertainty
about the momentum cannot be less than Planck’s constant divided by
four pi. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Heisenberg’s
uncertainty principle holds in a parallel way for other conjugate
variables, such as energy and time, angular momentum and orientation,
and cycle and phase. In each case, one variable is more particle-like
and the other is more wave-like, and thus, the variables are said to
be complementary. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Heisenberg
apparently took his uncertainty principle to be a basic postulate
from which all of quantum mechanics could be developed. He rejected
talk about the wave-particle duality and took a purely
instrumentalist approach which simply denied that there is any aspect
of the world that is not described by his matrix mechanics (or by
their equivalents in using the Schrödinger wavefunction). </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
equivalence of Heisenberg’s matrix mechanics and Schrödinger’s
equation means that the Heisenberg uncertainty principle can be
derived in a similar way from Schrödinger’s equation. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">The
solution of Schrödinger’s equation for a given situation yields a
wavefunction, which is a complete description of the quantum system.
But in order to predict a measurable property, it is necessary to
apply an appropriate mathematical operator to the wavefunction. The
operator yields an “expectation value” for that property, which
may be a precise value or an average value. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">But some
pairs of operators are not commutable, such as the position and
momentum of a particle. Though it is often possible to make precise
predictions of these properties, the prediction of one makes it
impossible to predict the other. That is, when one property is
predicted by one operator, the mathematical operation changes the
wavefunction and so the prediction made for the other property is not
the same as it would have been if the second property had been
predicted first. Since the order in which the operators are applied
to the wavefunction makes a difference in what they predict, it is
impossible to predict both properties at once. Thus, the conjugate
variables to which Heisenberg’s uncertainty applies turn out to be
the pairs of properties predicted by non-commutable operators.</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">When the
operator yields an expectation value that is just the average result
for an entire series of experiments, it can often be represented as a
superposition of different wavefunctions for each of which the
operator gives an expectation value. When the measurement is made and
one of them turns out to be true, the wavefunction is said to
“collapse,” because the system turns out to have one or another
of precise predicted outcomes. This is called the “collapse of the
wavefunction,” because it is assumed that prior to the measurement,
what actually existed was a superposition of different wavefunctions.
</font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">This
interpretation of the measurement of a quantum system exacerbates the
problem, for the superposed states of the system can evolve in
radically different ways. In the most famous example, a cat is locked
in a box with a devise triggered by an unpredictable beta decay that
will, with 50% probability, release a poison that kills the cat
within a certain period of time. But until someone looks to see what
has happened, there is a superposition of the two states, one with a
dead cat and another with a living cat, and reality only resolves
itself into one or the other possibility at the moment someone looks.
This implausible implication of measurement being the collapse of the
wavefunction is called the problem of &quot;Schrödinger’s cat.&quot;</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
Heisenberg uncertainty principle is, perhaps, the most general
statement of the puzzles of quantum mechanics, and a genuine
ontological explanation of quantum mechanics, if there is one, should
reveal the source of this limitation on our knowledge. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">B<img src="data:image/png;base64,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" name="TtsOtkCLQm_07" align="right" hspace="5" width="225" height="32" border="0">ell
correlations. </font>Recently, attention has focused on a final
quantum mystery, called “Bell’s Theorem” or “Bell’s
Inequality.”<sup><a class="sdendnoteanc" name="sdendnote1anc" href="#sdendnote1sym"><sup>i</sup></a></sup>
John Bell showed that quantum mechanics entails, in certain
circumstances, a statistical correlation between events occurring at
a distance that seems to be possible only if the events have effects
on one another that travel faster than the velocity of light. It
holds for interactions in which particles move away from one another
in opposite directions with opposite orientations of a “spin”. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>Spin.</b></i>
Spin is a quantum property that was first recognized with the
discovery of quantum field theory. The Schrödinger wavefunction is
the law of non-relativistic quantum mechanics, and a more complete
law was discovered by Paul Dirac when he combined the Schrödinger
wavefunction with Einstein’s special theory of relativity, that is,
taking the relationship it describes between space and time into
account. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">There was
an asymmetry between the time-dependent and time–independent
wavefunctions derived by solving Schrödinger equation. The
time-independent wavefunction, describing the spatial aspects of the
standing wave, is a <i>second order </i>differential equation,
whereas the time-dependent wavefunction, describing how the quantum
system unfolds in time, is a <i>first order </i>differential
equation. Dirac derived a time-dependent wavefunction that was a
second order differential equation, making time and space
symmetrical, as they are in the special theory of relativity.</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
is puzzling just what makes Dirac's derivation work, but it involved
several profound discoveries. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Dirac
discovered that there are twice as many solutions for the
wavefunctions than had been thought, half of them corresponding to
negative energy. This was the discovery of antimatter, such as, for
example, the positively charged electron as the negative partner of
the negatively charged electron, called the &quot;positron.&quot;</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Dirac
discovered that quantum particles have another property, called
“spin,” which was a new quantum number that was needed for
wavefunctions to describe fully any quantum situation. That is, spin
is a new quantum number (namely, <i>s</i>) needed to describe the
atom (along with Bohr’s numbers for the energy states of atoms (<i>n</i>),
a number for the orbital angular momentum of the electron (<i>i</i>),
and a number for its magnetic moment (<i>m</i>)). </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">It is
believed that the intrinsic spin of an electron has little to do with
a spinning electrical charge. The spin of a particle is defined
operationally as the strength of the magnetic force that results when
a magnetic field is imposed on the particle. Particles, such as the
electron, that have ½ spin (called “fermions”) have one of only
two possible magnetic moments (positive and negative). Since there is
no way for them not to have a magnetic moment, it is hard to see how
they could be a classical material object with a charge that is
somehow actually spinning. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>Bell’s
Inequality.</b></i> John Bell discovered a curious consequence of
quantum mechanics involving spin. The spin of a particle (either a
rest mass or a photon, which has a spin of 1) would seem to a
property that the particle carries with it, but a prediction made on
this assumption contradicts quantum mechanics. And it seems to have
been disproved empirically. This suggest that spin is a property that
depends, not on the particle itself, but on what happens elsewhere in
a much more inclusive system involving both particles. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">The system
is one in which two objects are generated in a way that requires them
to have opposite orientations of spin, and they move away from one
another in opposite directions. Since space is three dimensional, the
spin of a particle can be measured from three different, mutually
perpendicular directions. If one particles is measured as having as
having spin, say, up, in some direction, then the other particle will
never turn out to have anything but the opposite, down, orientation
of spin when it is measured in the same direction. This holds
regardless which of the three independent directions in space the
magnetic field is oriented, and quantum mechanics does not permit one
to infer from its spin in one direction what its spin in any other
direction is. Thus, if spin is a property that the particles already
have when they part from one another, the outcome of measuring the
spin of the particles that moved off one way from their creation from
one direction should not enable us to predict the spin of the other
particle when measured from a different direction. Bell showed that,
on this assumption, a certain inequality must hold about the
frequency with which measurements of spin in one particle in one
direction would correlate with measurements of the spin of the other
particle in one of the other directions. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">However,
quantum theory predicts and experiments have confirmed that this
inequality will be violated. When two objects are generated in this
way, and the spin orientation of one of these objects is measured in
one direction, it is possible to predict the outcome of a measurement
of the spin orientation (up or down) of the other object in an
independent direction of three dimensional space more often than the
Bell inequality allows. It is not a reliable prediction in any
particular case, but statistically it is more frequent than would be
possible, if the spin orientations of both objects were already
determined when they parted and they were simply carried away with
them, as the principle of local action would require. </font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif">Though the
two measurements can be made as far apart in space as one likes, it
seems that the only way the measurements could be correlated is if
the measurement of one object were somehow affecting the state of the
other. And since the two measurements can be made to occur as near to
one another in time as one likes, there are instances of this
phenomenon in which such an effect could hold only if something
travels between them faster than the velocity of light. This puzzling
correlation is not only a consequence of quantum theory, but has also
been confirmed experimentally, and thus, it seems that we must give
up the principle of local action. But it seems to violate the
principle of local action. Since the different outcomes are a
superposition of different wavefunctions, this is seen as just
another puzzles about the so-called &quot;collapse of the
wavefunction.&quot;</font></font></p>
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
puzzles of quantum mechanics have to do with understanding what in
the world corresponds to the Schrödinger equation. The “Copenhagen
interpretation” of quantum mechanics, developed by Bohr, is the
received view. It simply denies that it is possible to describe the
nature of what exists except by applying the classical conceptions of
particles or wave, which if not strictly speaking incompatible, are,
at best, complementary. Defenders of the Copenhagen interpretation
see the puzzles of quantum mechanics as deriving from its departures
from classical physics, as if classical physics were based on
intuitions ( or a form of imagination) that is anthropocentric and,
thus, merely subjective. And some go on to insist that the
uncertainty is a real indeterminism about what happens in the world. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
chief opponent of this view was Einstein. He was resisting the
reification of quantum uncertainty as indeterminism when he claimed,
“God does not play dice with the universe.” A view of the world
as being constituted by substances of some kind is what kept Einstein
from accepting quantum mechanics as the complete description of what
exists. His acceptance of spacetime as a substance made him most
sympathetic to Spinoza, for Spinoza believed that the world is a
single substance. But what seems to have kept Einstein from admitting
that such a substance could have indeterminism as a basic property
were his ontological instincts. </font></font></font>
</p>
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
what follows, I will elaborate the the assumptions of
spatiomaterialism in a way that explains ontologically why quantum
mechanics is true. It is, as I have warned, more speculative than the
rest of the argument of ontological philosophy. But it may suggest
the power of an ontological approach and vindicate Einstein’s view
of the nature of the world in at least one respect. </font></font></font>
</p>
<div id="sdendnote1">
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
<a class="sdendnotesym" name="sdendnote1sym" href="#sdendnote1anc">i</a><span lang="en-US">
See </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Cushing"><font color="#0000ff"><span lang="en-US"><u>Cushing</u></span></font></a><span lang="en-US">
and McMullin (1989) for discussions of this issue.</span></p>
</div>
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