Quantum Quandries - Part 2
The problem with Interference
Airy
patterns (named after George Airy, who was the first individual to provide an explanation
of the phenomenon) are a series of alternating, dark and light, concentric circles. These
circles are the result of the diffraction and interference patterns which are created when
a wave is sent through a circular hole. The alternating bands of light and dark are
manifestations of interference. The circular character of these bands is due to the
diffraction of the wave by the circular hole.
So-called
electron guns generate electrons by heating a metal filament. As the filament
heats up, electrons are released. The rate at which the electrons are released, as well as
the level of momentum which electrons have when released, can both be controlled. In fact,
one can fine tune the rate at which the electrons are released so that just a single
electron is emitted.
The
electrons are directed toward a glass screen, the back of which has been treated with a
phosphor paste. Such a treated screen is capable of detecting the presence of electrons.
Essentially,
the detection process works in the following manner. The inactivate phosphor molecules in
the paste tend to be in their lowest energy state which is known as the ground state.
When any
given phosphor molecule in the ground state is hit by an electron, the molecule becomes
excited by the transfer of energy from the electron's kinetic energy. When the phosphor
molecule enters into the excited state, it tends to return to the ground state by giving
off a photon.
The
intensity of the photon which is emitted will depend on either the rate or the energy (or
both) of the electrons that come in contact with the phosphor molecule(s). Finally, once
the phosphor molecule has returned from the excited state to the ground state by emitting
a photon, the molecule has been re-set, so to speak, to respond to the impact of further
electrons from the electron gun.
If one sends
a beam of electrons through a circular hole set up before a phosphor screen, the character
of the pattern on the screen will depend on the size of the hole through which the
electrons are sent. Above a certain size, the pattern on the screen remains
just a spot. However, the spot on the screen will become increasingly smaller as one
shrinks the size of the hole down to the critical limit.
On the other
hand, below a certain size value, the spot on the phosphor screen not only becomes
progressively larger as one reduces the size of the hole, but alternating bands of light
and dark concentric circles appear around the center spot of the pattern. When this
occurs, one is observing an Airy pattern.
The
character of the Airy pattern will change as one alters the voltage of the electron gun.
If, for example, one reduces the voltage, the Airy pattern expands. However, if one
increases the voltage, then, the Airy pattern will become more constricted. If one
continues to increase the voltage to a sufficient degree, then, eventually, the Airy
pattern will become a small dot.
One can use
the alteration in the character of the Airy pattern as a function of voltage to show the
relationship between an electron's momentum and wavelength. In other words, the electron
diffraction experiments provide one with a means of linking the particulate and wave modes
of the electron in a very fundamental way. In its simplest form, the relationship can be
stated as: p = h/L, where: p is the momentum, h is Planck's constant, and L is the
wavelength of the electron which is derived from Airy's formula: theta = 70(L/d) -'d'
being the diameter of the aperture through which the electrons are shot.
Although the
presence of the Airy pattern in experiments involving electrons does seem to indicate wave
phenomena are involved, nevertheless, one is confronted with a problem when one reflects
on the following consideration. These wave patterns are constructed and shaped by a set of
events that, according to all measurements, appear to be particle-like or discrete in
character. In other words, although the large scale character of the display on the screen
is an Airy pattern, which suggests a wave phenomenon, this pattern is the result of a
large number of individual electron collisions with the phosphor molecule, which suggests
a particle phenomenon.
Neither the
particle perspective nor the wave perspective, considered as individual explanations, is
capable of accounting for what is observed in the above outlined electron gun experiment.
Both a wave and a particle perspective need to be combined in order to provide a framework
that is capable of accurately describing what is observed.
Measuring quantum events: a lingering issue
Quantum
physicists do not have a satisfactory explanation for two questions which are of critical
importance to an understanding of what is really going on at the quantum level. The first
question concerns the measurement process- namely: what actually takes place during the
act of measurement of quantum events?
Secondly, to
what does the wave function give expression? Does it actually reflect something real, or
is it a happy coincidence which merely provides a key to calculating certain variables?
There are a
number of ways of raising the quantum measurement problem. They are all variations
on a basic theme.
Essentially,
the problem revolves around the following question: How does a determinate result (namely,
a measured particle with specifiable dynamic attributes) get generated from a state of
multiple possibilities or probabilities in which the particle is devoid of determinate,
dynamic characteristics (i.e., the pre-measurement state)? Another way of asking the same
sort of question is this: What is the nature of the transition process which takes a
quantum event (i.e., a pre-measurement phenomenon) and permits a classical event to evolve
out of it (i.e., the measurement phenomenon)? A third way of asking the same essential
question is as follows: What actually happens when the wave function collapses?
Although a
number of suggested resolutions to the quantum measurement problem have emerged during the
last fifty years, there are no differences among the various interpretative approaches as
far as the mathematical or experimental aspects of quantum mechanics are concerned.
They all accept the results of mathematical calculations, and they all agree on what can
be expected to be observed in different experimental circumstances. Consequently, at the
present time, there is no experimental means of determining if any of these
interpretations is 'the' correct interpretation of the nature of quantum reality.
According to
the Copenhagen approach to quantum theory, one will not be able to find an
explanation for the world of our everyday experience in the realm of quantum reality. One
starts, instead, with the world on the macroscopic level as a given and uses quantum
theory as a means of mapping certain kinds of engagement relationships between the
macroscopic measuring devices of the classical world and various aspects of the quantum
level of reality.
Although one
can employ quantum theory to make accurate predictions about various aspects of the way
classical measuring devices engage quantum reality, quantum theory cannot explain: (a) why
such engagements have the character they do; how such engagements come about; or, (c) what
the precise character of the relationship is between classical reality and quantum
reality. Indeed, from the perspective of the Copenhagen school of quantum theory, the
realm of quantum reality remains forever inaccessible to our classical modes of
experience.
Moreover,
according to the Copenhagen school, the quantum realm is beyond our comprehension since it
operates in a way which defies and eludes logical or rational analysis. Consequently, as
far as this school of thought is concerned, the quantum measurement problem can never be
answered in any definitive, satisfactory manner.
John von
Neumann took a different approach to the quantum measurement problem from
that of the Copenhagen perspective of Bohr and Heisenberg. Unlike the latter individuals,
von Neumann did not feel comfortable with a bipartite division of reality into classical
and quantum realms. Von Neumann preferred a unified view of reality, but he maintained
that reality is entirely quantum in character, without any trace of classical influences.
Von Neumann
maintained that quantum theory does not constitute a method for relating classical
measuring devices and the non-classical quantum realm. He described everything in terms of
quantum proxy waves, but he distinguished between different states of the proxy wave. More
specifically, he speaks of Type I and Type II processes.
Type I
processes involve proxy waves outside the context of measurement. These sorts of processes
consist of proxy waves expanding throughout the universe. Type II processes, on the other
hand, give expression to the contraction of the proxy wave in the context of measurement.
While the
contraction of the normally expanding wave of possibility during a Type II process results
in a determinate outcome, the outcome is still, nonetheless, a proxy wave rather than a
classical entity of some sort. When physicists talk about the collapse of the wave
function, they are referring to a Type II process.
Irrespective
of whether one is referring to a Type I or Type II process, the way in which yon Neumann
construes the proxy wave is in opposition to way in which most modern physicists have come
to treat the proxy wave. Whereas in the latter case, the proxy wave tends to be considered
as a convenient methodological device without any physical reality, von Neumann considers
the proxy wave to have physical reality.
Consequently,
for von Neumann, the quantum jump which occurs when a Type II process replaces a Type I
process (i.e., the wave function collapses) describes an actual physical event. However,
there are a number of questions, concerning the physical character of the jump, to which
neither von Neumann, nor anybody else, has been able to provide a satisfactory answer :
(a) just how does the jump from a Type I to a Type II process take place? (b) at exactly
what point during the process of measurement does the collapse of the wave function occur?
Von Neumann
failed to come up with a solution that provided details concerning the physics of the
jump. He eventually decided the 'cause' of the jump is the human consciousness which is
part of the Type II measurement process. In other words, according to von Neumann, the
dynamic properties of a particle come into being with an act of consciousness. In effect,
consciousness creates, at least in part, the properties of a particle.
Von
Neumann's 'consciousness-creates-reality' theory sounds very similar to approaches to the
quantum measurement problem which are rooted in an observer-created-reality (e.g.,
the theories of Fred Wolf). However, there are fundamental differences
between the two perspectives.
In the
latter case, the character of reality arises as a function of the choices made by a given
observer concerning which dynamic property to measure. Thus, if one focuses on the
conjugate properties of position and momentum, a decision to measure a particle's position
will affect one's interaction with the particle's momentum. As a result, the observer
would have affected the mode of property through which the particle manifests itself to
the individual.
In addition,
in an observer-created quantum interpretation, one does not have to use human beings to
make the observation. In other words, from the perspective of this approach to the
interpretation of quantum reality, the 'observer' does not have to be conscious in order
to be able to affect the property mode through which a given particle manifests itself.
Thus, one can use machines or various forms of technology to act as a surrogate observer.
However, in
von Neumann's 'consciousness-created-reality' approach to the interpretation of quantum
theory, machines cannot create reality since they have no consciousness. Determinate
values for a given dynamic property can only be generated through the presence of
consciousness. Consequently, whatever the nature of the machine/quantum reality
interaction, the results require an act of human consciousness to provide those results
with a determinate value.
Another
difference between the 'consciousness-created-reality' position and an
'observer-created-reality' position is as follows. Whereas the latter approach determines
only what property will be manifested and not its precise value, consciousness-created
reality specifies a particular value for the property which is to be manifested.
Neither the
'observer-created-reality' approach nor the 'consciousness-created-reality' approach is
giving expression to Bishop Berkeley's contention that existence is a function of
perception. Both of the former views are speaking only about the dynamic properties of
various quantum entities.
The
so-called static properties of a particle, such as mass or charge, have a substantial,
permanent reality independently of whether or not they are observed. These static
properties are not created by either the act of observation or the presence of
consciousness.
In addition
to his distinction between Type I and Type II measurement processes, von Neumann put forth
an argument which he claimed proved that there could be no hidden or deep reality with
respect to the dynamic properties of a particle. According to von Neumann, if one wished
to claim dynamic properties are intrinsic to the structural character of a given particle,
then, descriptions of the of such a particle must necessarily come into conflict with the
predictions of quantum physics.
Phase entanglements, pilot waves and configuration space
David Bohm
came up with a counter-argument to von Neumann's 'proof' in 1952. According to Bohm, one
of the essential characteristics of reality concerns its quality of undivided wholeness.
Central to
his perspective is the notion of phase entanglements. Unlike normal
waves of the everyday world which separate cleanly following interaction, the proxy waves
associated with quantum entities do not separate cleanly following interaction. The
respective phases of the different quantum entities become intertwined. Apparently, the
reason why the proxy waves behave differently from the everyday variety of wave concerns
the kind of space through which each sort of wave is given expression. Whereas normal
waves are transmitted in 3-space, proxy waves are transmitted in what is known as configuration
space.
Each quantum
entity has a proxy wave (known as a "pilot wave") which exists in
three dimensions of configuration space. If one has n quantum entities interacting with
one another, then, the associated proxy waves of these interacting particles will occupy n
x 3 dimensions of configuration space. However, rather than there being n different waves
in configuration space, there is just one wave in n dimensions.
Consequently,
the phase character of this wave becomes very complex, but that character is of a unified,
though multi-dimensional nature. In fact, from the perspective of individual proxy waves,
the phases of these waves appear to be entangled with one another.
One of the
functions of the pilot wave is to convey information, instantaneously, to the particle
concerning any changes which are encountered by the pilot wave. This information is used
by the particle to adjust its dynamic attributes, such as position or momentum, in
accordance with the character of the information transmitted via the pilot wave.
Among the
contextual changes encountered by the pilot wave are those that involve acts of
observation or measurement. The dialectic between a particular act of, say, measurement
and the pilot wave would alter the character of the pilot wave's form to reflect certain
aspects of that process of measurement.
This
alteration in waveform character would, then, be transmitted to a given particle, and the
particle would alter its position or momentum accordingly. With different kinds of
observational or methodological engagements, different sorts of pilot wave forms would
arise.
Although
Bohm argued that the dynamic properties were intrinsic to a particle, he also provided a
means, through the agency of the pilot wave, for those properties to be: (a) sensitized to
environmental or contextual changes, and (b) capable of manifesting appropriate sorts of
adjustments. Thus, Bohm had proposed a model which permitted particles to possess a
definite momentum and position at all times. Yet, his model was, nonetheless, still able
to generate results that mirrored the predictions of quantum mechanics - something which
von Neumann had claimed so-called hidden variables could not do.
The feature
of phase entanglement gives rise to an intriguing, but problematic, possibility. More
specifically, in theory, the idea of phase entanglement suggests the possibility of
action-at-a-distance in which events in one part of configuration space are
capable of being transmitted instantaneously to other parts of configuration space despite
the fact that the quantum entities with which the proxy waves are associated may be
separated by distances which prohibit (if one accepts the tenets of Einstein's special
theory of relativity) the possibility of instantaneous communication.
However, one
must keep in mind that configuration space is a mathematical construct and does not
necessarily have any actual ontological counterpart. Moreover, the multidimensional aspect
of configuration space (which is at considerable odds with the, apparently, limited
dimensionality of our everyday experience) led many physicists to conclude that the waves
occupying such space were not 'real' physical waves.
Is quantum theory Incomplete?
Although
Einstein accepted the idea that quantum theory is capable of accurately describing all
experimental results, he, nonetheless, continued to express his distaste for, among other
things, the intrinsic random quality of quantum theory. He did so by contending that
quantum theory was incomplete. Because of the inherently statistical character of quantum
theory, Einstein believed the theory contained lacunae in relation to certain aspects of
physical reality. In short, while quantum theory might provide a complete description
of measured phenomena it did not provide a complete description of reality.
In 1935
Einstein, along with Boris Podolsky and Nathan Rosen, put forth the first of a series
thought experiments. Einstein believed such experiments would demonstrate the incomplete
nature of quantum theory. As originally conceived, the experiment focused on two electrons
which had correlated momentums at the beginning of the experiment.
David Bohm
came up with a simpler version of the same idea when he substituted
polarization-correlated photons for the momentum-correlated electrons of the EPR
experiment. The following discussion uses Bohm's version of the experiment, but the
principle involved is the same in both cases.
In Bohm's
experiment, two photons are emitted from a given light source. These photons exhibit a
form of phase entanglement which is known as the state of parallel polarization. In
this state, the angle of polarization of each photon is the same as the other photon's
angle of polarization.
The state of
parallel polarization actually reflects an aspect of configuration space in which the two
photons manifest a single waveform of determinate value. In other words, while neither
photon, individually, has a definite proxy wave associated with it, the two photons
exhibit phase entanglement and, therefore, do have a definite waveform associated with
them as a combined unit.
Essentially,
the question which Bohm raises with his experiment (and, the same question is raised in
the slightly different experimental version conceived of by Einstein, Podolsky and Rosen)
is as follows. Will either of these photons have a definite angle of polarization after
their point of release but prior to the time that either of them is measured at
some subsequent point where they have been separated from one another by distance during
some given period of elapsed time?
From the
perspective of the Copenhagen school of quantum interpretation, the dynamic properties,
one of which is the angle of polarization, cannot have any definite value outside of the
context of measurement. The determinate value only emerges during the process of
measurement.
According to
Bohm (and Einstein), the particle will have determinate dynamic properties in between the
time of release and its subsequent measurement. Furthermore, since the two particles are
traveling in opposite directions at the speed of light, there can be no communication
between the photons concerning what is happening to one another during the process of
their respective measurements.
This is so
because of the restrictions of the locality assumption which are imposed by the special
theory of relativity. If one has ignorance about the character of the dynamic property of
either of the particles when they are in between release and measurement, this is a case
of classical ignorance not the intrinsic ignorance of quantum randomness.
In effect,
the thought experiments of Bohm and EPR, are logical arguments about the possibility of
certain aspects of reality falling beyond the boundaries of quantum theory.
Logical arguments do not prove quantum theory is wrong or that quantum theory makes
predictions which can be shown to be incorrect. What such arguments suggest is that
quantum theory is not able to account for certain aspects of reality which occur outside
of the context of measurement and, therefore, is incomplete.
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