** by Ben Best **

Near the end of the nineteenth century many physicists believed that physical theory had been virtually completely discovered. Lord Kelvin expressed this view, with the qualifier that "two small clouds" remained on the horizon: (1) the negative results of the Michaelson-Morley experiment and (2) the failure of the Rayleigh-Jeans law to predict the distribution of radiant energy in a black body. These "small clouds" were soon unleashing the thunderstorms of relativity and quantum theory.

Thirty years later, however, some leading physicists were again attempting to declare the end of physical knowledge. This time, however, the claim was not so much that physics had the means of explaining all phenomena, but that physics had reached the limits of its capacity to explain. The search for causal laws was declared fruitless because of the claim that the threshold of acausal randomness had been discovered — with the further implication that there is ultimately no objective reality. This is the philosophical essence of the Copenhagen Interpretation of quantum theory. And it is an interpretation which does not follow strictly from physics.

The Copenhagen Interpretation was primarily the product of Neils Bohr and Werner Heisenberg, who were strongly supported by Max Born, Wolfgang Pauli and John von Neumann. Among those opposed to the Copenhagen Interpretation have been Albert Einstein, Erwin Schroedinger, Louis de Broglie, Max Planck, David Bohm, Alfred Landé, Karl Popper and Bertrand Russell. While those supporting the Copenhagen Interpretation constitute a "school" and an "orthodoxy", those opposed to it have widely divergent views. But the latter have been uniformly vilified as too simple-minded or too "old fashioned" to understand such "modern" ideas as acausality and positivism. Soviet physicists also opposed the Copenhagen Interpretation, but on the grounds that it is an "idealism", to be contrasted to a "dialectical materialist" view of reality.

The essential controversial features of the Copenhagen Interpretation are (1) the Uncertainty Principle (also called the Indeterminacy Principle) of Heisenberg and (2) the Principle of Complementarity of Bohr. With the passage of time the Copenhagen Interpretation has been more specifically identified with a concept known as "the collapse of the wave function" (also called "the reduction of the wave packet") as formulated by John von Neumann. These ideas will be examined in turn.

Heisenberg's Uncertainty Principle asserts that the product of position
and momentum uncertainty for any particle will be more than a certain multiple
of Planck's constant. Since ** momentum** is the product of mass and
velocity, and since the

What seemingly began as a simple measurement problem under specific
circumstances became gratuitously generalized into a metaphysical assertion.
Although the original thought experiment was a causal demonstration which
assumed an underlying deterministic position and velocity (momentum), the
Copenhagen Interpretation began to deny that the electron ** has** a
definite position or velocity. From the positivist idea that it is
meaningless to discuss the existence of something which cannot be measured
(position and velocity, within certain limits) came the idea that the electron
is an unreal, causeless "possibility" which only achieves actuality
upon observation. Thus positivism became twisted into subjectivism (some say
"solipsism") and the idea that the observer somehow

Obviously a physician who attempts to measure a patient's blood pressure is faced with a problem. What she measures is not simply blood pressure, but the blood pressure of a person having his blood pressure taken by a physician. A physician would be wiser to look for indirect means of determining true blood pressure than to assert that her "observer-created" reality is all the reality that exists — and that the patient has no blood pressure until she tries to measure it. Similarly, means other than bombardment of photons might be possible for determining the position and velocity of an electron.

A photographic plate containing the track of an electron can be used to
determine position and velocity within less than the uncertainty limit. In
a rather questionable bit of rationalization, Heisenberg denied the evidence
of the photographic plate by asserting that his Uncertainty Principle is only
relevant to ** predicting** the future, and that "this knowledge
of the past is of a purely speculative character", adding "It is
a matter of personal belief whether such a calculation concerning the past
history of the electron can be ascribed any physical reality or not."
For some reason, most physicists chose a personal belief which denied
physical reality and conformed to the Copenhagen Interpretation.

Bohr's Principle of Complementarity arose out of the difficulty physicists were having in their attempts to determine whether quantum phenomena such as light are particles or waves. But complementarity is not a solution. Instead, it is an assertion that no solution exists and that physicists know all that can be known about the question. So it would be well to examine specifically the context from which complementarity arose.

Because of the straight lines (rays) evident in light propagation, Newton believed that light is composed of particles. But diffraction effects and other evidence increasingly led others to the belief that light is a wave. By the time of Maxwell's Equations (two centuries after Newton's work), light was understood to be purely wavelike — simply a small part of an electromagnetic spectrum ranging from the very long radio waves to microwaves to light and to the very short X-rays and gamma waves. But then experimentation with the photoelectric effect led Einstein to the conclusion that light is "quantized" in the form of photons. In fact, the shorter the electromagnetic wavelength (and hence, the more energetic the wave), the more particle-like an electromagnetic wave appears. Compton showed that when a beam of X-rays of sharply defined wavelength falls on a graphite target, the wavelength of the scattered radiation is a function of the angle of scattering — indicating that energy is lost during "recoil" of a photon colliding with an electron.

Louis de Broglie suggested that all matter, not just electromagnetic
radiation, has this dual wave/particle character. Thus, something with an
extremely particle-like character like a one kilogram baseball moving at ten
meters per second will have a wavelength of "infinitesimal" length
associated with it — 25 orders of magnitude smaller than the diameter of a
hydrogen atom (** ie**, 10

Erwin **Schroedinger's Equation** is a differential equation of a
particle of given mass subject to forces varying in time & space. The
solutions of Schroedinger's Equation are de Broglie matter waves
(**psi**) associated with the motion of the particle. Comparisions can
be made between the electromagnetic-wave equation and Schroedinger's
matter-wave equation. Schroedinger's Equation contains a complex
(imaginary, ** i**) term, implying that the de Broglie wave
functions are mathematical entities which cannot be imputed to have physical
existence. Some physicists regard this fact as a blessing insofar as it
prevents anyone from asking what is "waving" — the question
that led to the fallacy of the existence of

Einstein suggested that the square of the amplitude of the electromagnetic
wave (**epsilon ^{2}**) could be interpreted as the average number
of photons per unit volume (wave intensity, energy density, photon density).
Similarly, Max Born proposed something like a squared de Broglie matter
wave (the

An equation which describes particle locations in terms of probabilities
does not provide a visual model of the quantum micro world. Bohr's Principle of
Complementarity held that we can ** never** build a visual model of
the microworld based on analogues with objects in the macroworld. The closest
we can come to a model is to regard the two mutually exclusive classical
concepts of

When an electron is actually observed, what is seen is a particle.
But ** where** the electron is likely to be observed is described by
a wave function (the

For some, this interpretation of observation goes beyond the positivist
idea that it is meaningless to describe what is not being observed — into the
idea that ** consciousness** somehow controls a physical event.
Would an amnesia victim who suddenly forgot what he had just observed cause a
particle to "uncollapse" back into a wave function? Not likely. In
fact, a "wave function" incident upon a photographic plate will
"collapse" into a point (particle) whether or not the plate is
examined immediately. The Copenhagen Interpretation regards the "collapse
of the wave packet" as a fundamental, irreducible concept — meaning one
should not try to analyze the "mechanism" of the collapse. But the
trajectory of an electron in a cloud chamber looks very much like that of a
moving particle, despite Heisenberg's claim that it is senseless to speak of
"the path of an electron". Does the electron "recollapse"
at every point of condensation? Einstein and von Neumann declared that
quantum theory is not appropriate to describe individual physical systems
(particles), but is only relevant to large numbers of such systems
("ensembles"). All that ever "collapses" is our knowledge
of the system, according to Einstein.

An experiment involving circular diffraction, and the famous two-slit experiment, illustrate the most perplexing behavior of subatomic particles/waves.

If monochromatic, coherent light (laser light) of an appropriate
wavelength is projected onto a screen containing a cirular aperture of
appropriate size, a screen on the far side of the aperture will display a
bull's-eye (series of concentric rings) known as an **Airy disk**.
The Airy disk is deemed the consequence of the circular diffraction of light
waves through the aperture. Yet if electrons (or photons)
are fired individually, at one minute intervals, onto an aperture,
after a period of weeks a photographic plate on the far
side of the aperture will display an Airy disk. Moreover, the smaller the
aperture, the larger the Airy disk, precisely as predicted by the uncertainty
relation. Since the electrons have emerged through the aperture
one-at-a-time, there can be no question of them interfering. Instead, the
wave function describes the probability of finding an electron at a point in
space. The Airy disk has dark rings where the most electrons have struck
the photographic plate (the grainy character of the rings clearly indicates
their composition of individual particles striking the plate).

For the two-slit experiment, one can imagine firing classical particles
(bullets) at a panel containing two slits in **Figure 1a** and
observing the distribution of the particles against a screen (target). As
shown at the far right of **Figure 1a** — and on the left of
**Figure 1b** — the target will have two "mounds"
of particles.

Next, one allows classical waves (water waves) to propagate toward a
panel with two slits as in **Figure 2a**. The waves will diffract at
the slits and produce the interference pattern shown at the far right of
**Figure 2a** and on the left of **Figure 2b**.

Finally, one can fire electrons from a heated tungsten filament toward the
two-split panel as in **Figure 3a**. It appears that we are firing
bullet-like objects toward the panel, but when we look at the distribution
at the far right of **Figure 3a** — and on the left of
**Figure 3b** — we see interference patterns. At this
point we are tempted to think that we must have been mistaken, that the
electrons must have really been waves. To clarify the matter we fire the
electrons one at a time, but we still get the interference pattern of
**Figure 3b**. But this pattern is the cumulative result of many
electrons. Each individual electron merely adds one small point (as expected
from a particle) to the cumulative distribution pattern (an interference
pattern, as expected from a wave). If the single electron were a "wave" that
could go through both slits and produce interference, why does it make a
single spot on the screen rather than an image which is spread-out? We might
try to determine which slit the electron goes through by directing a
light-beam toward the slits. But such a light-beam must be of a wavelength
less than the distance between slits in order to distinguish which slit the
electron went through. Light of such short wavelength may be just energetic
enough to disturb the electron (as in the Uncertainty Principle thought
experiment). Sure enough, when the light is energetic enough to distinguish
which slit the electron went through, we get the distribution of
**Figure 1b** on the screen — meaning that our efforts to study the
slits have altered the result.

What can be concluded from this? Advocates of the Copenhagen Interpretation say these experiments support their theories of acausality, nonobjectivity of the electron and of a wave function which "collapses" into a particle when it hits the screen. Confronted with such perplexing evidence, the Copenhagen Interpretation appears no less contradictory than any other interpretation. Several "deterministic" explanations will be mentioned.

In THE FEYNMAN LECTURES ON PHYSICS, Richard Feynman described the double-slit interference experiment for single particles as being the only mystery in quantum mechanics. The two-slit experiment was originally a thought experiment based on the results of electron crystal-diffraction. The experiment has subsequently been carried-out many times using slits — with the predicted results. The panel containing the slits in the experiment contains atoms. There is no telling how the electron might be interacting with the matter in the panel at the slits — in fact, the electron which strikes the target screen might actually be one that was originally in the panel.

Two theories of **parallel universes** have been proposed to explain the
phenomena seen for the circular aperture and the two-slit experiment. These
theories are simply interpretations that do not make predictions, and cannot
be falsified. In the more naive theory, an electron confronted with the two
slits causes the universe to split in two — with the electron going through
one slit in one universe and the other slit in the other universe. This
"explanation" fails to explain the appearance of interference.
A more subtle parallel universes theory holds that an infinite number
of parallel universes exist at all times and that "shadow"
electrons (or photons) from the parallel universes cause interference with
the particles in our universe.

But in the experiment in which electrons (or photons) are fired through the circular aperture one-at-a-time, there is no need to hypothesize any sort of interference from "shadow" particles. The Airy Disk can simply be described as a probability distribution of particle destinations resulting from interaction of the particles with the aperture. The fact that the size of the Airy Disk is due to the size of the aperture is persuasive evidence for particle-aperture interaction being the cause of the distribution that looks like an interference pattern.

The distribution of the electrons in the two-slit experiment can similarly be attributed to interaction of electrons with the slits rather than interference with "shadow" electrons. The fact that bombarding electrons with light energetic enough to distinguish which slit the electron went through causes a particle-like distribution need not be interpreted as some metaphysical interference of consciousness. A simpler explanation is that increasing the velocity of the electron by light bombardment reduces the interaction of the electron with the slit. At high energies the DeBroglie wavelength of the electrons become too short to diffract at the slit. If "shadow" electrons from parallel universes were interfering, then increasing the velocity of the electrons by light bombardment would not result in elimination of interference. (I realize that Occam's Razor is subjective, but hypothesizing an infinite number of parallel universes strikes me as the most uneconomical of all possible explanations.)

David Bohm has become famous for his "hidden variables" explanation. Just as a smoke particle under a microscope is seen to "jiggle" in response to unseen atoms colliding with it (Brownian motion), so too oscillations of an electron in the wave function could be the result of unseen "hidden variables" which can propagate through both slits. Instead of being "shadow" electrons from parallel universes, these hidden variables could simply be smaller subatomic particles. Positivists of the Copenhagen Interpretation quickly dismiss the concept of "hidden variables" on the basis that it is meaningless to consider the existence of the unseen. But we should not forget that the arch-positivist Ernst Mach long denied the existence of atoms on the grounds that they are beyond sensory confirmation. John von Neumann proved a theorem which he claimed demonstrated that hidden variables could not explain quantum theory — but 34 years later John Bell (of Bell's Theorem) showed that one of von Neumann's assumptions was impossible.

Einstein regarded Bohm's "hidden variables" as a "cheap" solution to the quantum quandary. He challenged indeterminacy from two alternative hypotheses, one very "classical", and one far less classical than the Copenhagen Interpretation. The more classical view was his statistical interpretation of quantum mechanics. In this interpretation, a particle may possess a definite position and momentum, but quantum mechanics can only make statistical predictions of what they may be — within a range. In Einstein's more radical unified field theory interpretation, he suggested that (on a subatomic level) classical position and momentum may be two manifestations of a singular underlying reality (much like mass and energy). Both interpretations regarded indeterminate randomness as a limitation of human knowledge, rather than an inherent property of reality.

To Heisenberg, an electron is a wave-like "potentia" until the wave "collapses" into a point by striking the photographic plate. By Einstein's statistical interpretation of quantum mechanics, however, an electron has a discrete position and momentum at all times during its flight, such that the wave function (and the Airy disk) is only meaningful as a statistical description of the behavior of a large number of particles — not of an individual particle.

Einstein was by no means alone in denying that quantum mechanics precludes determinism. Erwin Schroedinger himself believed his equations to be completely deterministic — and maintained that view his whole life. Schroedinger was impatient with the idea that events in the microworld only acquire reality when they are observed. To show the silliness of that view, he came up with the "thought experiment" of a cat in a box which could be killed by a poison gas released by a mechanism attached to a geiger counter responding to a weakly radioactive sample. If a radioactive decay event has a 50% chance of occurring within a 5-minute interval, then the cat has a 50% chance of being killed by poison gas released by the geiger counter in the 5 minutes. Thus, the macroworld and the microworld are linked — if a radioactive decay event has no reality until it is observed, then the life or death of the cat has no reality until the box is opened to see if the cat is alive.

Amazingly, "Schoedinger's cat" has more often been interpreted
as an illustration of "observer created reality", rather than the
** reductio ad absurdum** Schroedinger intended. The logical consequence
of this interpretation is that there is no sound in a forest when a tree falls
if there is no one there to observe it. In fact, this interpretation implies
that it is meaningless to ask whether a tree has fallen if there is no
observer. (Einstein once asked Neils Bohr if the moon exists when no one is
looking at it.)

For those who believe in parallel universes, Schoedinger's cat is alive
in some universes and dead in others. The **Many-Worlds Interpretation**
(**MWI**), as it is most widely known, has been defended by such prominent
physicists as Stephen Hawkings & Steven Weinberg, although neither of
these men regard the theory as more than a mathematical formalism. Other
physicists — most notably
David Deutsch — do, however, ascribe physical
reality to the innumerable parallel universes and believe that anything that
can happen must have happened in many of those universes. According to MWI
the wave function does not collapse — every quantum state really exists in
some universes. (For more on MWI see the
Many-Worlds FAQ.)

Again, my "Occam's Razor bias" is that it is outrageous to propose countless parallel universes being generated to satisfy a model — conveniently interacting/noninterating in just the right ways to create just the right results — such as "quantum" interference with our universe (probability-wave "interference", no less) — without other interaction. MWI "space" is attributed the infinite density capacity of an infinite amount of matter. Explanations are a way to make sense of the universe. By contrast, MWI seems to make nonsense of the universe. Better to have no good explanation than to accept a bad explanation for the sake of having an explanation.

There is one more experiment which is crucial to understanding the
philosophy of quantum theory and that is the thought experiment of Einstein,
Rosen and Podolsky (often referred to as the **EPR Paradox** by those
who regard it as paradoxical). Imagine a "conjugate pair" of
particles which are the result of the decay of a single larger particle.
Assuming that these two particles do not interact with other matter, they
will fly-off in directions which are opposite. Conservation of momentum
demands that their velocities be the same. Suppose that we bombard one of
the particles with high energy light (as in the Uncertainty Principle thought
experiment). We can thus determine its position (or momentum) to as much
precision as we like, and thereby ** calculate** the position (or
momentum) of the other member of the pair. Thus, the assertion that the other
member of the pair does not

A more rigorous description of EPR assumes a two-particle system in which
the two particles move away from each other until they are separated by a
great distance. Although quantum mechanics dictates that it is not possible
to measure the momentum (**p**) of a particle and its position (**x**)
simultaneously to within less than an uncertainty limit, it does allow that
for two particles (**particle 1** and **particle 2**), the
sum of the momenta (**p _{1}** +

The essence of the EPR experiment was Einstein's claim that quantum
theory did not provide a ** complete** description of all that could be
known about a system, as the Copenhagen Interpretation claimed. Bohr's reply
to EPR was that a particle and the instrument that measures it constitute an
indivisible system and that measurements of the first particle constitute
a constraint on future predictions about the behavior of the second particle.
Einstein failed to see how this response constituted an answer to his charge
that quantum theory was incomplete (

But David Bohm made a major alteration to EPR which made EPR more of a testable hypothesis than a thought experiment. Schroedinger's wave equation had been generalized by Pauli to include the spin quantum number. In Bohm's version of EPR, a pair of protons in a singlet state which split and head-off in different directions will have opposite spin. To measure the spin of one particle would thereby "collapse" the Pauli wave function and instantaneously determine the spin of the other particle at whatever remote location it may be. There are problems with this modification of EPR, however. For one, proton spin is quantized and has properties which make it very alien from the familiar concept of spin seen in macroscopic bodies. For another, three dimensions of spin must be measured to determine the actual, total spin — and measuring any one of these components disturbs the other two.

John Bell found a solution to the second problem, however, in the form
of an inequality now known as **Bell's Inequality**. **Bell's Theorem**
states that a violation of Bell's Inequality is equivalent to a refutation
of EPR. A further modification of EPR replaced paired protons with paired
photons having opposite polarizations. This alteration has the advantage that
if a signal is communicated from one photon to the other at the instant of
"collapse", it ** must** travel faster than light if it is to
reach the conjugate photon to "collapse" it.

Polarized light can be thought of as light travelling through space like
a spinning knife. One can imagine a detector like jail-cell bars. If the
knife is spinning in a vertical plane in the direction of its motion, it will
pass through the prison bars (be detected). If the bars are wide enough, the
knife could be spinning in a slightly diagonal plane (between horizontal and
vertical) and still pass through the prison bars. The plane in which the
knife is spinning can be compared to the direction of polarization of light.

Imagine that a pair of photons are emitted from a central point (C) in
space (see **Figure 1**) and propagate in opposite directions towards
a polarization detector to the right (R) and to the left (L), each located
a distance of one light-year from C. The method of photon production (a
positronium source of correlated pairs of photons) guarantees that their
polarizations will be the same. Both Bohr and Einstein would agree that
if a photon-pair is produced and the detectors are both oriented vertically
(as in **Figure 1**), a detection of a vertically-polarized photon
at L in one year after photon-pair production will invariably correspond to
a detection of a vertically-polarized photon at R. Similarly, neither
detector will detect horizontally-polarized photons. Imagine now that the
orientation of the left detector is rotated 30° ** clockwise** in the
plane perpendicular to the line from L to R, as in

Bell's Theorem concerns a prediction about what should happen in the
set-up of **Figure 3**, which is similar to **Figure 2**
except that the detector at R has been rotated 30° ** counterclockwise**
in the plane perpendicular to the line from L to R. Bell claimed that
the locality assumption (

The first experiments to test Bell's inequality for photon polarizations were not sophisticated enough to preclude signals between the two photons L and R communicated at the speed of light. But apparatus used by Alan Aspect at the University of Paris in 1982 produced results that would require a signal many times the speed of light. However, the apparatus is not yet sophisticated enough to detect all but a small portion of the emitted photons. If Bell's inequality holds for all photons, it must be explained why the apparatus would select photons in precisely the manner predicted by quantum mechanics. It could also be asked whether oddities of photon spin (which is poorly understood) are well enough conceived that one can say with confidence that the experiment replicates EPR.

For a critique of the statistical methods of Aspect's experiment based on "subtraction of accidentals", see The Tangled Methods of Quantum Entanglement. For a critique questioning the timing constraints in Aspect's experiment see Does Bell's Inequality Principle rule out local theories of quantum mechanics.

But given that the experimental results are correct, that it replicates EPR and that Bell's inequality is violated, what does that say about the nature of reality? David Bohm has not rejected his belief in hidden variables or the incompleteness of quantum theory — instead choosing to reject nonlocality — believing that the signals are instantaneously communicated (faster than light). Others reject supraluminal communication and the objective determinateness of noncommuting observables of subatomic particles. One theorist even suggested that information from the first particle can travel backward in time to the point of the pair production and then travel forward in time to the second particle — arriving at the precise moment of measurement. In any case, denying the simultaneous reality of position and momentum of an electron is not sufficient to guarantee its non-reality, insofar as its mass and charge can be determined to within any known experimental limits.

In their struggle to understand experiments, physicists may challenge anything and everything. They challenge linear time, induction, deductive logic, relativity, quantum theory, reality, causality, reason, etc. In a sense it is healthy to regard nothing as sacrosanct, but without reason & order science degenerates into incoherent babble. Laymen listening to the far-out speculations of desperate physicists tend to grasp at every bizzare hypothesis as proven fact. Some are excited by the idea that reality is as random, muddled, ambiguous, contradictory and subjective as their own thought processes. Physicists themselves sometimes confuse obscurity with profundity or mathematical agility with understanding. They lose humility, ceasing to believe in a vastness of undiscovered physical law beyond present knowledge. The ultimate challenge of being scientific is to retain imaginativeness, openmindedness, skepticism and an intolerance for contradiction within a single frame of mind.

The majority of physicists make no attempt to form models of reality,
concerning themselves only with mathematical prediction — although without
an explicit metaphysical denial of the existence of objective reality (which
would be a model of reality, *e.g.*, the Copenhagen Interpretation). I
think this approach indicates an implicit acceptance of both causality and
of the objectivity of reality. I favor the idea that the so-called paradoxes
of slits and circular apertures can be explained by particle-slit
(particle-aperture) interaction and a statistical interpretation. My second
choice would be hidden variables — not in the sense of particles, necessarily,
but in the sense of undiscovered phenomena that currently make quantum
theory incomplete.
(See Is
QM a complete theory?.)

I also think that belief in causality
& the objectivity of reality need not (and cannot) be predicated on
an ability to explain subatomic phenomena based on analogies to
macroscopic phenomena. A belief in causality & objective reality which
incorporates an acknowledgement that the behavior of subatomic particles
must inevitably be somewhat strange when compared to our macroscopic world
represents a pragmatic synthesis of "predictivism" and
"realism".

[A philosophical perspective on this essay can be found in my
piece Thoughts on Physics and Reality]

[For a collection of quotes by scientists, quasi-scientists and
pseudo-scientists on the subject of quantum physics see
Quotations for the Backyard Quantum Mechanic ]

[For a critique of the quantum metaphysics of Roger Penrose and
New-Ager Fred Alan Wolf see my piece
Comments on Two "New Age Physics" Books]

[For a brief comment on how the Many-Worlds Interpretation is associated
with string theory, see my piece
The Standard Model of Particle
Physics]

[For comments on the attempt to link Quantum Theory with Freedom of
the Will see my piece
A Case for Free Will AND Determinism]