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.

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. 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, 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.

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 have a precise position (or momentum) until it is measured (as the Copenhagen Interpretation demands) appears to be false. But, of course, we can't really know this unless we actually measure the position (or momentum) of the other member -- which is prohibitively difficult.

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 (p₁ + p₂) and the distance between the particles (x₂ - x₁) can be measured to within any desired accuracy. It is thus conceivable that measurements of the momentum-sum and the interparticle distances could be made for a two-particle system near the planet Mercury and that particle 1 could proceed in its course (its velocity not affected by gravity or other particles -- ignored for the sake of example) to Earth, while particle 2 proceeds to Mars. A signal travelling at the speed of light could take fifteen to twenty minutes to reach particle 2 from particle 1. A measurement of the momentum of particle 1 is made to within such high precision that knowledge of the position of particle 1 is destroyed. It nonetheless allows the momentum of particle 2 to be calculated to within the same precision. Moreover, the position of particle 2 could be measured with very high precision, destroying knowledge of its momentum. But since the momentum of particle 2 had been calculated, knowledge of the position and momentum of particle 2 prior to the latter measurement was determined to within less than the uncertainty limit. Thus, particle 2 possessed a more definite position and momentum than quantum theory could calculate. Thus quantum mechanics is shown to be incomplete. The great distances between particle 1 and particle 2 are used to prohibit the possibility that the determination of the momentum of particle 1 to calculate the momentum of particle 2 somehow communicates a definite momentum to particle 2 ("collapses its wave function") by a signal which moves at the speed of light or less.

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 (i.e., not the final word as a description of the universe). Karl Popper also failed to see the relevance of Bohr's reply and never met a physicist who could justify it to Popper's own satisfaction. Popper finally concluded that it was Bohr's authority, rather than his counter-argument, which let many physicists to believe that the "EPR Paradox" had been refuted.

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.