San José State University
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Quantum Mechanics, the Copenhagen Interpretation,|
the Bell Theorem and the Nature of Atomic Reality
Quantum mechanics developed in a dramatic chain of events in the late 1920's. The old quantum physics of Planck, Einstein and Bohr was deemed inadequate. Werner Heisenberg, working with Bohr, Born and Jordan made the first major development, matrix mechanics, but this was soon superceded by the wave mechanics of Erwin Schrödinger. Heisenberg initially rejected wave mechanics but Schrödinger and Paul Dirac both gave proofs that matrix mechanics and wave mechanics were equivalent theories. Wave mechanics became the preferred formulation of quantum mechanics. Wave mechanics involved a variable, called the wave function, for particles that was analogous to quantities involved in optics. The question was what that quantity represented. Max Born asserted that the squared magnitude of the wave function was a probability density. When this was communicated to Bohr in Copenhagen Bohr said that he and his group had never thought of the wave function being anything but that.
Bohr and his group went on to give a more radical interpretation to the results of wave mechanics. Not only was there a probability density function for a partical that represented the degree of indeterminancy of the partical but that the particle did not exist as a particle until it was subjected to some observation or measurement. This interpretation, which came to be known as the Copenhagen Interpretation, was resisted by other physicists, notably Einstein and Schrödinger. Einstein carried on a decades long debate with Bohr on this matter. Einstein formulated thought experiments that were intended to counter the Copenhagen Interpretation, but in each case Bohr was able to show that the thought experiment failed to contradict the Copenhagen Interpretation.
The American physicist John Wheeler gave an interesting analogy to explain the Copenhagen Interpretation. He was once involved in a game called Twenty Questions. One person leaves the room and the others choose a word. The person who left is allowed twenty questions to identify the chosen word. In Wheeler's case when he left the room the others decided to play a trick on him and not choose any word. As the game progressed they gave him answers that were consistent with previous answers. Wheeler noticed that at first the answers came quickly but later there were delays as the answerers ponder which answer would be consistent with the previous answer. The set of possible words became narrower and narrower as the game went on. Finally there was only one word that that it could be and Wheeler got it right. Wheeler noted that this was like the Copenhagen Interpretation. The word did not exist until the questions established it. According to the Copenhagen Interpretation the particle does not exist until the circumstances of the experimental measurement are specified.
In 1935 Einstein, in collaboration with Podolsky and Rosen, published an article that involved a more sophicated thought experiment. Electrons form spin pairs; i.e., two electrons with opposite spins linked together. Einstein envisioned an experiment in which the electrons in a spin pair are separated and at some distance from the separation the spin of one electron is measured. This means that the spin of the other member of the pair has to be compatible with that measurement. If the electrons do not exist as particles until the moment of measurement then there would have to be some communication between the two members of the former pair. Einstein deemed this spooky action at a distance. Such communication would involve a signal traveling faster than the speed of light in a vacuum. If the electrons exist as particles after their separation there is no problem with the correlation of their spins. That left the Copenhagen Interpretation in some doubt.
In 1964 the Irish physcist, John Stewart Bell, published an article that derived an inequality that would have to be satisfied if the separated members of an electron spin pair existed as particles after their separation. This is now known as the Bell Theorem. The name that was given to the separated pairs under the Copenhagen Interpretation is entanglements. Such entanglements in principle could exist for any separation distance.
The Bell Theorem was just an interesting proposition until Alain Aspect and his colleagues in France decided to test it. It was not feasible to use entangled electrons for the testing and polarized photons were used instead. The result was that the Bell inequality was violated. So apparently the separated particles did not have particleness after their separation until they were subjected to measurement. However note that this did not necessarily vindicate the Copenhagen Interpretation. There are other alternatives to the particleness of entangled photons after their separation and before their measurement. Nevertheless the results of Aspect and other tests of the Bell Theorem are interpreted as having vindicated the Copenhagen Interpretation.
The proof of the Bell Theorem and its experimental testing by Aspect have to be examined in fine detail.
(To be continued.)
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