Given the results of the Aspect experiments,
it would appear that the journey is over and the final conclusion has
been made: experiments show that Quantum Mechanics is correct and complete,
and the EPR paradox put forward by Einstein is somehow invalid. Clearly,
there is some truth to this statement. The predictions made by the
hidden variable theory contradict the experimental
results. The Quantum Mechanical results held up
to within the accuracy of the experiment. But, what was wrong with the
hidden variable approach? At this point, we must return to the only
assumptions made in John Bell's paper. The fundamental assumptions were
that results are separable and local.
What would it mean if we rejected the separability condition (and wrote the probability as P(a,b,h) instead of A(a,b,h)B(a, b,h)) ? Non-separability means that after two systems have interacted and moved apart, measurements on the state of one of the systems affects the state of the other system. The problem with rejecting this assumption is that one calls into question one's ability to accurately carry out an experiment. One does an experiment by isolating a system and then, under controlled circumstances, one varies the quantities involved; one assumes that one can prepare the system over and over again and then place it into an isolated state so as to take repeated measurements. But, if the system is somehow tied to other systems outsie of the experiment one wishes to conduct, then there is not only no way of isolating the system but there is also no way to set up a controlled experiment.
On the other hand, what would it mean to reject the locality condition? The main problem here is that the wavefunction collapses instantaneously. How does it do that? The two systems must then have a method for communicating at infinite speeds - speeds in excess of the speed of light. The first counter to this point is that the wavefunction can collapse faster than the speed of light and still not violate Special Relativity because the collapse of the wavefunction cannot transmit information. Reducing the wavefuntion picks out one of a set of possible results at the measurement end and, instantaneously, puts the other system into a particular state. But, since we cannot control which state our local system falls into, we cannot force the system far away into any particular state. Therefore, we cannot send any information. Although this approach may sneak by a violation of Special Relativity on a technicality, it still runs head-first into General Relativity. Einsteins theory of General Relativity describes the nature of spacetime. In order to do this, a manifold is setup on which all events must take place. More specifically, events and particles must have a definite location in order for General Relativity to make any sense. Secondly, General Relativity expressly prohibits events which are spacelike separated from having any connections. This incompatibility is what gives rise to one of the many problems encountered when we try to combine General Relativity with Quantum Mechanics.
Where does this leave us? Well, there are two main points which we should take away from this. First, reality is not what it might appear to be. Although we may want to disbelieve Quantum Mechanics because it is too bizzarre, nature seems to come out in favor of it. Secondly, we should focus our attentions not on testing Quantum Mechanics as we have done here, but rather on studying how non-locality and non-separabilty might impact Relativity and our concepts of nature.