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It has often been suggested that quantum mechanical experiments produce results that are inconsistent with classical notions of causality. Bell has proven this is true of the mathematics of quantum mechanics but the issue is still an open one with regard to nature. I believe the problem is not with classical ideas of causality or mathematics but with the conceptual framework with which we view experimental results. It is important to deal with this issue explicitly because it is not possible to fully understand the class of models I propose unless one can think about them in an unconventional conceptual framework.
Consider our inability to simultaneously determine a definite position and momentum for a particle. This result is mathematically related to our inability to simultaneously fix a position and frequency for a classical wave. The only wave that has an exact position is an impulse and that is an integral over all frequencies. We do not think that this implies any breakdown in classical notions of causality. The behavior of a classical wave is completely determined just as the behavior of the quantum mechanical wave function is completely determined.
If point like particles do not exist, it makes no more sense to speak of their position than it does to speak of the position of a classical wave. If what we observe as position is the focal point of a nonlinear transformation of the wave function then position is a property of this transformation or interaction and not a property of the particle itself. If these transformations result from a process of converging to a stable state consistent with the conservation laws then the information that determines the detailed characteristics of this transformation may be spread out over a substantial region of space and may propagate in ways that are outside of any accepted theory.
Once two particles interact subsequent observations of one particle puts constraints on observations of the other even after the particles and their wave functions have become separated. It is quantum entanglement in the mathematics of quantum mechanics that is responsible for violations of Bell's inequality and it is the experimental phenomenon of quantum entanglement that makes nature appear to be inconsistent with classical causality.
The energy and momentum in a classical wave is distributed throughout the spatial region occupied by the wave. If two classical waves overlap physically there is no clear way to distribute the energy or momentum at a particular point between the two waves. Once the two wave functions for particles in a multi-particle system become entangled how do they become disentangled? The wave function in the existing theory is of limited help if it only represents the average or statistical behavior of the wave function. If observations of the particles involve convergence to a stable state consistent with the conservation laws the the detailed behavior of the physical wave function is dramatically different from and far more complex than its average or statistical behavior in the existing model. Certainly `disentanglement' will occur if the wave functions of two particles become sufficiently separated. At short distances tests of Bell's inequality will reveal time delays that allow the correlations to be determined by information that propagates locally. At sufficiently great distances the correlations will revert to those consistent with a local hidden variables model. It will appear as if the entangled system collapsed spontaneously into two independent systems. This difference between the existing theory and the class of models I suggest is not limited to Bell's inequality. Perhaps there are experimental tests of quantum entanglement that can more easily be conducted over large distances to discriminate between these alternative theories.
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