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Delayed determinism



Because this model breaks most of the symmetries of the linear finite difference equation the classical conservation laws are not enforced at the local level. There can be a small discrepancy at any single point and these discrepancies can accumulate in a statistically predictable way. However discreteness and absolute time symmetry combine to create a new class of conservation laws. The information that enforces them does not exist at any given point in space or time and cannot be determined by a classical space time integral. Instead it is embedded in the detailed structure of the state and insures that the same or similar sequence of states will be repeated. The local violations of the conservation laws can never accumulate in a way that would produce irreversible events.

Information throughout the light cone of a transformation puts constraints on what stable states may result. A system may start to converge to two or more stable states but none of these convergences will complete unless one of them is consistent with the conservation laws. The time of the focal point of this process (for example the time when a particle interacts with a detector) and the time when the event is determined, i.e. cannot reverse itself are not the same thing. Since all interactions are reversible in this model the time when an event completes has no absolute meaning. It can only be defined statistically, i.e., the time when the probability that the event will be reversed is less than some limit. Quantum mechanics, because it does not model events objectively, cannot be used to compute the probability that an event will be reversed. We must use classical statistical mechanics. As a practical matter we probably need to limit timings to macroscopic measurements where the probability of the measurement being reversed is negligible. In the model we propose statistically irreversible macroscopic events are determined by many reversible microscopic events, i.e. the nonlinear transformations of the wave function. It is important to recognize that use of classical statistical mechanics to define the occurrence of events implies that quantum mechanics is an incomplete theory. It is an assumption consistent with the broad class of theories in which there are objective microscopic events or processes that contribute to create macroscopic events.

The distribution of the information that enforces the conservation laws is not modeled by any accepted theory and is not limited by the dispersion of the wave function for the individual particles. This information may be distributed throughout the entire experimental apparatus including both the particle source and the detectors. When quantum entanglement was first discovered there was some thought that it would disappear once the wave function for the entangled particles were spatially separated[18,7,9,8]. Aspect's earlier experiments[2] tested this. These results indicate that quantum entanglement is not limited by the spatial dispersion of the wave function. In a model like the one we are suggesting the linear evolution of the wave function is only part and by far the simplest part of the picture. Information that enforces the conservation laws through quantum entanglement may evolve in ways that are not remotely close to linear wave function evolution. The only reliable measure of nonlocal quantum entanglement is with direct macroscopic measurements of time.

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