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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