Dear Kory and Hal,
Kory's idea strongly reminds me of the basic idea explored by John Cramer in his "Interactional" interpretation in that it takes into account both past and future states. Please see:
One thing you might wish to bear in mind is that David Deutsch has pointed out that Cramer's idea is equivalent to the Many worlds interpretation, but I can not find the exact quote at this time. ;-)
The main problem that I have with any CA based model is that it explicity requires some from of absolute synchronicity of the shift functions of the cells. I see this as a disallowance of CA based models to guide us into our questions about the appearence of a "flow of time", it assumes a form of Newton's "Absolute time" from the onset!
Only if you think of a physical implementation of a CA, which is what people here try to avoid (I think).
In addition, it has been pointed out be several CA experts that CAs are equivalent to universal Turing Machines and if UTMs are incapable of deriving QM and its phenomena then neither can CAs.
Just to be clear (because your term "deriving" is a little ambiguous), but UTM
can emulate (perfectly simulate) any quantum piece of matter including
quantum computer (just dovetail on the superpositions). This entails an
exponential slow down, but as we search to define time from inside this is not
a problem. As I say in my other post, the real problem is the apparent computability
of matter/physical processes. Newton physics would not have been falsified I would have
pretend having find a refutation of comp, for comp makes reality much weirder than