"Eliezer S. Yudkowsky" <sentience@pobox.com> writes:
> It seems to me that all CAs (cellular automata) are inherently
> incompatible with the spirit of Special Relativity, at least in the
> current formalism. CAs have what we might call a One True Space of
> Simultaneity, the prohibition of which was the entire point of having
> Special Relativity in the first place.
Not really, I have the strong impression that what Einstein wanted was the frame independence of physical laws, not to say anything about space and simultaneity (which was the implications of the basic postulates). If the physical laws behave different in one frame than the others then relativity doesn't hold, but there could be a frame that is special in some sense (like the CA "rest" frame) but this special property cannot be detected from the inside of the world.
> Maybe you could alter the formalism to fix that. Frankly, I don't think
> so. CAs separate space and time into neat little independent Newtonian
> coordinates. I don't see how you can have one objectively correct
> universal separation into discrete cells and not have neat little
> Newtonian coordinates. In Special Relativity spacetime is continuous,
> and the transformation of some axis from space into time is also continuous.
You could have a different grid, like a hyperbolic one where the CA time does not correspond to the physical time. The cells would have a connectivity that is not as simple as in ordinary euclidean CAs.
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