Mike Lorrey, <firstname.lastname@example.org>, writes:
> Ah, an excellent point Hal. What geometries would in fact make the
> speed of light the same in all directions? It would seem to me that it
> would only be the same in all directions if every possible point on the
> surface of a cell were equally likely to be in contact with any other
> adjacent cell, therefore we imply the uncertainty principle.....and
> quantum mechanics.
One way you can do this is by redefining the coordinate system on the plane. Map point (x, y) inwards by a factor of sqrt(x^2 + y^2) and you map the square at unit coordinates into a unit circle. This defines a new metric for distance and should make velocities the same in all directions in a CA model. You'd then have to choose a CA so that when rigid macroscopic objects are rotated, they'd automatically change size appropriately based on this new metric. It would be complicated but could be done in theory. I think this is the kind of work which you'd have to do to try to show that our universe could be a CA.
And by the way, even if the universe can be nicely modelled by a CA, it wouldn't mean that someone is running it on their computer. It can be modelled now by differential equations but that doesn't prove that there is an analog computer running it somewhere. The CA model would just be a new and (hopefully) simpler model of the underlying structure of the universe.