Mike Lorrey, <mike@lorrey.com>, 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.
Hal