> Light, in their model, is a disturbance propagating at the maximum
> speed of one cell per tick in the CA. And in fact CA workers often
> do refer to one cell per tick as "the speed of light" by analogy to
> relativity theory. In section 9.3 the authors attempt to show that
> all uniformly moving observers will measure the speed of light to be
> the same in all directions. But again I didn't find the argument clear
> or persuasive. For one thing, it would seem that the geometry of the
> CA array should be relevant. In a three dimensional cubic geometry CA
> (which they choose without discussing other polyhedral geometries),
> disturbances can propagate faster in the diagonal direction than along
> the axes. Living in such a CA would seem to give a set of preferred
> directions. They don't seem to discuss this effect. They don't have
> a clear definition of how clocks and rulers would be expected to work,
> making it hard to interpret their explanations of what people would see.
> Overall I can't help feeling that they have jumped past the hard parts
> with some handwaving and vague arguments. If the universe is a CA, it
> would seem that there ought to be some constraints on the properties it
> would have. Their arguments would apply to virtually any CA, and that
> can't be right.
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.