Eliezer S. Yudkowsky, <email@example.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. The whole problem with CAs, that
> the speed of light will appear different to different observers, derives
> from the fact that there are absolute positions (the cells) and thus
> absolute velocities.
That's a good point. There are a couple of ways out, though. The first is to say that there *is* an absolute frame of space and time, but that Lorentz transformations govern the relationships between moving coordinate frames. If you do this then it follows that the speed of light is the same in all frames and that the absolute frame can't be distinguished from other frames. Technically they didn't need to reject the luminiferous ether to accommodate the Michelson Morley experiment. But the ether, or any absolute frame, becomes undetectable and so is philosophically unattractive. As you say, it is counter to the spirit of SR even if perhaps technically compatible with the equations.
In that paper, http://xxx.lanl.gov/html/physics/9810010, the authors emphasized the one aspect in which CAs are entirely compatible with relativity, which is that they are inherently local. The authors then claimed to have a way to show that the speed of light would be the same in all moving frames in their CA model, but I think they were just talking through their hats. (I'm surprised that a paper like this was published in what I have found in the past to be a very reliable forum, the LANL physics archive.)
> 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.
I learned SR from the book I recommended earlier, Spacetime Physics, and that book is permeated with the philosophical view that spacetime is primary, that space and time are just different angles on the underlying reality of spacetime. (I mean this quite literally, different angles in hyperbolic geometry.)
It does seem that the separation of space and time is inherent to the CA model. You could set up a four-dimensional CA array which might represent spacetime in some sense, but then what would it mean for the CA to evolve? You've already incorporated what we call "time" in the four dimensional CA. It just doesn't fit.
> One might say that Special Relativity says that "real" things occupy a
> continuum between rules and data, while in Turing machines things are
> separated into rules and data. Another of the many reasons to
> best-guess that the physical Universe is noncomputable. And also a
> rationale for Power-class technologies like Greg Bear's "descriptor
> theory", or being able to change the laws of physics: I think we'll
> find that there's no rigid distinction between substance, law, and
> metalaw, and that all three can be changed. Well, now I'm getting
> Eganic, so I better sign off.
I wouldn't go this far. I view relativity as being a concrete and really rather prosaic theory, just one which does not map too well to our mental models. It is a problem with our minds, though, not a problem with reality. You have spacetime, you have matter, and you have rules for how they influence each other. Our conventional philosophical views of the nature of reality are compatible with relativity, just not our specific intuitions about how space and time behave.