From: hal@rain.org
Date: Sun May 16 1999 - 16:14:41 MDT
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. 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.
Hal
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