Re: tech: digital physics
Mon, 10 May 1999 18:33:09 -0700

Eugene Leitl apparently wrote:

> I'm exstatic. They have a mailing list. They have a bibliography.
> This is how I found this gem here:
> The origin of the universal speed limit

I am reading this CA paper, and I have a couple of concerns about it.

The main claim of deriving special relativity from CA theory is in section 9. They say:

: Special Relativity theory is founded on two basic postulates:
: (1) The velocity of light in a vacuum is constant and is equal for all
: observers in inertial frames (inertial frame is one in which Newton?s
: law of inertia is obeyed).
: (2) The laws of physics are equally valid in all inertial reference
: frames.

which is OK. But they claim that there is no explanation of why (1) is true in terms of (2). Actually from what I understand (1) follows from (2). The Maxwell equations for electromagnetism predict the existence of EM waves which travel at a speed determined by various properties of the vacuum. If you measure those properties the speed works out to c, the speed of light. Hence Maxwell's equations predict that light propagates at a speed of c. If you assume (2) then it will propagate at c in all inertial frames, hence (1) follows.

Now, here is their explanation for (2) in terms of the universe as a CA:

: The second postulate of special relativity states that the laws of
: physics are equally valid in all inertial reference frames. Stated
: in a weaker form, there are no preferred reference frames to judge
: absolute constant velocity motion (or inertial frames). This latter
: form is easily explained in CA theory, by remembering that all cells
: and their corresponding rules in the cellular automata are absolutely
: identical everywhere. Motion itself is an illusion, and really represents
: information transfers from cell to cell. To assign meaning to motion
: in a CA, one must relate information pattern flows from one numeric
: pattern group with respect to another group (the actual cell locations
: are inaccessible to experiment). Therefore, motion requires reference
: frames. Unless you have access to the absolute location of the cells,
: all motion remains relative in CA theory. In other words, there is no
: reference frame accessible by experiment that can be considered as the
: absolute reference frame for constant velocity motion.

This is so vague as to be meaningless. There is no reference to any properties of the CA other than that it can let patterns "flow" from place to place (somewhat like gliders in Conway's Life). Does it really follow from this very general property that the laws of physics would be the same in all reference frames? Just because patterns can flow, it follows that absolute velocity can't be detected, and that physics is the same for all uniform observers? I don't think so.

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.