Ripped from sci.physics.relativity 5/27/00
"Sure it exists, island--- we are talking about it! :-)
You (or were you just quoting someone else?) meant to say that the
principle of relativity is (presumably) an idealization.
In particular, those on the trail of the elusive quantum theory of gravity
mostly now agree that "time" is an illusion arising in the classical
approximation, and that on sufficiently small scales, "spacetime" begins
to look like a multiply connected "foam", and on still smaller scales,
consists of discrete (quantized) area elements having a purely
combinatorial relationship to one another. In the elegant "spin foam"
approach, spacetimes are objects in a category whose objects are arrows
"transforming" something like a Feynman diagram into a new diagram. The
great thing about this is that one can hope to make Feynman's notion of a
path integral rigorous, by passing from integrals over enormous spaces of
paths to sums over combinatorial relationships. Much remains to be done
to even lay the mathematical foundations for this approach to quantum
gravity, but this approach does have the attractive feature that it is
sufficiently general that it should apply to all other approaches. Thus,
it is more likely than anything else which people are working on right now
to play a role in the ultimate theory (perhaps much modified, probably in
the direction of still greater mathematical sophistication, which
ultimately means simplification).
At any rate, the point is that "everyone knows" that Lorentz covariance
may turn out to be merely an illusion which arises in the classical
approximation. The details of how this happen must explain why the
standard model of particle physics (which is set up in the "arena" of the
Minkowski vacuum) works so well, and why gtr works so well, in order for
the quantum theory of gravity (and everything else) to be acceptable. To
a surprising degree, it is already well understood how this should happen,
at least in the context of well understood "toy models" which are
presumably similar in some respects to the full quantum theory of gravity.
Home Page: http://www.math.washington.edu/~hillman/personal.html"
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