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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.

Chris Hillman

Home Page: http://www.math.washington.edu/~hillman/personal.html"

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