Unity of Spacetime and Matter
Date: Thursday, December 02, 2004 @ 20:18:39 GMT Topic: Science
Russell E. Rierson writes: Interesting ideas!:
http://www.imath.kiev.ua/~symmetry/Symmetry99/art64.pdf
http://arxiv.org/abs/hepth/0312127
Higher symmetry is analogous to a spinning coin. The coin has two states, heads or tails, but while it is spinning neither state is determined, yet both states exist. The coin is in a state of both/or. When the coin stops spinning, it hits the table and the symmetry is broken as it becomes either heads or tails; the coin enters a lower energy[broken symmetry] state.
Our particular universe appears to have been generated through "symmetry breaking," where the lowerenergy universe becomes frozen out through a series of accidents. That is to say, the elegant symmetry principles specify what sort of dice were rolled to produce our world.
Symmetry and randomness become inseparable, e.g. just as the symmetry between heads and tails is essential to the randomness of a coin toss.
It seems that the NavierStokes equations can also apply to spacetime at the Planck length, in terms of spacetime turbulence?
From the POV of quantum theory, the reason why the linearized Riemannian metric is screwed, becomes quite simple. IT does not take into consideration "violations" of the Lorentz boost at the Planck scale.
It appears that spontaneous symmetry breaking only works for infinite spaces; basically because in a finite[compact] space, there exists a finite probability for the multiplicity of differently oriented wouldbe vacua to tunnel into one another and thus, the true vacuum is a linear superposition of them all. More specifically, any observable transforming a nontrivial entity under the symmetry, retains a zero vacuum expectation value.
It is abundantly clear that for a local theory, the compact space should be harder and harder to distinguish from infinite space, the larger and larger it gets, with the caveat of empirical restriction to experiments for some fixedfinite volume of space, of course. For gauge boson mass generation via the Higgs mechanism, one requires a compact space, where the Higgs vacuum expectation value vanishes, and hence, the gauge boson mass must apparently vanish also. Much to our chagrin, gauge bosons should acquire, or appear to acquire mass, only at the infinite limit.
Alas, the escape route, out of this dilemma would be to realize the true nonlinear aspect of the symmetry.

