Saturday, February 19, 2005

Space-Time Warps & Theory of Everything

All dynamical force fields (and geometrodynamic “force-without-force”) fields come from locally gauging a global symmetry of the dynamical action. The initially dynamically broken global symmetry is restored by the compensating gauge field. Any preferred frame is an emergent SBS effect in the lowest energy state that leaves the dynamical symmetry intact. Curvature and torsion in the Einstein-Cartan “tetrad”/”Ricci rotation coefficients” extension of 1916 general relativity (GR) are analogous to string vortex lines in superfluid helium. In 1916 GR the Ricci rotation coefficients Au^bc are not independent dynamical fields, but are dynamically determined from the non-trivial anholonomic tetrads bu^a that are the compensating gauge fields from locally gauging T4 into Diff(4) (AKA GCT) because O(1,3) is not yet locally gauged as it is in Shipov’s theory. There is a curious cross-play in that the disclination-curvature strings are characterized by rotations of a vector parallel transported around a closed loop, whilst the dislocation-torsion strings are gaps in second order in the attempt to close the loop. Roger Penrose shows that gaps in third order appear even in torsion-free 1916 GR. The curious cross-play is that the curvature disclination rotations about closed loops come from the local-gauging of the translational group T4 of special relativity generated by total energy-momentum Pu, whilst the torsion dislocation gaps come from the local-gauging of the Lorentz group O(1,3) of special relativity generated from the spin-orbital angular momentum J = L + S (space-space rotations) and the boosts connecting coincident inertial frames in instantaneously uniform relative motion. The curious cross-play is this dual switching between T4 locally gauged to Diff(4), and O(1,3). The lack of preferred space-time frames with “absolute velocity”, as in the usual interpretation of the Michelson-Morley experiment, means that the vacuum symmetry is not spontaneously broken with respect to the boost sector of O(1,3). If there is such a broken symmetry then a particular “rapidity” (direction in4D space-time) of “absolute rest” is selected in a finite space-time domain, much like a particular 3D space direction is selected in a ferromagnetic domain. Cahill and Consoli have challenged this assumption in independent papers, which, however, are not consistent with each other. It’s too soon to know if there is any merit to these empirical claims, but if there is, their proper explanation is “More is different” spontaneous broken symmetry (SBR), this time in the off-mass-shell macro-quantum coherent vacuum relative to O(1,3) and possibly Diff(4) rather than the on-mass-shell macro-quantum coherent ground states of equilibrium superfluids (U(1)), ferromagnets (O(3)) and non-equilbrium lasers (U(1)) and living bio-membranes as in H. Frohlich's theory. (U(1)).

Bu = bu^aPa = (Goldstone Hologram Phase of Higgs Ocean),u

{Pa} = Lie algebra of T4

guv(Einstein LNIF) = (&u^a + bu^a)(Minkowski LIF)ab(&v^b + bv^b)

&u^a are the trivial holonomic tetrads (Kronecker deltas) connecting the curved base space to the quasi-flat tangent space fiber.

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