What's The Big Deal?
Origin of Arrow of Time simply explained below.
Nick Cook of Jane's Defence Weekly in "The Hunt for Zero Point" mentions a torsion field as a possible explanation for the alleged Nazi "Time Machine" experiment of Victor Schauberger in the final days of WWII. This is of interest because Nick also says that Schauberger's work influenced Podkletnov's work that was apparently also tested by Tony Robertson of NASA/STAIF?
Hammond has a nice historical discussion of torsion fields as a gauge force theory. The fact is that you get a theory of gravity as space-time curvature from matter stress-energy density currents (4 translation parameters), and torsion from quantum spin and orbital rotational currents (3 space rotations + 3 Lorentz boosts or space-time rotations).
This excludes the 4 special conformal translations and the dilation that will give more "force" fields in addition to curvature and torsion. I use "force" loosely since the "geometrodynamic" view eliminates force. We can use either depending on what level we are talking. For example, the curvature field derives ultimately from the Kleinert elastic world crystal lattice distortion field that comes from the "More is different" (P.W. Anderson) macro-quantum coherent hologram phase of the virtual electron-positron PV condensate. Einstein's metric field is the "spin 2" elastic strain tensor of the Kleinert spin 1 compensating gauge force field from locally gauging the 4 space-time translations infinitesimally generated by the total energy-momentum 4-vector Pu. The curvature field comes from 1-dim string topological defects in the spin 0 scalar PV condensate corresponding to disclination defects in the world crystal lattice spacing Lp* that is a scale-dependent variable. Although the electron is a 4-component Dirac spinor field, the PV condensate is a spin 0 scalar macro-quantum order parameter from a BCS pairing of two spinor fields. A spin 1 vector order parameter is also conceivable with new classes of topological defects. The additional torsion field corresponds to dislocation defects in the scalar order parameter. These defects are phase singular strings on which the order parameter vanishes like in the core of a vortex in a superfluid. Andrei Sakharov's "metric elasticity" for emergent smooth c-number ODLRO Einstein gravity corresponds to P.W. Anderson's "More is different" "generalized phase rigidity" (basis for "world hologram" of Lenny Susskind), and to inverse of Ed Witten's string tension alpha'^-1 and the "quantum of area" Lp*^2 of non-perturbative Loop Gravity.
G*/c^4 ~ (G*h/c^3)(hc)^-1 = Lp*^2/hc = alpha'/hc = (String Tension)^-1 = (Phase Rigidity)^-1 = (Metric Elasticity)
The world hologram entropy of a 3D region of space with bounding area A is S/k ~ A/4Lp*^2 (k = Boltzmann's constant)
For the expanding FRW universe with scale factor R(t) (in units of length)
Lp* = Lp^2/3R(t)^1/3
The thermodynamic entropy of the Universe is therefore,
S(Universe)/k ~ R(t)^2 /4Lp^4/3R(t)^2/3 ~ R(t)^4/3
This explains the Arrow of Time of the Second Law of Thermodynamics in terms of the spatial expansion of the Universe and it also explains why the entropy of the Universe is zero at the Big Bang because R(0) = 0. What's the Big Deal?
The effects of the extra dimensions of hyperspace is to promote Newton's G from a constant to a renormalization group flow scale-dependent running coupling parameter G*(s) at scale s in the sense of the continuous wavelet transform generalization of Wigner's phase space density and Green's function propagators based on the rigid Fourier transform.
On May 29, 2004, at 12:43 PM, Jack Sarfatti wrote:
A: No. So we eliminate that.
Equation (28) p. 604 of Richard Hammond's "Torsion Gravity" Rep Prog Phys 65 (2002) is interesting. It is, for a metric theory with zero non-metricity tensor, but with torsion S
R = Ro + 4(S^u;u - S^uSu) + SuvwS^u^v^w - 2SuvwS^v^w^u
Where ; is covariant derivative with respect to only the 1916 symmetric Levi-Civita connection for parallel transport of tensor fields in the curved-torsioned space-time.
In the ordinary non-gravitating vacuum Ro i.e. the zero torsion Ricci curvature scalar vanishes.
That leaves for the exotic vacuum field equation
Ruv + 4(S^u;u - S^uSu) + SuvwS^u^v^w - 2SuvwS^v^w^u = 0
4(S^u;u - S^uSu) + SuvwS^u^v^w - 2SuvwS^v^w^u = /\zpfguv
Could we interpret the torsion field as a cosmological field. This does not seem like a good idea. Since the torsion field comes from locally gauging the Lorentz group, it is a classical field with no necessary connection to zero point energy density.