Friday, April 27, 2007

Ed Witten & Lenny Susskind lament on absence of an "organizing idea" for M Theory (equivalence principle was the organizing idea for Einstein's 1915 GR). They need lament no more - it's the same organizing idea!

There has been a recent flurry in letters in Physics Today - a bit odd in that Weinberg seems unfamiliar with Hehl's work, yet Hehl gave famous lectures on torsion theory at Institute of Advanced Study in Princeton published in Rev. Mod. Phys. 1976.

Hehl lectures on Einstein's GR as a limiting case of a local Poincare group theory. Utiyama's & Kibble's work on that done in ~ 1961. However, Hehl makes IMHO the incorrect assumption that the torsion field is generated only by the micro-quantum spins hence it does not propagate as a far field wave. Richard Hammond has shown that this assumption is not necessary and indeed there is experimental evidence against it. The coupling should be to the total 4D angular momentum field tensor of all sources including orbital (for 3D part) both real and virtual - the latter includes IMHO both repulsive dark energy and attractive dark matter as negative and positive quantum pressure exotic vacuum phases respectively of a quintessent /\zpf locally variable microscopic -> macroscopic field.

96% of our possibly pocket Hubble bubble universe on the overpopulated cosmic landscape of eternal chaotic inflation (self-created Gott-Li?) is random incoherent off-shell virtual quanta acting as the external "wood" source pump of the "marble" Higgs-Goldstone coherent vacuum condensate field whose Goldstone phase(s) modulation is the smooth c-number emergent warped Einstein-Cartan fabric of spacetime. The Calabi-Yau extra-dimensions are from the 6 "angle parameters" from locally gauging the Lorentz-group whose implied full 4D rotation tensor is the torsion source in the same way that the full 4D translational group's implied "matter" stress-energy tensor is the curvature source. Why only choose the quantum spins of on-shell quanta in the former?

That all non-gravity fields, both real and virtual, participate as sources is part of the equivalence principle.

To be a bit more precise

The 4-parameter translational group's Lie algebra of "observable charges" forms the global total energy-momentum 4-vector of all the source fields. These global integrals are over local stress-energy tensors of the non-gravity fields whose dynamical actions are gauge invariant with respect to the localized Poincare group where curvature and torsion are derived from more fundamental compensating gauge potentials at the square root tetrad + spin connection Cartan 1-form "substratum" level. Supersymmetry is natural in the substratum as is the coupling to spinor field sources. Difficulties in properly defining the integrals at the derived quadratic geometrodynamical level and in trying to include the gravity field itself requiring asymptotic flatness are not relevant to the more fundamental point here. As Penrose et-al point out the pure gravity vacuum field does not have a local self-source stress-energy tensor even though there is total energy-momentum in the vacuum gravity field.

Similarly, the 6-parameter space-time translation group is generated by integrals of the 4D rotational source field tensors of all the non-gravity fields. These 6 parameters are the dimensions of the local Calabi-Yau fiber.

J = L + S

S = quantum spin

L = orbital angular momentum

is only for the 3 space rotations of the Lorentz group's Lie algebra. Hehl, oddly only takes S as the source of the torsion field. This is not even a covariant choice IMHO.

In addition there are the 3 boosts (spacetime rotations) that will contribute to the torsion field.

Gennady Shipov has the germ of this idea in his concept of the "oriented point" needing 2 metrics 4D translation and 6D rotational - the latter years before string theory's construct of the Calabi-Yau fiber space.

The Calabi-Yau space fiber is compactified in a anisotropic way in general so that the above simple spheres look more like

But the idea is clearly similar. Shipov had years before M theory was a glimmer in Witten's eye.

The Kaluza-Klein radii are Ri i = 1 ... 6

Kaluza-Klein charges are ei ~ G*^1/2h/cRi

G* is running gravity coupling constant of the secondary spin-2 geometrodynamic field.

Note that the renormalizable spin-1 vector tetrad fields have dimensionless couplings

(G*h/\zpf/c^3)^1/2 for each vertex in the Feynman diagrams where /\zpf is the quintessent field -> Einstein's cosmological constant in large space scale limit.

The reciprocal of this is the Bekenstein BIT number of deSitter future horizons i.e.

Wheeler's IT FROM BIT

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