Tuesday, December 28, 2004

World Hologram 1

On Dec 28, 2004, at 11:36 AM, Jack Sarfatti wrote:

gu'v'|coordinate = Xu'^u(P)Xv'^v(P)(Minkowski)uv =/= (Minkowski)u'v'

gu'v'|intrinsic = Xu'^u(P)Xv'^v(P)(1/2) Lp^2(Coherent Goldstone Phase)(,u ,v)


Where in my theory

guv = (Minkowski)uv + (1/2) Lp^2(Macro-Quantum Coherent Goldstone Phase)(,u ,v)

where ,u is the ordinary partial derivative in the holonomic coordinate basis.

Note that the separate terms on RHS are not GCT tensors individually only their sum is. Also there is no perturbation theory here. The second term on RHS is not "small" compared to first.

*The intrinsic curved spacetime geometry must obviously originate in the post-inflationary world hologram Macro-Quantum Coherent Goldstone Phase second order partial derivatives.

Note that there are 16 second-order partial derivatives. The mixed partials {01, 02, 03, 12, 13, 23} need not commute when there is a torsion field, but if they do, that leaves 10 independent parameters. There are 64 = 4^3 3rd-order partial derivatives for the connection non-tensor and torsion tensor fields and there are 4^4 = 256 4th-order partials for the tidal curvature subject to constraints that cut that down to 20 in the presence of matter and 10 in the classical /\zpf = 0 non-gravitating non-exotic vacuum with zero dark energy/matter density for the conformal curvature tensor. Also the partial derivatives of the macro-quantum Goldstone phase of the Higgs field may be minimally coupled gauge covariant relative to U(1)xSU(2)xSU(3). Note that the virtual electron-positron PV condensate has U(1)xSU(2) coupling even though the net charge is zero.

A GCT comes from the generating function of a canonical transformation overlap transition function, which is obviously the guv|coordinate piece that Z is looking for.

Chi(x^u,x^u') where x^u and x^u' are two local coordinate charts with common support in a neighborhood of physical event P.

The Jacobian matrix of the GCT at P is

Xu'^u(P) = Lp^2Chi,u'^u(P)

The mixed partials here, one from each chart, obviously DO NOT COMMUTE.


Xu^v'Xv'^w = Kronecker Deltau^w etc.

gu'v'(P) = Xu'^u(P)Xv'^v(P)guv(P)

= Xu'^u(P)Xv'^v(P)[(Minkowski)uv + (1/2) Lp^2(Coherent Goldstone Phase)(,u ,v)]

= (Minkowski)u'v' + (1/2) Lp^2(Coherent Goldstone Phase)(,u' ,v')]

(1/2) Lp^2(Coherent Goldstone Phase)(,u' ,v')

= Xu'^u(P)Xv'^v(P)(Minkowski)uv - (Minkowski)u'v'

+ Xu'^u(P)Xv'^v(P)(1/2) Lp^2(Coherent Goldstone Phase)(,u ,v)]


Coherent Goldstone Phase (x^u') = Coherent Goldstone Phase(x^u) + Chi(x^u,x^u')

Is this consistent?

That is

Xu'^u(P)Xv'^v(P)(Minkowski)uv = gu'v'|coordinate =/= (Minkowski)u'v'

Xu'^u(P)Xv'^v(P)(1/2) Lp^2(Coherent Goldstone Phase)(,u ,v) = gu'v'|intrinsic

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