## Wednesday, November 23, 2005

On Nov 23, 2005, at 8:29 AM, Jack Sarfatti wrote:

bcc
OK thanks. :-)

Remember, I derive GR from the coherent Goldstone phases of the vacuum order parameter. The basic formula is extremely simple

B = Lpd(Goldstone Phase)

B is non-trivial curved part of the tetrad 1-form.

Lp^2 = hG/c^3

This is analogous to

v = (h/m)Grad(Phase of Pilot Wave)

in Bohm theory and in superfluid theory.

That is, replace the quantum of circulation h/m for the "liquid" by the quantum of "length" for the covariant "supersolid" "metric elastic" (Sakharov) vacuum.

Note that when there are multiple Goldstone phases in the Higgs-Goldstone field vacuum degenerate manifold

V = G(incoherent false vacuum without gravity)/H(coherent vacuum with gravity)

The basic zero form is the product of the independent Goldstone phases.

For example: if

V = G/H ~ S2

there are 2 independent Goldstone Phase Fields THETA & PHI for the geometrodynamic "monopole" stable topological defect from second homotopy group PI(S2) ~ Z

Coherent vacuum 0-form is (THETA)(PHI)

dL = B(S2) = Lpd[(THETA)(PHI)] = Lp[(dTHETA)(PHI) + (THETA)(dPHI)] length operator

dA = LpdB(S2) = Lp^2(dTheta)/\(dPHI) =/= 0 area operator

"Volume-without-volume" = World Hologram = Singular Gauss Theorem

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

is quantized in units of Lp^2(integer) = Lp^2(Sphere Wrapping Number)

from non-trivial second homotopy group ~ Z of V(S2) = G/H

Therefore I TRIVIALLY DERIVE the Bekenstein "Black Hole Thermodynamics" conjecture.

Similarly, the singular form of Gauss's theorem is

Closed surface integral of dA surrounding a point defect in the vacuum order parameter

= Interior volume integral of 'd'dA

This is the Bohm-Aharonov effect for geometrodynamics. That is,

'd'V is the "Volume-without-volume" operator. That is, exactly like in the Bohm-Aharonov effect 'd'V is locally zero, but is globally non-zero.

We are literally Edwin Abbott's "FLATLANDERS" in this theory, i.e. Holographic projections of 2D data.

Forget Loop Quantum Gravity - we don't need it.

Forget "Quantum Foam" - we don't need it and experiment will show it's not there - if I am right here.

'd'V is the holographic projection "image" of the data on dA.

On the other hand, if we have THREE GOLDSTONE PHASES

V(S3) = G/H

Then dV =/= 0 even locally!

On Nov 23, 2005, at 1:42 AM, Carlos Castro wrote:

Dear Jack :

Look at the appendix in hep-th/0203221. Tomboulis
derives
a Gravitational Action from an underlying dynamics
involving fermions.
effective action

This is why I thought of your work.

Best wishes

Carlos

--- Jack Sarfatti wrote:

Thanks.

But what I am doing is different. They assume GR. I
am DERIVING GR
from the Higgs-Goldstone vacuum field. No one has
ever even thought
of that before I mean deriving the tetrad field from
the Goldstone
phases directly.

On Nov 22, 2005, at 1:30 AM, Carlos Castro wrote:

Dear Jack and Tony :

For your interest in Cosmological models building,
....I am attaching a paper based on I.Segal and my
work, where the conformal group, Anti de Sitter,
etc
is very important. The relevant part concerning
my
work is how I derived ( from first princples )
that
the vacuum energy density is the geometric mean
between the Planck and Hubble scale ( ref-[10 ]of
attached paper ).

You may want also to look at Tomboulis paper :
Photons and Gravitons as Goldstone Bosons and the
Cosmological Constant.
hep-th/0203221.

Best wishes

Carlos