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.
He does not start with GR but instead GR emerges as an
effective action
This is why I thought of your work.
Best wishes
Carlos
--- Jack Sarfatti
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
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