## Saturday, November 26, 2005

Feynman's Rainbow 1

On Nov 26, 2005, at 9:00 PM, Jack Sarfatti wrote:

bcc

re:

B = Lp'd'(Goldstone1xGoldstone2x...) = curved part of Einstein-Cartan tetrad 1-form

e.g. n independent Goldstone phases for

V(order parameter) = G(unordered vacuum)/H(ordered vacuum) ~ S1xS1 ... (n times)

nth Homotopy Group(S1xS1x...) ~ Z (or at least not simply the identity group)

"The Greek approach brings with it the full force of the logical machinery of mathematics ... such as Murray's [Gell-Mann] classification of particles. The Babylonian approach allows a certain freedom of imagination ... without worrying about rigor and justification ... In fact, physicists employing this kind of thinking sometimes violate the formal rules of mathematics, or invent strange new (and unproved) math of their own based on their understanding of experimental data ... Feynman considered himself a Babylonian ... Murray was more a Greek" Feynman's Rainbow p. 25
http://www.fotuva.org/feynman/feynman's_rainbow.html

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