http://amazon.com SUPER COSMOS

http://en.wikipedia.org/wiki/J._Richard_Gott


Some formal additional details.

Basic rule is to put an Lp factor with each d since [d] = 1/Length

Lpd is dimensionless.

Below I took Lp = 1 for simplicity i.e. everything measured relative to Lp

Lp^2 = hG/c^3 = quantum of area

For the S2 vacuum manifold at the Planck time with 2 independent
Goldstone phases describing linearly independent displacements of the
vacuum order parameter in G/H fiber space at a fixed space-time event x

B = Lpd(ThetaPhi) = (LpdTheta)Phi + Theta(LpdPhi)

Note I do not shift the position of Theta & dPhi as Robert Israel
suggests. That ad hoc formal rule is clearly inappropriate to the
physics. dTheta & dPhi correspond to two orthogonal displacements in G/H
fiber space, therefore dTheta/\dPhi is a sensible angular area element
in G/H.

Indeed, dB = 2Lp^2(dTheta)/\(dPhi) is the geometrodynamic AREA FLUX DENSITY

B is the local frame invariant

B = Bu^Jdx^u&J

Where the Einstein-Cartan tetrad is

eu^J = Iu^J + Bu^J

Einstein's geometrodynamic field is then

guv = eu^J(Minkowski)JKev^K

ds^2 = guvdx^udx^v local scalar invariant (no "/\" there of course)

Note that

C = dB = Cuvdx^u/\dx^v = Cuv^Jdx^u/\dx^v&J

The holographic quantization of area is that the global flux integral of
the 2-form area flux density C around a NON-BOUNDING 2-cycle surrounding
a point (neutral gravity) monopole defect in the Higgs field vacuum
coherence is quantized as

IntegerLp^2

Integer is the "wrapping number" around the surrounding closed surface
that has no boundary but is, itself, not a boundary of the interior
volume, from

Second Homotopy Group of S2 in 3D base space = Z

Now cosmologically the non-bounding closed surface is a space-like slice
of the future light cone of any point event in the Planck scale vacuum
phase transition. If our detector is inside the future light cone, then
we are under the causal influence of that initial point event. This is
the WEAK holographic principle.

One can also imagine that at the Planck scale the "quantum foam" is full
of these STABLE point topological defects (uncharged gravity monopoles)
like the holes in a sponge. This gives the STRONG holographic principle
that the information content of any local interior volume is completely
determined by its non-bounding closed surface. Each geometrodynamical
degree of freedom then occupies area Lp^2. For now we ignore possible
changes in Lp^2 from hyperspace large dimensions.

On Dec 9, 2005, at 12:30 AM, Jack Sarfatti wrote:
Imagine that the first Planck scale vacuum symmetry breaking at ~ 10^-44
seconds has the stable point monopole topological defect with vacuum
manifold (this is not a magnetic monopole of the EM field, but, rather,
a geometrodynamic monopole.

V(Planck) = G(false unordered vacuum)/H(ordered vacuum) = S2

i.e. Second Homotopy Group PI(S2) = Z

the integers are 2D "wrapping numbers" around a sphere surrounding the
point defect in physical based space rather than 1D winding numbers
around a circle surrounding the line defect in physical base space when
First Homotopy Group PI(S1) = Z.

The discrete wrapping numbers come from the single-valuedness of the
local macro-quantum vacuum coherent order parameter of the inflating
emergent curved space-time universe shown in the picture below from
Richard Gott III. Gott ist Gut! ;-)

These are obviously the Hawking-Beckenstein BITS that is a trivial
result from the generic Higgs field vacuum coherent order parameter if
the order parameter manifold is S2.

Note that these surrounding surfaces in physical 3D space are cycles
that do not bound of dim 2 & 1 respectively.

The vacuum manifold S2 in fiber space, coincidently has an S2
surrounding surface of the point defect in physical 3D space.

The macro-quantum vacuum coherence order parameter is LOCAL and this
explains how local curved space-time emerges from the nonlocal quantum
substratum. There is also an entropy drop here. However, Richard Gott
and Li-Xin-Li explain the low entropy of early self-creating universe as
a Planck scale time-loop CTC in which only retarded photons having
redshifts in the inflating universe can give a stable globally
self-consistent curved vacuum.

pastedGraphic.jpg

The red arrows are the retarded zero rest mass photons getting
redshifted. The inflation starts in the white neck part where G - H.

http://www.sns.ias.edu/~dejan/CCS/wo...t.III.eng.html

OK the Second Law of Thermodynamics is explained by globally
self-consistent time travel to the past in the sense of Igor Novikov's
idea (that I got independently years before I knew of Novikov's view).

How about the 't Hooft-Susskind hologram?

Again assuming V(Planck 10^-44 sec) = S2

from below

Next consider an S2 fiber. This has TWO functionally-independent
"orthogonal" Goldstone phases Theta(x) and Phi(x), i.e. 3 real scalar
fields where

tan(Theta) = phi(x)1/phi(x)2

tan(Phi) = phi(x)2/phi(x)3

Note the tangent of the angle from phi(x)1/phi(x)3 is not independent of
the first 2 because sum of squares of direction cosines add to 1.

Physically the two angles polar and azimuthal describe linearly
independent displacements in 3D fiber space.

Define the 0-form Theta(x)Phi(x)

The exterior derivative d on a 0-form is like a gradient operator in
base (x) space. The sphere S^2 is a fiber at each point x in base space.

The exact 1-form is

B = d(ThetaPhi) = (dTheta)Phi + Theta(dPhi)

The non-vanishing 2-form is

C = dB = 2d(Theta)/\d(Phi) =/= 0

Because d(Theta) is not "parallel" to d(Phi)

This is an angular area element in vacuum manifold fiber space not
physical space.

Of course dC = 0

The non-closed exact 1-form B is essentially the curved part of the
Einstein-Cartan tetrad field that is roughly the square root of
Einstein's metric tensor field.

It's non-vanishing 2-form is the geometrodynamic flux density analogous
to the magnetic flux density.

B is also the compensating potential in the local gauging of the
translation T4 group as well as emergent from the S2 internal symmetry
breaking at the initial Planck phase transition.

Simply use the Bohm-Aharonov singular extension of Gauss's theorem

The integral of the 2-form C around the closed nonbounding surface is
equal to the integral of dC in the interior volume. Even though dC = 0
locally and near the surface nevertheless the global integral is
quantized. This is basically the World Hologram that all the physics of
the interior is coded on the surrounding surface of the point defect
that defines the Planck scale vacuum phase transition.

That the 3-form dC = 0 locally is analogous to the Bohm-Aharonov effect
where the 2-form dA = 0 on the path of the electrons where A is the EM
1-form potential. The electrodynamic case is for an S1 fiber. In
contrast the geometrodynamic case is for an S2 vacuum manifold fiber. In
other words the World Hologram is the Bohm-Aharonov effect for the
geometrodynamic field with a point (neutral) gravity monopole defect in
the initial Planck-scale Higgs field.

On Dec 8, 2005, at 11:15 PM, Jack Sarfatti wrote:

On further thought:

On Dec 8, 2005, at 10:49 PM, Jack Sarfatti wrote:

On Dec 8, 2005, at 10:26 PM, Robert Israel wrote:

Note, by the way, that if B = d(Theta Phi) = Theta dPhi + Phi dTheta,
then dB = dTheta /\ dPhi + dPhi /\ dTheta = 0, not 2 dTheta /\ dPhi.

On Dec 8, 2005, at 10:49 PM, Jack Sarfatti wrote:

Why did you reverse the order? What rule makes you do that?


That's not what I wrote, I wrote below:

B = d(Theta Phi) = (dTheta)Phi + (Theta)dPhi

dB = (d^2Theta)Phi + (dTheta)/\(dPhi) + (dTheta)/\(dPhi) + (Theta)(d^2Phi)

= 2(dTheta)/\(dPhi)

Unless you simply ad hoc impose the additional axiom?

B = d(Theta Phi) = Theta dPhi + Phi dTheta

which seems artificial.


On Dec 8, 2005, at 10:05 PM, Jack Sarfatti wrote:

For spontaneous symmetry breakdown of the ground state of a system
described by one real scalar field order parameter, phi(x)1 the vacuum
manifold G/H in a renormalizable quartic potential has the topology S0
with only 2 possible discrete values of the Goldstone phase 0 or pi.

The topological defect there where the order parameter vanishes is a 2D
domain wall in physical 3-space.

Dim(Vacuum Manifold) + Dim( Stable Topological Defect in Physical Space)
+ 1 = Dim of Physical space

0 + 2 + 1 = 3

For two real scalar fields the single Goldstone phase describes a vacuum
manifold with the topology of the circle S1. Dim of the topological
defect in physical space is the 1-D string.

1 + 1 + 1 = 3


For three real scalar fields with two independent Goldstone phases, the
vacuum manifold has dim 2, the topological defect has dim 0, i.e. a
point monopole.


2 + 0 + 1 = 3


The effective quartic "Mexican Hat" potential here is

V = a(phi1^2 + phi2^2 + phi3^2) + b(phi1^2 + phi2^2 + phi3^2)^2

The degenerate minima of V is a sphere S2 of radius eta, where

eta^2 = phi1^2 + phi2^2 + phi3^2

The direction cosines in the vacuum manifold fiber space are, at fixed x
in base space

phii/eta

dV/dphij = 0

d^2V/dphij^2 0

One can generalize this to include anisotropies in fiber space. What
happens then?

Obviously S2 - S1 - S0 in fiber vacuum manifold order parameter space.

i.e. topological defects in physical space go from point to line to
surface. That is from monopole to vortex to domain wall.

Corrected 3rd Draft
On Dec 8, 2005, at 9:32 PM, Jack Sarfatti wrote:


On Dec 8, 2005, at 7:31 PM, Jack Sarfatti wrote:

The standard lore is all exact forms are closed.

I suggest that this theorem is not true in general, but is true only in
a special case.


Formally,

B = dA

B is exact

dB = d^2A = 0

B is closed

because

d^2 = 0

these are all local statements

OK, consider a circle fiber S1 over a base space in a fiber bundle.

S1 has a Goldstone phase Theta that is the 0-form Theta(x) where x is in
the base space.

You can think instead of 2 real scalar fields phi(x)j where

tan(Theta) = phi(x)1/phi(x)2

In this case all exact forms are closed as everyone takes for granted.

That is

A = Theta

B = dTheta

dB = d^2Theta = 0 locally

Next consider an S2 fiber. This has TWO functionally-independent
"orthogonal" Goldstone phases Theta(x) and Phi(x), i.e. 3 real scalar
fields where

tan(Theta) = phi(x)1/phi(x)2

tan(Phi) = phi(x)2/phi(x)3

Note the tangent of the angle from phi(x)1/phi(x)3 is not independent of
the first 2 because sum of squares of direction cosines add to 1.

Physically the two angles polar and azimuthal describe linearly
independent displacements in 3D fiber space.

Define the 0-form Theta(x)Phi(x)

The exterior derivative d on a 0-form is like a gradient operator in
base (x) space. The sphere S^2 is a fiber at each point x in base space.

The exact 1-form is

B = d(ThetaPhi) = (dTheta)Phi + Theta(dPhi)

The non-vanishing 2-form is

C = dB = 2d(Theta)/\d(Phi) =/= 0

Because d(Theta) is not "parallel" to d(Phi)

This is an angular area element in vacuum manifold fiber space not
physical space.

Of course dC = 0

Next consider 4 real scalar fields phi(x)j, j = 1,2,3,4

We now have 3 independent angles Theta, Phi, Chi with a S3 fiber (e.g.
Vacuum Manifold).

Now consider the 0-form (Theta)(Phi)(Chi)

The exact 1-form is

B' = d(ThetaPhiChi) = BChi + (Theta)(Phi)(dChi)

The non-vanishing 2-form is

C' = dB' = C(Chi) + B/\(dChi)

The non-vanishing 3-form is

dC' = D' = C/\(dChi) + dB/\(dChi)

of course the 4-form dD' = 0.