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R. Kiehn's "physical vacuum" and my "emergent gravity."



 
 
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Old November 24th 06, 06:55 AM posted to sci.math,sci.physics.relativity,sci.philosophy.tech,sci.physics.particle,sci.astro
Jack Sarfatti
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Default R. Kiehn's "physical vacuum" and my "emergent gravity."

Kiehn is not easy to read, but I am beginning to get a handle on what he
is trying to say and how it relates to my emergent gravity theory in my
equations below:

When I claim to have derived Einstein's theory of curvature gravity
extended to torsion (Kibble 1961) as an emergent theory I mean precisely


1. C^a^b = A^adB^b - B^bdA^a

2. e^a = I^a + C^a^a Einstein-Cartan tetrad 1-forms

3. W^a^b = C^a^b - C^b^a spin-connection 1-forms

Where A^a and B^b are 8 0-form Goldstone phases of a 9 real component
Higgs vacuum ODLRO field.


4. T^a = de^a + W^ac/\e^c Kibble-Shipov torsion 2-form

5. R^a^b = dW^a^b + W^ac/\W^c^b Curvature 2-form for geodesic deviation

6. L(Einstein-Hilbert-Cartan) = {abcd}R^a^b/\e^c/\e^d Action Density
for the Free Gravity Field

7. Universal minimal coupling of gravity field to all non-gravity fields
using the equivalence principle in which all Minkowski metrics nab in
the non-gravity actions are replaced by

guv = eu^aev^bnab

i.e. in local invariant form

ds^2 = guvdx^udx^v = e^aea


The EIGHT FOLD WAY of the Goldstone phases (0-forms A^a & B^b) are part
of THE NINE real Higgs fields.




http://www.physics.gla.ac.uk/ppt/ind...arch/higgs.htm

The above simplest case is n = 2 where the vacuum manifold is S1' and
closed loops S1 surround line (vortex) defects, which have stable
quantized Bohr-Sommerfeld circulation because the first homotopy group
mappings H1(S1 - S1') = Z(integer winding numbers).

i.e. n = number of real Higgs field local order parameters of the
coherent vacuum zero point energy damping down the cosmological constant.

n - 1 = number of independent Goldstone phases.

This is first order homotopy for stable defects

1 + dimension of stable defect + dimension of hypersurface surrounding
defect = dimension of spacelike slice.

for 3D space, above picture is for quantized string vortex defects
surrounded by closed loops.

In world lattice in 3D space, it's closed 3D surfaces surrounding point
defects.

In 9D space you have a lot of BRANE choices.

Kiehn is concerned with topology change beyond reversible
diffeomorphisms, hence an extension of Einstein's gravity to include the
irreversible arrow of time. More on this anon.

His definition of vacuum is odd. He seems to want a square matrix of
0-forms with non-vanishing determinant. My Goldstone phase 0-forms are
not a square matrix. Also he has "action" as a 1-form. The
Einstein-Hilbert field action is a 0-form. However, I can relate to
other things he says when he gets to 1-forms and 2-forms and then even
to 3-forms.

My Kibble tetrads and spin connections are 1-forms from localizing
T4xO(1,3) are all encoded in the matrix C^a^b above.

The torsion T^a is a 2-form.

The curvature R^a^b is a 2-form.

We can make 3-forms like e^a/\T^b etc.

later ...

I don't yet understand how to calculate the Pfaffians.

Jack Sarfatti

"If we knew what it was we were doing, it would not be called research,
would it?"
- Albert Einstein
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