Saturday, November 17, 2007

Note the EM vector potential A(em) is compared to the tetrad e^I, i.e. (2.101) & (2.105). Really A(em) should be compared with A^I(gravity) where the torsion field vanishes.

e^I(gravity) = I^a(1905SR) + @A^I(gravity)

where from P.W. Anderson's "More is different" emergent complexity I posit

A^I(gravity) = M^I^I = (dTheta)^I(Phi)^I - (Theta)^I(dPhi)^I


F^I(gravity) = DA^I ~ 2(dTheta)^I/\(dPhi)^I + w^IJ/\A^J

w^I^J = M^[I,J]

M^I^J = (dTheta)^I(Phi)^J - (Theta)^I(dPhi)^J

DF^I = 0

D*F^I = *J^I

D*J^I = 0

The 8 Goldstone phases form 2 Lorentz group 4-vectors THETA^I and PHI^J. Their 2 magnitudes THETA & PHI are the 2 effective Goldstone phases of the world hologram for 3D + 1 spacetime. This requires 3 real Higgs fields living in our 3D spacelike world. The possible stable topological defects are domain walls S0 vacuum manifold, line vortices S1 vacuum manifold, and point monopole defects S2 vacuum manifold. The 3D "spin network" is a "Abrikosov" lattice of point monopoles connected by line vortices. The finite cores of these soldered defects is the residual random zero point energy density from the pre-inflation false vacuum just like in superfluid helium. The residual 6 Goldstone phases lead to the internal symmetry Calabi-Yau space. E8 obviously applies to my 8 post-inflation Goldstone phases. Since the magnitudes THETA & PHI can be imaginary as well as zero and real, the 3D Goldstone phase space is non-compact. Brane worlds are simply the stable topological defects in the space of the 9 real Higgs fields that form the 8 Goldstone phases.

Horizon area is quantized and the number of area quanta N is the wrapping number of the non-trivial 2nd homotopy group using the S2 vacuum manifold of all 3 Higgs fields for the "visible universe" - the top of the iceberg as it were. Each real Higgs fields is essentially a "space dimension" in order to have stable topological defects where subsets of the real Higgs fields vanish leaving subsets of Goldstone phases undefined i.e. Berry phase singularities.

The area element is ~ dTHETA/\dPHI with N quanta, N = # Bekenstein bits

The volume element is d(area element) = 0, i.e. volume without volume (Wheelerism)

The world hologram imaging equation is Jack Ng's equation

&L = (Lp^2L)^1/3 = N^1/6Lp

L = scale of the dominating horizon, which in our universe is the Hubble scale of the retro-causal future de Sitter horizon with dark energy (DE) density

t00(DE) = hc/NLp^4 ~ 10^-29 gm/cc

N ~ 10^122

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