Post-Inflation World Hologram Emergent Gravity

Global conservation laws require global symmetries.

Tuv^,v = 0

,v = ordinary global T4 partial derivative

Tuv = stress-energy current density local AFFINE tensor of non-gravity
matter fields i.e. only for global Poincare group!

globally conserved integrals for Pu exist no problem in accord with
usual ideas of energy-momentum conservation.

In 1915 GR above picture breaks down replaced by

Tuv^;v = 0

;v = T4(x) covariant derivative from bilinear forms of e^a and its
gradients (e.g. Rovelli's eq 2.89 in Ch 2 of "Quantum Gravity")

All the trouble of Roger Penrose's "nonlocal gravity field energy"
leading to wrong theories like the Yilmaz theory embraced by Eric Davis
et-al, abandoned by Yilmaz himself it is alleged, come from

[Tuv(matter) + tuv(gravity-matter)]^,v = 0

Now tuv(gravity-matter) though still an AFFINE T4 tensor is not a GCT
T4(x) tensor.

This is THE TROUBLE.

General relativity breaks, in particular, global T4 symmetry inducing
general transformations between locally coincident observers Alice and
Bob in arbitrary relative motion including accelerations, jerks et-al to
all orders. This is different from simply painting new coordinate labels
for a fixed local observer. I will call the latter non-physical
"redundant gauge transformations" as distinct from the former physical
"local frame transformations." This issue also arises in Yang-Mills
internal symmetry field theory with global special relativity for the
internal transformations of the electromagnetic, weak and strong forces.
"Solved" for special relativity quantum field theory by Faddeev & Popov
using Feynman path integrals - very complicated with ghost fields that
violate spin-statistics connection in 3D+1 spacetime, i.e. spin zero
fermion ghosts. Feynman tried to apply this to GR "quantum gravity" as
well, but with a global flat background I think missing all important
non-perturbative strong field phenomena.

The special relativity total 4-momentum Pu of any field or set of
coupled fields are global integrals of local stress-energy density
currents on 3D spacelike surfaces.

Because of causality they are not observables, only the local current
densities are.

Total 4-momentum Pu are the Lie algebra "charges" of the 4-parameter
global translation subgroup T4 of the 10-parameter global Poincare group
that is the universal symmetry group defining 1905 Special Relativity
that is a GLOBAL theory, i.e. inertial frames span the entire universe.
See Julian Barbour on difficulties with this conception, but that need
not concern us here.

Carmeli et-al in "Gravitation, L(2,C) Gauge Theory and Conservation
Laws" Ch 4 gives historical summary

1. Einstein's local gravity field nonsymmetric non-tensor

2. Landau-Lif****z's symmetric fix

Both above have the Bauer paradox, i.e. the non-physical repainting of
coordinates for the same observer of the Galilean relativity form

x^0' = x^0

x^j' = f^j'(x^j)

ji,j = 1,2,3

change tuv(gravity, matter)

3. Moller's version

4. SL(2,C) local tensor

however none of the above are satisfactory

Note that Carmeli's SL(2,C) is incomplete. He is simply doing Utiyama
1956 local gauging of only 6-parameter Lorentz group. Doing that gives
both disclination curvature from dilocation torsion gap - his gauge
field. Locally gauging only 4-parameter T4 to GCT T4(x) gives only
disclination curvature without torsion (H. Kleinert) This causes
confusion in the literature from formalists who do not have the H.
Kleinert world crystal lattice physics picture to guide their intuition.
Tensors came from crystallography in the first place.

Note adding quantum gravity makes the world crystal lattice spacing a
fractal "wavelet" ~ N^1/6Lp, N is the wavelet ZOOM parameter, i.e. if
you measure a length L, the quantum uncertainty in L is

(1) &L = (Lp^2L)^1/3 from Wigner

However, from Bekenstein - World Hologram

(2) L^2 ~ NLp^2

substitute (2) in (1) to get

(3) &L ~ N^1/6Lp

N = number of Bekenstein BITS on the dominating causal "horizon," e.g.
FUTURE RETRO-CAUSAL dark energy de Sitter observer-dependent
cosmological horizon ~ 10^122 for our pocket universe in the multiverse,
which as a bonus explains "Arrow of Time" (2nd Law of Thermodynamics).

The physical local frame transformations of 1915 GR come from locally
gauging ONLY T4 to T4(x) the compensating gauge potential is the piece
of tetrad A^a where

e^a = e^audx^u = I^a + @A^a

ds^2 = guvdx^udx^v = e^aea is Einstein's 1916 GR

@ is a dimensionless renormalizable coupling constant

I^aIa = ds^2 for 1905 special relativity

I^au(x) is curvilinear in non-geodesic frames defined relative to
Minkowski spacetime. Otherwise it is Kronecker delta in Global Inertial
Frames GIFs.

e^a is a Minkowski 4-vector.

Let L^a'a be a Lorentz group transformation

e^a' = L^a'ae^a

However,

I^a' = L^a'aI^a + X Not a Minkowski tensor because of inhomogeneous
term X

A^a' = L^a'aA^a - X/@

keeping total e^a a Minkowski 4-vector

formally the same as e.g, U(1) EM internal symmetry gauge transformations

When A^a = 0, then X = 0

i.e. I^a' = L^aaI^a is strictly only for global T4 frame
transformations, X =/= 0 is only for local T4(x) transformations.

The dislocation torsion field 2-form is the formal Yang-Mills spin 1-field

T^a = de^a + w^abce^b/\e^c

The disclination curvature 2-form (that can include torsion parts) is

R^a^b = dS^a^b + S^ac/\S^c^b

S^a^b = - S^b^a = S^a^budx^u is spin connection 1-form where

S^a^b = w^a^bce^c

Note that when A^a = 0

R^a^b = 0

Einstein's vacuum field equations are Rovelli's (2.9)

{I,J,K,L}[e^I/\R^J^K + (Dark Energy Curvature)e^I/\e^J/\e^K] = 0

{I,J,K,L} = antisymmetric Minkowski tensor - this is a classical cubic
Yang-Mills field equation that is t'Hooft renormalizable if quantized.

Note the substratum decomposition

e^a = I^a + @A^a

in my emergent gravity world hologram model

@ = 1/N^1/3

A^a = M^a^a diagonal elements of world hologram "destiny"
(retro-causal) matrix of 8 vacuum ODLRO post-inflation Goldstone phases
from 9 real Higgs spin 0 fields.

torsion field part of spin connection is

S^a^b = M^[a,b] = - S^b^a

in gr-qc/0602022