Zielinski's Problem and Emergent Gravity

Note that Dirac’s argument for the quantization of the product of
electric and magnetic monopole charges based on a Goldstone phase
string singularity uses a singular gauge transformation in which the
gauge potentials are zero everywhere-when except on the branch cut
jump string. This same idea taken from internal symmetry groups to
the spacetime symmetry groups is simply Einstein’s equivalence
principle! That is, the space-time geometrodynamical gauge potentials
are the curved tetrads, so that the singular gauging away of the
geometrodynamical potentials corresponds to the weightless geodesic
LIF frames in which special relativity works to a good approximation
not too far from the “singularity,” The Dirac string "quantization"
of charges seems to correspond to the Bekenstein area quantization of
horizons (event and particle).

"The Question is: What is The Question?" J.A. Wheeler

Paul Zielinski has been obsessed with the issue of how to distinguish
inertial force effects from intrinsic curvature effects. There is
actually no way to do so in Einstein's theory. That is the "gravity
force" the "g" the "weight" is always a reaction to a non-gravity force
pushing the test particle off its natural geodesic worldline. The
presence of curvature is completely irrelevant since curvature by
definition is "geodesic deviation" between neighboring test particles
each on geodesics.

That said, there is a deeper sense, an interesting question, beneath
Zielinski's vague yearnings and misfocus on the secondary Levi-Civita
connection field. The proper arena for what Zielinski is after is at the
tetrad level where Kibble, in his famous 1961 JMP paper where gravity is
derived properly as a local gauge theory of the 10-parameter Poincare
group of globally flat special relativity, in easily missed "footnote
13" makes the non-perturbative split

Einstein-Cartan tetrad 1-form = Flat Minkowski trivial tetrad + Curved
Tetrad

The Curved Tetrad is derived from the compensating SPIN 1 renormalizable
world vector field from locally gauging the 4-parameter translation group.

Similarly the Einstein-Cartan spin-connection 1-form is from locally
gauging the 6-parameter Lorentz group of tetrad rotations at a fixed event.

More on the math of this in next note - however

Spin connection 1-form is, in terms of my 8 Goldstone vacuum ODLRO
phases is

2S^a^b = 2S^a^budx^u ~ (Theta)^a/\(dPhi)b - (Theta)^b/\(dPhi)a

- (dTheta)^a/\(Phi)^b + (dTheta)^b/\(Phi)^a = - 2S^b^a

Where the Einstein-Cartan tetrad is the diagonal form

h^a = I^a + K[(Theta)^a/\(dPhi)a - (dTheta)^a/\(Phi)^a]

I am assuming here for now a dimensionless coupling

K = 1 where in general

K = UV Length/IR Length

e.g. Lp^2/\ ~ 10^-122 for cosmology

Note that the curvature 2-form is

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

So we have the essential structure of Einstein's 1916 in terms of the
Goldstone phases of the vacuum ODLRO fields. No-go theorems by Weinberg,
Adler or any of the Pundits are completely irrelevant to this
macro-quantum emergent gravity model.

The standard zero torsion constraint is that

dh^a + S^ab/\h^b = 0

Note that if h* is dual to h

h*h = Identity

This gives a kind of "unitarity" constraint

A^a= K[(Theta)^a/\(dPhi)a - (dTheta)^a/\(Phi)^a]

Symbolically (neglecting indices for now)

IA + A*I + A*A = 0

from

h = h^a&a = I

That Waldyr Rodrigues pointed out.

Jack Sarfatti writes:

Paul Zielinski has been obsessed

Well, it's sure lucky no one around *here* ever gets obsessed.

Lee Rudolph