## Monday, August 28, 2006

Graviity Emergent from the Dirac Substratum

Geodesic deviation is nonlocal even though the Riemann curvature tensor is
local.

How can that be? Since you can even measure it locally?

But you cannot. As soon as you measure geodesic deviation, the LIF
breaks down. You never measure the local curvature tensor itself only its nonlocal
footprint so to speak.

OK, then what about the water drop argument put forward by Ohanian and
Ruffini ("O&R") in their "Gravitation and Spacetime", Ch 1?

That's non-local!! The LIF is defined only to the extent that the geodesic deviation is below the threshold of detection! That's the whole point!!!!!! Ruvwl(x) is formally local but it is not directly measurable - it's inferred from

d^2(x-x)^u/ds^2 = (x-x')^l(dx^w/ds)(dx^v/ds)(Ruvwl)

All the quantities here apart from are independently measurable.

(Ruvwl) is a nonlocal smear or average over scale (x - x') invariant spacetime separation of the 2 geodesic test particles.

EEP is only good for a single test particle observer - as soon as geodesic detection is detectable LIF needs to be made smaller!

So when you detect geodesic deviation you no longer can use only ONE LIF - you have two mobile LIF geodesic tetrad frames tilted relative to each other.

e^j(x + dx) = e^i(x){i^ju|x}dx^u

(ej|ei) = (Minkowski)ij

(eu|ev) = guv curvilinear metric

All you did Paul was to CONTINGENTLY CHOOSE THE SHELL HOVERING LNIFs, that may not even exist in general, and call them INTRINSIC ACCELERATION.

All test particles do have invariant 4-acceleration magnitude of course. For geodesics it's ZERO.

Note that their are 6 "phases" for relative rotation of the tetrad frames and 4 more if you include infinitesimal translations. Add the Weyl dilatation to get the 11-dim manifold of M-theory.

It's the orientations of the mobile Cartan tetrad frames + dilation that is analogous to the internal gauge groups U(1), SU(2), SU(3) Yang-Mills.

As soon as you get a geodesic deviation signal filtered from the noise, that means your measurement is NO GOOD. You must reduce resolution or make your scale smaller until you hit rock bottom "Planck scale" that may be much larger than 10^-33 cm ending the hierarchy problem "desert." Wheeler's system is consistent!

PS in g00 = 1 + V(Newton)/c^2) static metrics

But from POV of LOCAL GAUGE THEORY here Poincare group is locally gauged as if it is internal Yang-Mills, the CONNECTION is the YANG-MILLS POTENTIAL

i.e
;u = ,u + {u|^i^j}Aij

where Aij are, in general the 10 generators of the global Poincare group

i.e. 4 translations + 3 space rotations + 3 space-time boosts

{u|^i^j} is the LC connection here with TORSION beyond Einstein 1916

LOCALLY GAUGE GL(4,R) to get 6 more generators and phases?

The connection field components are like the "phases" of Yang-Mills.

In simplest U(1) em

e^iPHASE(ELECTRIC CHARGE) operates on a matter source field

PHASE is like connection component or like 3 phases of SU(2) & 8 phases of SU(3) etc.

BUT MY EMERGENT GRAVITY has the DIRAC SUBSTRATUM!

THIS PART IS REALLY NEW ORIGINAL TO ME, AND ME ALONE.

e = I = I' + A

I is the IDENTITY action on the tangent bundle of mobile LIF Einstein-Cartan frames as Waldyr Rodrigues says.

Think of analogy in Hilbert space

I = Sum|i)(i| completeness

remember macro-quantum ODLRO is OVERCOMPLETE

Also remember MY SOLUTION to ~ 10^122 cosmological constant problem

Vacuum condensates PSI SUCK UP random zero point energy! They have zero entropy and zero quantum vacuum fluctuation!

(0|PSI|0) =/= 0 HIGGS FIELD

(0|PSI^2|0) - |(0|PSI|0)|^2 = 0 exactly

unlike electric field ZPF in Puthoff's & Haisch's theory.

I = eu^idx^u&i = IDENTITY Cartan 1-FORM

dA ~ dTheta/\dPhi

is my new discovery of the SPIN 1 renormalizable Dirac Substratum of emergent SPIN 2 gravity from EPR pairs of the A quanta!

A obey a Yang-Mills theory with A-balls like glue-balls & Wheeler geons.

dA is something like the loop quantum gravity area operator

There is no volume operator in sense of world hologram.

The key dimensionless parameter coupling is obviously

Lp*^2/\ = (hG*/c^3)/\ = (number of BITS of pocket universe)^-1

G* slides like renormalization group flow - weak at large scale, strong at small scale maybe from the extra dimensions from above?

The L-C connection is essentially a non-tensor gauge potential from
locally gauging the translation group. It has no covariant tensor
part! You confuse the transformation with the thing transformed.

So you say, but I think this was refuted by Poltorak.

He made a mistake of conception.

No, according to Poltorak, as a purely mathematical matter, you can
extract a (2,1) general tensor from the L-C connection. This is the
non-metricity tensor Q of the general affine connection A that effects
the L-C decomposition.

This is all in his papers.

This makes no physical sense at all. In Einstein's GR Q = 0!!!