Friday, October 28, 2005

Weinberg-Witten theorem refuted

George Chapline first mentioned this apparent fly in my ointment for emergent gravity.
Now that I watched Ed Witten talk about it above, I see why the theorem, while technically true, is physically irrelevant because it provides a correct answer to the WRONG Question.

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

Weinberg & Witten proved that you cannot make a massless spin 2 graviton from a local gauge theory in 4D Minkowski space-time. Well that's fine, because my theory for the emergence of curved 4D space-time from local massless gauge theory in unstable 4D Minkowski space-time does not have any gravitons or quantum foam as a matter of principle. Therefore, whilst the theorem, I'm sure is mathematically correct, it is physically irrelevant IMHO.

Strangley, DeWitt, Witten, Weinberg et-al do not seem to know about the Einstein Hole Problem. No wonder Lubos Motl panned Rovelli's online "Quantum Gravity" book, because it shows that, contrary to the folklore superstition given by Witten at the Sidney Coleman Fest at Harvard that you cannot have local gauge invariant observables in general relativity, in fact you can when you use Einstein's idea of "local coincidences" P rather than bare local coordinate points x subject to the Diff(4) group x -> x' =/= x. Indeed all the Diff(4) orbits of any given x in the manifold are like gauge transformations for the internal groups and form an equivalence class {x} for a single P = {x}. That is, look at Fig. 2.4 p. 49 to see the idea.
"The diffeomorphism moves the nonflat region as well as the intersection point of the two particles a & b from the point x = B to the point x' = A. The LOCAL OBJECTIVE EVENT P on which to PIN local Diff(4) observables is Einstein's "local coincidence" a SCATTERING of 2 particles a and b. True the old pre-GR idea of the objectivity of points in Minkowski space-time does not work in GR as it kind of worked in QED. DeWitt, Weinberg, Witten et-al have seemed to overstate the problem making it a lot harder than it need be.

Given a LOCAL Vacuum ODLRO parameter PSI, I do NOT mean PSI(x) in Witten's sense. I mean PSI(P), where P = {x} = Manifold/Diff(4) the COSET equivalence class of all bare manifold points connected by Diff(4) local coordinate transformations. .Diff(4) is the local gauging of T4 in Minkowski space-time.

P is a COINCIDENCE COLLISION of particles a & b as explained by Rovelli in his 2.2. This is basically what Einstein finally understood after much struggle to be sure.

Now, the curved part of the Einstein-Cartan tetrad field is

B(P) = (hG/c^3)^1/2'd'argPSI(P)

where 'd' means there are Goldstone phase = argPSI(P) singularities of Bohm-Aharonov "Flux-without flux" in which, including the singularities on the interior of the non-bounding 1-cycle:

DeRham Integral of the 1-form 'd'(argPSI(P)) on a non-bounding 1-cycle surrounding the singularity does not vanish and is indeed, in stationary Bohr-Sommerfeld sense, quantized from the single-valuedness of PSI(P). That is, using a QUASI-Stoke's theorem, it's AS IF

Line integral of B over non-bounding loop = Surface integral of "Curl B" (in 4D).

That is, in heuristic notation

d'd'argPSI =/= 0 GLOBALLY even though d'd'argPSI = 0 locally on the nonbounding loop. The interior surrounding argPSI singularity makes the outer loop not a boundary.

This is quantized Flux without flux.

Einstein's local metric field is the symmetric tetradic bi-linear form of the EEP

ds^2(P) = guv(P)dx^udx^v = (1^I + B(P)^I)nIJ(1^J + B(P)^J)

B(P) = B^I&I

&I dual to dx^I

I,J in tangent space, nIJ is constant Minkowski metric.


Therefore, I LEAPFROG over Weinberg-Witten theorem. It is irrelevant. We do not RE-QUANTIZE an emergent BOTTOM -> UP c-number ODLRO field whose Goldstone phase gives Einstein's 1915 GR!

What happens at the singularities where the Higgs Amplitude |PSI(P)| = 0 is NO QUANTUM GRAVITY FOAM, but MASSLESS FLAT QUANTUM FIELD THEORY.

But is it in 2+1 D on virtual holographic boundary of curved 3+1 interior as Witten mentioned? Could be. I have been thinking massless pre-inflation false vacuum was 3+1 but maybe it is 2+1?

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