Jack, this is very important, right?
It might help me (and a lot of us struggling to understand) if you could write very sort answers to the following questions:
1) If gravity = tetrads = spin-1 = renormalizable, then do you have renormalizable quantum gravity formulation?
I believe so. But I am not expert in the details of t'Hooft's 1972 paper for which he got the Nobel. That my formulation falls within his paper seems self-evident to me, but I could be wrong here.
Or is it old news because you have essentially classical gravity, and it is only when you have (nonclassical) gravitational quanta that normalization becomes problematic for gravity theories.
I do not understand your sentence. The steps I use are:
1. Local gauge principle
2. 10-parameter Poincare group P10 of 1905 special relativity
3. A^a is the compensating "curvature" "Yang-Mills" spin 1 vector classical field from locally gauging ONLY the 4-parameter subgroup T4 of P10. The gauge transformations are precisely Einstein's local coordinate transformations of 1916. This was shown by Kibble clearly in 1961! t'Hooft's argument is when you quantize the classical A^a field. In t'Hooft "a" is an internal index. In my theory "a" is the tetrad Minkowski space index. The Lie algebras are not the same, t'Hooft's Lie groups are compact, P10 is not, but the formal structure seems to me to be essentially the same as far as physics is concerned.
From Rovelli I think
S^a^b = w^a^bce^a which gives instantly the FORMAL Yang-Mills structure for gravity!
S^a^b is the "spin connection" whose independent torsion field dynamics comes from locally gauging the 6-parameter Lorentz subgroup of P10 that Einstein did NOT do in 1916. This is the new torsion field physics of dark energy IMHO.
ds^2 = guvdx^udx^v = e^aea found in Rovelli's "Quantum Gravity"
My original WORLD HOLOGRAM Ansatz - completely original to me, and perhaps wrong, is
e^a = I^a + (1/N)^1/3A^a
I^a is the global Minkowski space-time tetrad 1-form
A^a is the intrinsically CURVED tetrad 1-form.
A^a is obviously a spin 1 vector field under the Lorentz group
A^a' = L^a'aA^a
L^a'a' is a Lorentz transformation
A^a = A^audx^u
A^au' = X^u'uA^au
X^u'u = Einstein local coordinate transformation (aka GCT) = T4 local gauge transformation.
A^a is a GCT INVARIANT!
N = Bekenstein's BITs
i.e. N = Surrounding 2D Area/4Lp^2
Lp^2 = hG/c^3 ~ 10^-66 cm^2 = quantum of area
G = Newton's gravity constant
Surrounding Area here has no boundary, but is itself not a boundary because it encloses N point defects in the macro-quantum coherent vacuum ODLRO order parameter with three real Higgs spin 0 scalar fields that is the "fabric of 4D spacetime". These point defects are somewhat like the simple poles (Residue)(z - zi)^-1 of a complex function w = f(z) of complex variable z.
Note also A^a = M^a^a
S^a^b = M^[a,b]
M^a^b = dTheta^a/\Phi^b - Theta^a/\dPhi^b
Theta^a & Phi^b are 8 zero-form Goldstone phase Lorentz 4-vectors whose two magnitudes Theta & Phi (3 real Higgs fields) make the point monopoles of the geometrodynamic field (AKA fabric of 4D spacetime).
This is the WORLD HOLOGRAM of "Volume without volume" that there is a 1-1 correspondence between an area quantum and its hologram image "volume quantum".
2) What are the [gravitational] quanta in your theory?
Obviously there are 3 kinds, spin 0 gravi-scalar, spin 1 gravi-vector and spin 2 gravi-tensor AKA "graviton".
This is completely elementary because Einstein's metric field guv is a quadratic form in A^a i.e.
ds^2 = guvdx^udx^v = I^aIa + N^-1/3(I^aAa + A^aIa) + N^-2/3A^aAa
N^-1/3 term gives only spin 1 quanta
N^-2/3 terms gives ALL THREE! spin 0, spin 1, spin 2 from elementary quantum field theory when
A^a classical field is replaced by A^a(classical ODLRO) + A^a(quantum fluctuation) as in Gorkov's theory of BCS superconductor for example.
Is there any graviton-like entity that emerges? Is there any need for one?
Explained above. Spin 0, spin 1 & spin 2 gravitons.
3) What happens in your theory at the Planck scale, where the uncertainty principle "demands" the existence of complementary huge (or should we say "massive") momentum and energy fluctuations?
Planck scale is trivial. It's when the post-inflation field order parameter vanishes like at the point monopole defect. No big deal. Same as in Yang-Mills quantum field theory. I have reduced gravity to a Yang-Mills theory. When the order parameter vanishes curvature and torsion also vanish - we are back to special relativity quantum field theory! This IS the pre-inflation false vacuum! The core of the point monopole is a small remnant of the pre-inflation false vacuum. This is really simple and elegant conceptually. The point monopoles are the equilibrium points of Hagen Kleinert's world crystal lattice. There disclination defects are curvature and their dislocation defects are torsion. Torsion induces curvature, but not vice versa. This is obvious from the local gauge theory of P10 BTW.
4) Is it not these fluctuations which drive the nonlinearities in GR to dominate and thus make the standard formulations analytically intractable and/or unrenormalizable? Is this the basic quantum gravity conundrum, or is that something else?
I have no idea what you mean. Again:
1. Lorentz vector classical field theories WHEN QUANTIZED are renormalizable in general says t'Hooft 1972
2. The Einstein-Cartan tetrad theory of curvature and torsion is clearly formally a vector classical field theory.
That's all folks.
5) Does your theory have a way around this conundrum? How so?
There is no conundrum here only a badly formulated question.
"The Question is: What is The Question?" (J.A. Wheeler) :-)
Jack Sarfatti wrote: OK I need a copy of the current STAIF Log 1 paper that the referees have. :-)
What's good about tetrads is that they are spin 1 vector field like Yang-Mills they are renormalizable because of t'Hooft's work - was it in 1972? Formally my A^a is same structure as t'Hooft's Yang-Mills - that he used compact internal SU(2) & SU(3) and I use non-compact Poincare group is not an essential difference in regard to renormalizablity I suspect.
On Sep 11, 2007, at 5:11 PM, Andrew Beckwith wrote:
That is a start.
Now I want you to make a short, one paragraph description of what you just said.
A PARAGRAPH. Not a long one.
Start with the quantum fluctuations in a spin 1 vector field. Then jump from there
to the tetrad field theory.
If your theory has such a compact description of it, you need to include
this in the paper. That in itself is a MAJOR result. And it should definitely
be in your STAIF Log 1 paper.
I cannot stress how important this is.
i gave you my definition which is more than adequate for this paper's
quantum foam is trivial in my tetrad A^a field theory - same as quantum
fluctuations in any spin 1 vector field
quantum foam = virtual A^a quanta in QGMD
just like virtual photons are virtual A quanta in QED
my theory is much simpler than the previous theories
quantum foam = zero point fluctuations in the A^a field where
e^a = I^a + (1/N)^1/3A^a already in paper
ds^2 = guvdx^udx^v = e^aea = I^aIa + (1/N)^1/3(I^aAa + A^aIa) + (1/N)^2/3A^aAa already in paper
no big deal on "quantum foam"