On Nov 28, 2010, at 2:37 PM, Paul Zielinski wrote:
On Nov 28, 2010, at 1:29 PM, Paul Zielinski wrote:
Look, I'm not trying to undermine your condensate model. I'm just trying to see how it plays out physically. How it may be capable of explaining gravitational attraction in physical terms.
Gravity attraction is explained exactly the same as Einstein explained it - geodesics in curved spacetime.
My condensate - tetrad model gives emergent
Guv + kTuv = 0
as the end product.
Hence gravity attraction is explained.
Your tetrads describe vacuum Weyl curvature as observed from moving reference frames.
Right. In principle they describe Ricci curvature also where Tuv =/= 0 as well. For example, one can imagine tiny strain gauges implanted in the Earth. Or drill holes and lower detectors on cables - those would be static LNIFs.
The E-H field equations determine Ricci curvature at the source. How does you model bridge that gap? How do you get Ricci curvature from the Goldstone phases? Doesn't your formal analogy relate the Goldstone phases directly to the vacuum tetrads?
The vacuum is still there even when Tuv =/= 0. One does not literally have to have actual detectors in place. That is impossible. The point is the Einstein field equations
Guv + kTuv = 0 + initial/boundary/final conditions
describe the GMD field.
A particular representation for guv is a pattern of LNIF detectors that could be there in a counterfactual sense. If you put one there you would get the numbers given by the guv solution.
For example when you write the SSS solution for a black hole outside its horizon
gtt = 1 - rs/r = - 1/grr
rs/r < 1
g(r) ~ (c^2rs/r^2)(1 - rs/r)^-1/2 ---> infinity as r ---> rs from the outside ~ Unruh temperature
that only works for the static rocket detectors in Hawking's picture!
Similarly for the deSitter solution in the static LNIFs where we are at r = 0 in Tamara Davis's Fig 1.1.
gtt = 1 - / ^2 = - 1/grr
r < /^-1/2
g(r) --> 2c^2(/ )(1 - / ^2)^-1/2 ---> infinity as r ---> /^-1/2 from the inside only when / > 0.
g(0) = 0 we are on a de Sitter geodesic.
but which way is g(r) pointing? - is the question.
gtt = 1 + 2VNewton/c^2
when VNewton = -c^2rs/r
-dVNewton /dr = -c^2rs/r^2 attraction pointing toward smaller r
In contrast when VNewton = -c^2/ ^2
-dVNewton /dr = +2c^2/
therefore dS / > 0 is virtual boson dark energy repulsion away from r = 0.
In contrast, AdS / < 0 is closed loop virtual fermion dark matter attraction toward r = 0.
Note, there is no event horizon at r = /^1/2 in the AdS case.
Note that the potential / ^2 has QCD-like asymptotic freedom as r --> 0 and it also has confinement as r ---> /^-1/2
when / ~ 1/fermi^2 instead of / ~ 1/Area of future horizon
where the parallel Regge trajectories for hadronic resonances are explained i.e. hadrons as rotating black holes in Salam's f-gravity.
Or is there more to your model than that? Can you really get matter-induced Ricci curvature from the Goldstone phases of the post-inflation condensate?
Since I get Einstein's field equation - short answer is yes.
The point is once I derive the tetrads for LIFs from the gradients of the Goldstone phases then simply use standard arguments that Einstein used to introduce Tuv with his Guv.
Technically I get the curvature 2-form R^I^J from the Goldstone phases including their 3rd order "jerk" partial derivatives - hence the kind nonlocality that we see in radiation reaction in charged particle mechanics leading to Wheeler-Feynman type picture - from Dirac's anticipatory picture using advanced potentials. Clearly the third order partial derivatives demand Aharonov's post-selection final boundary condition.
The basic field partial differential equations of Einstein are really 3rd order not second order in the Goldstone phase Cartan 0-forms from the cohering of the false vacuum into the present vacuum at inflation!
If you impose flat space decoupled from time, i.e. Galilean group that's Newton's gravity force picture.
You can still have Newtonian gravity in Minkowski spacetime, but it would violate the maximum signal propagation speed c.
Curved spacetime eliminates Newton's gravity force and replaces it by the invariant pattern of geodesics in curved spacetime.
The equivalence principle is a qualitative PHYSICAL gap that cannot be crossed over to the electro-weak-strong forces.
I'm not sure what this means.
You have a formal analogy between the Goldstone phases and the tetrads of GTR. Why not flesh that out with physical explanations?
I have. The physical explanation is exactly the same as that for superflow in superfluids - except now it's a 4D supersolid with plastic distortions of the point gravity monopole defects in the condensate. You simply do not understand what I have been saying in its fullness.
As to the vacuum fine. But how do you get Ricci curvature at the source? And how do you get from that to the Weyl curvature of the vacuum? No Ricci curvature, no E-H field equations. What I don't understand is how you get an analog of Ricci curvature from your tetrad-Goldstone phase analogy. Also why do you need diffeomorphism gauge invariance?
I don't need it. Nature needs it.
Well I disagree.
As you know I think you are mistaken here.
I've given you a clear cut mathematical argument as to why this fails, based on the geodesic equation.
I think your argument is based on a profound misunderstanding of the physical meaning of Einstein's GR. So I don't accept it. It's too easy to get lost in all the excess baggage formalism that is a dense fog hiding the physics.
All that means is that locally coincident accelerating LNIF frames see the same objective curved spacetime invariant patterns of geodesics and their relative deviation.
I have a complete physical picture - not just formalism.
Yes of course Riemann curvature is no problem, it's a tensor quantity. The problem is that gravitational deformation of the geodesics is locally determined by the metric gradients g_uv, w(x), and not the curvature R^u_vwl(x).
You are mistaken here. This is the key error in your attempt. You don't understand that the Levi-Civita connection from first-order partial derivatives of the metric tensor does not affect the gravitational deformation pattern of the tangent bundle of geodesics. The Levi-Civita connection only describes the acceleration of the detectors measuring the non-accelerating geodesic test particles. The gravity deformation is only the covariant curl piece of the Levi-Civita connection with itself. Those are second-order partial derivatives of the metric tensor, but they are, at a deeper level of the Dirac substrate - third-order partial derivatives of the eight coherent Goldstone phases of the post-inflation vacuum superconductor whose point -ike monopole defects form the Kleinert world crystal lattice.
Active diffeomorphism invariance implies that there is no physical distinction between coordinate artifacts
g'_u'v', w(x') =/= 0 (1)
on the one hand, and actual geometric gradients
g'_uv, w(x) =/= 0 (2)
on the other. I say this is simply wrong. The gradients (2) deform the geodesics; the gradients (1) do not. The transformations (2) accelerate free test with respect to the source (or vice versa); while the transformations (1) do not. That is a physical distinction. I would have thought you'd be better off without it. I know this is Rovelli's hobby horse, but I think I can knock it and the "hole" argument down in 3-4 lines. Babak and Grishchuk didn't get that far in their paper.
I don't believe you.
I showed you the argument based on the geodesic equation Jack. Ball's in your court.
OK, explain why there is no physical distinction between (1) and (2) above, with reference to the geodesic equation. FYI some top people in foundations of physics reject active diffeomorphism invariance as distinguishing GTR from any other theory based on a spacetime manifold -- e.g., Cartan's spacetime formulation of Newtonian theory.
I don't believe them because they do not understand the physical meaning of Einstein's GR. They know how to manipulate the formal symbols, but lack the physical understanding.
You can disagree Jack, but don't try to tell me this is a "crank" position. It's not.
It is a mistaken model. It's wrong because you have made a false premise. Your starting point is mathematically and conceptually wrong. The first-order metric gradients do not change the objective pattern of the geodesics as you assume.
The real gravity field comes from the set of coherent vacuum phase gradients analogous to superflow.