On Feb 7, 2006, at 8:16 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
bcc
The key formal idea of the Bohm-Aharonov effect is closed non-exact forms, i.e. nontrivial homotopy.
The original Bohm-Aharonov effect was for a closed inexact 1-form e.g. IT EM 1-form A, superfluid 1-form v etc.
In every case single-valuedness of the BIT field implies quanta of flux of some kind, magnetism & circulation in the 2 above examples. The point is that the 2-form in this S1 case is locally zero and it's quantized flux without flux through the closed loop surrounding the line defect in the BIT field.
A 1-form A = Audx^u
is obviously a SPIN 1 vector field.
But gravity is SPIN 2
We need at least 2-Goldstone phases S2 vacuum manifold
The closed inexact 2-form of interest is obviously the AREA 2-form and its surface integral is quantized - hence Hawking-Bekenstein a piece of cake. It's volume exterior derivative is locally zero hence world hologram of t Hooft and Susskind is trivial if you look at in the right way!
This shows that the primordial inflation field must have 2 Goldstone phases for emergent Einstein gravity.
OK. Looks really interesting. I'll have to study all this in more detail.
On Feb 7, 2006, at 4:13 PM, Paul Zielinski wrote:
Thanks.
Let's kick the dog-and-pony show aside for now while I have a look at this.
OK :-) Will you be at Specs tonite? I owe you a drink.
Later, probably around 10 pm.
We have some good dialogue for a theater of ideas piece.
Yeah.
But I'm not kidding about that LC decomposition. I think I may actually have it licked. But I need to run it by a mathematician.
Waldyr could tell you. But I think you are chasing a Mirage in same way Dan Smith is with his Eschaton and his "phenomenology."
There are natural LNIF observers the HOVERING ONES for the SSS Vacuum Metric. You can arbitrarily select them as your base and then any detectors in relative acceleration to them is a natural split. But it is not objective. It's like selecting the Hubble flow as a base line where the CMB is isotropic. You can do it. It's convenient to do it for many purposes, but it completely contingent, nothing intrinsic. It's like choosing the Greenwich meridian for navigating the oceans. Useful? Sure. Of fundamental importance? No.
So, for example, when you write
goo = 1 - rs/r = -1/grr
that's a very convenient representation for hovering LNIF observers at fixed r > rs. It's simple, it's easy to calculate the 4th rank curvature tensor components in that representation etc.
OK I translated your verbal analysis into the algebra of GR in that last message.
Yes. Actually your analysis is quite helpful.
I took the degenerate case first, i.e. LNIF rest frame of test particle stuck to the detector (a spring scale). It's like choosing a circle when you are looking for an ellipse with 2 "centers" or, in my case, two Goldstone phases for the inflation field not 1. ;-)
The point is to distinguish the force on the test particle pushing it off geodesic, from the generally different force on the detector pushing it off its geodesic.
Yes. The rest frame of the detectors is what I call the "observer frame of reference".
The doing of a weight measurement of the test particle by the detector is a degenerate case where both of those forces are identical because the test particle and the detector are relatively at rest both pushed off geodesic identically.
I've been treating the weight and the scale as test objects, not as detectors. You can analyze what happens to the pointer on the scale in any frame of reference, and with frame v a lot less than c the pointer reading doesn't change under
mere frame acceleration. Of course if you accelerate the *rest* frame of the weight and the scale, the pointer reading will change, but then you have accelerated their actual motion.
This is all pretty obvious, but it took a long time to get to this because you were not being clear to my mind.
Your example of you falling past me on the scale is your META-measurement of my weight measurement.
Yes, exactly -- which has to be consistent with the regular analysis of the problem.
Yeah, but this is all straight-forward and I do not think there is any gold in this mine.
The specification of observers is what determines the representation of the geometrodynamic field. The standard text book SSS vacuum solution
g00 = 1 - rs/r = - 1/grr
r > rs
is for HOVERING LNIF observers at constant r and no tangential velocity.
Right.
This is like specifying a gauge constraint.
OK.
What that might mean in internal symmetry is an interesting question since specifying the electromagnetic gauge is always a bit of a mystery divorced from direct operational meaning.
P = p - (e/c)A
(e/c)A as the field momentum stuck to the electron of momentum p
A -> A + gradChi
psi -> e^iChi psi
may have a more direct meaning?
Also setting the gauge like DivA = 0
is it only formalism or is there some secret physical meaning latent there?
Good questions. A deeper physical model might help answer them.
Z.
Jack Sarfatti wrote:
longer version is at http://qedcorp.com/APS/EmergentGravity.pdf
On Feb 7, 2006, at 1:57 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Feb 6, 2006, at 8:34 PM, Paul Zielinski wrote:
In Jack's theory, the gravitational field is a macro-coherent BEC.
That I say is the INFLATION FIELD.
That's a concrete physical model. What we have been arguing about is exactly how to relate such a model to conventional GR at the phenomenological level, and how best to interpret GR in order to facilitate this.
This is a non-problem since I simply REPRODUCE Einstein's 1915 GR field equation in basically ONE LINE!
OK.
The formula for the curved tetrad in terms of the 2 Goldstone phases of the vacuum BEC.
OK.
Why do you need *two* Goldstone phases?
READ MY PAPER! It took me a long time to realize the ONE GOLDSTONE PHASE is not enough!
I need TWO to DERIVE semi-rigorously by GLOBAL topological homotopy methods
1. Hawking-Bekenstein area quantization and black hole entropy CONJECTURE
2. 't-Hooft-Susskind world hologram CONJECTURE
i.e. VOLUME WITHOUT VOLUME
as simply Bohm-Aharonov FLUX WITHOUT FLUX
Original B-A effect was with only ONE PHASE this demands SPIN 1 1-form is closed but not exact.
Gravity B-A effect needs TWO PHASES this demands SPIN 2 2-form is closed but not exact!
The quantized EIGENVALUES of the AREA OPERATOR must correspond to SPIN 2 that DEMANDS a closed non-exact 2-form i.e. an antisymmetric second rank tensor is the geometrodynamic area operator in the tetrad substratum of geometrodynamics!
3. Pioneer anomaly
On Feb 7, 2006, at 6:00 PM, Jack Sarfatti wrote:
Thanks. But will Ginsparg let it stay there?
On Feb 7, 2006, at 5:35 PM, Creon Levit wrote:
Its up on the archive. I just downloaded it.
Jack Sarfatti wrote:
On Feb 7, 2006, at 12:56 AM, Jack Sarfatti wrote:
Remember an earlier version of this paper received several independent endorsements from people I did not know and who did not know each other. I had to cut it down. The size limit now is 1 megabyte BTW.
Your submission gr-qc.jsarfatti.4800 was accepted.
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Abstract will appear in mailing scheduled to begin at 20:00 Tuesday US Eastern time (i.e., Wed 8 Feb 06 01:00:00 GMT).
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\Paper: gr-qc/0602022
From: Jacob Sarfatti Dr.
Date: Tue, 7 Feb 2006 08:39:00 GMT (801kb)
Title: Emergent Gravity
Authors: Jacob Sarfatti
\ Einstein's equations of general relativity are derived from a model of the coherent vacuum inflation field with two Goldstone phases. Area quantization is derived from single valuedness of the inflation field. The world hologram conjecture is derived as the Bohm-Aharonov effect for a closed inexact geometrodynamic area 2 form.
\\
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