Loops, Knots, Gravity
On Dec 24, 2004, at 1:06 PM, Alex Poltorak wrote:
It is only natural that gauge connections used in quantum gravity and
other unification theories are dynamic, while my affine connection is
At some point Alex next year I will read your ontology paper to see what you are really doing. I need to understand the physical motivation before I look at the math closely. What is clear to me is that there is no real relation between what you are doing and what Paul is doing.
The reason is very simple -- the connections describing physical
fields must be dynamic while my affine connection used in Part I of my
GR17 paper DOES NOT describe any physical field whatsoever.
Yes, and this is what I do not understand.
It is a
mathematical device used to separate the physical information about
gravitational field per se from the information about a coordinate
system, in which this field is described.
Again I do not understand how this is possible unless it fits my
LC connection 1-form = Exact 1-form + Non-Exact 1-form
idea because from Penrose I see how to connect that kind of mathematics directly to Einstein's 1916 GR
The info in the coordinate system would then be the Exact 1-form part that makes no contribution to the intrinsic tidal curvature. There is no reason to expect the Non-Exact 1-form to be a 3rd rank GCT tensor relative to the (LC) connection ;w itself as Paul wishes. That is a false idea I think. The only GCT tensor there is guv;w = 0.
It has no more meaning than
the base 2 in binary numbers. Just as any number may be represented in
a binary form, any L-C connection may be represented as the difference
between an arbitrary affine connection and its tensor of nonmetricity.
This I do not understand.
This is just a fact of differential geometry.
My use if this
mathematical device to reformulate the classical GR does not change the
theory any more than its reformulation in terms of tetrads. However,
just as in the case of tetrad reformulation, it sheds some interesting
light on the nature of the gravitational field and its conservation
The only real modification of the classical GR is described in Part III
of my paper, where the affine connection is no longer arbitrary as in
Part I, but is defined by the choice of the RF and the theory describes
the gravitational field in a NIFR having GR as a special case of the
gravity in IFR. If you read the paper instead of judging it based on
the hearsay, you will see it very clearly, just as you easily followed
my logic during our delightful conversation in Dublin.
I have told Paul repeatedly that I have no present opinion on your work until I have a chance to really think about it. What I object to is Paul's invoking your work as a justification for his when he admits he cannot explain your work in his own words. I do not understand yet how you mean "RF", "NIFR" and "IFR". Paul seems to use these terms in the GLOBAL special relativity sense whereas in GR only LOCAL FRAMES have meaning. :-)
The modern Ashtekar approach does start with connections as the fundamental dynamical variables. I am beginning to suspect that the nonlocality of gravity energy and the curvature without curvature of Vilenken-Taub's thin wall of dark energy are related to the global holonomy of the Wilson loops that we see in Berry phases, in Bohm-Aharonov-Josephson effects - all coming from the topological defects in the SINGLE-VALUED vacuum coherence local order parameter which is how I realize Andrei Sakharov's 1967 idea of Einstein's curved spacetime as emergent METRIC ELASTICITY = PW Anderson's "phase rigidity". Cartan's forms and the Hodge-DeRham integrals seem a good formalism to use here. The "loop-knot" formalism may be the most powerful technique. I don't know.
I get a "area" quantum from my Bohmian method that is characteristic of loop quantum gravity. It is also equivalent to a string tension. I get all that trivially without extra dimensions that may be unstable (Penrose).
From: Jack Sarfatti [mailto:email@example.com]
Sent: Thursday, December 23, 2004 5:21 PM
To: Paul Zielinski; SarfattiScienceSeminars@YahooGroups. com;
Cc: Alex Poltorak; ItalianPhysicsCenter
Subject: Loops, Connections & Knots
There is a unified view of electroweak-strong and gravity as
renormalizable Wilson holonomy loop local gauge theories where the
connections for parallel transport of physical fields in internal spaces
and spacetime respectively are the fundamental background independent
non-perturbative NON-RIGID dynamical variables.
This is why Alex's "RIGID AFFINE CONNECTION" is not a proper way to look
at General Relativity. The issue here is the physical idea. The essence
of Einstein's relativity is the RENUNCIATION of all absolute RIGID
background dependent connection fields.
"The space of loops offers a natural arena for the quantum theories of
connections." A. Ashtekar
I add ODLRO macro-quantum "BCS" theory to that.
There is a "loop transform" is it related to a "wavelet transform"?
Quantum gravity states depend on knot generalizations of Loops. How does
this carry over to ODLRO spontaneous breakdown of vacuum symmetry in pre
-> post inflationary phase transition?