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What is the recent development of Loop Quantum Gravity

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tom.stoer
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Nov21-11, 12:15 AM
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Quote Quote by qsa View Post
so what was the purpose of the reformulation then.
To avoid the notoriously difficult Hamiltonian and to provide a tractable formulation from which results (especially in the semiclassical regime) can be derived more easily. The problem is that the underlying conceptual issues are still there but show up in a different (and not so obvious) way.

One issue is this: usually the PI (including vertex and measure) is derived via the Hamiltonian; in the new models this derivation is avoided (intentionally b/c the Hamiltonian itself is still poorely understood). The question remains in which way the dynamics of the SF models is related to the original formulation (our understanding is restricted to the kinematical level).
marcus
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Nov21-11, 02:30 PM
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Quote Quote by tom.stoer View Post
To avoid the notoriously difficult Hamiltonian and to provide a tractable formulation from which results (especially in the semiclassical regime) can be derived more easily. The problem is that the underlying conceptual issues are still there but show up in a different (and not so obvious) way.

One issue is this: usually the PI (including vertex and measure) is derived via the Hamiltonian; in the new models this derivation is avoided (intentionally b/c the Hamiltonian itself is still poorely understood). The question remains in which way the dynamics of the SF models is related to the original formulation (our understanding is restricted to the kinematical level).
I think this is a fair account as far as it goes, but leaves off the conceptual/aesthetic motivation---which I think is a factor both with Bianchi and with Rovelli.

The drive to discover new ways to think the world---new ways to visualize geometry and how it responds to measurement---new quantum concepts of geometry in other words.

I mentioned that as I see it the new models we are talking about are aharo-bohm, polytopes, and zakopane.

A. The aharo-bohm model is based on topological defects embedded in a flat manifold. The curvature lives on the defects. Rovelli discussed it as a side aspect, possible alternate way to see things, in the zako lectures. It's exciting that Freidel adopts it in the FGZ paper.

B. The polytope model (e.g. work by Bianchi) has the nodes of the network be fuzzy indefinite uncertain polyhedra. I find it interesting to imagine space built of such things. Whenever theory has several versions it provides opportunity researchers to learn something by investigating the extent to which they are equivalent or not equivalent. Quantum relativists are growing a new area of imagination.

C. A key step in zako model dynamics, according to Rovelli, was presented at conference by Bianchi in January 2010. It has conceptual elegance. The boundary state is a labeled network of measurements, enclosing a labeled foam of process.
There is this injective map of SU(2) reps into SL(2,C) reps, which they simply denote by the letter f. This map f contains all the calculation. There is a remarkable mental economy here: All the clutter is removed so that one can readily see what is happening.


======the rest of this post is just notes on sources========
polytope: http://arxiv.org/abs/1009.3402
Pirsa video: http://pirsa.org/10110052/ "Q'tum polyhedra in LQG"
polytope-related: http://arxiv.org/abs/1011.5628

aharo-bohm: http://arxiv.org/abs/0907.4388
Google "pirsa bianchi" and you get http://pirsa.org/11090125/
"Loop Gravity as the Dynamics of Topological Defects"
aharo-bohm related: http://arxiv.org/abs/1110.4833 (FGZ)

zako history: http://arxiv.org/abs/1004.1780
"I emphasize in particular the fact –pointed out by Eugenio Bianchi [2]– that the dynamics of the theory has a very simple and natural definition, largely determined by general physical principles. It is given by a natural immersion of SU(2) representations into SL(2,C) ones. A simple group theoretical construction (Eq. (45) below) appears to code the full Einstein equations.2"
Reference [2] is to Bianchi's talk at a January 2010 conference at the Sophia-Antipolis campus.
http://wwnpqft.inln.cnrs.fr/previous.html
http://wwnpqft.inln.cnrs.fr/pdf/Bianchi.pdf
"2 Note added in proofs: For a much simpler and straightforward presentation of the dynamics of the theory, which does not require the full intertwiner space machinery, see [3]."
Reference [3] http://arxiv.org/abs/1010.1939 is to a strip-down feynman-rules presentation developed in Moscow, see page 1 of “Simple model for quantum general relativity from loop quantum gravity.”
tom.stoer
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Nov21-11, 04:09 PM
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marcus, nearly everything what you are saying is related to the kinematical properties (and this is exactly where canonical LQG and SF are equivalent); but the issues are due to unknown or not well defined properties of the full dynamics (Hamiltonian, vertex, measure, ...)
marcus
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Nov21-11, 07:08 PM
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Quote Quote by tom.stoer View Post
marcus, nearly everything what you are saying is related to the kinematical properties (and this is exactly where canonical LQG and SF are equivalent); but the issues are due to unknown or not well defined properties of the full dynamics (Hamiltonian, vertex, measure, ...)
Quote Quote by marcus View Post
zako history: http://arxiv.org/abs/1004.1780
"I emphasize in particular the fact –pointed out by Eugenio Bianchi [2]– that the dynamics of the theory has a very simple and natural definition, largely determined by general physical principles. It is given by a natural immersion of SU(2) representations into SL(2,C) ones. A simple group theoretical construction (Eq. (45) below) appears to code the full Einstein equations.2"
Reference [2] is to Bianchi's talk at a January 2010 conference at the Sophia-Antipolis campus.
http://wwnpqft.inln.cnrs.fr/previous.html
http://wwnpqft.inln.cnrs.fr/pdf/Bianchi.pdf
"2 Note added in proofs: For a much simpler and straightforward presentation of the dynamics of the theory, which does not require the full intertwiner space machinery, see [3]."
Reference [3] http://arxiv.org/abs/1010.1939 is to a strip-down feynman-rules presentation developed in Moscow, see page 1 of “Simple model for quantum general relativity from loop quantum gravity.”
The whole idea of the Moscow feynman-rule presentation (1010.1939) was to show how to do the dynamics in a really concise streamlined way. By dynamics, I mean calculate (generalized) transtion amplitudes.

The core idea in the zako formulation is again transition amplitude dynamics. That is the motivation for the setup where you have a labeled network boundary state enclosing a labeled foam process.

Perhaps the most remarkable thing about the zako formulation is that it captures the dynamics in such a simple way---with the injection f: SU(2) reps --> SL(2,C) reps.
I speculate that this was contributed by Bianchi. Rovelli seems to be crediting him with the idea on the first page (third paragraph) of 1004.1780.
tom.stoer
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Nov22-11, 01:19 AM
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But the dynamics of SFs can neither be derived nor can it be shown to be equivalent to an underlying canonical structure. In that sense the two approaches are still incomplete.

The problem is that there are two possible ways to check (in a limited sense) whether dynamical structures are 'correct'. Either you can show their equivalence (which we can't for canonical LQG and SFs) or you can for at least one of them show that it agrees with experiments (which we can't, either). In addition the accessable semiclassical sector misses certain underlying features of full QG b/c the limit washes away hbar-corrections and may be blind for off-shell properties of the full theory.

That means that - yes - "... the dynamics of the theory has a very simple and natural definition, largely determined by general physical principles ... and appears to code the full Einstein equations" but that this is by far not sufficient to resolve all conceptual issues and prove that the QG regime itself is described correctly. The Einstein equations are nothing else but a preliminary test for consistency.

marcus, don't get me wrong: the new models are of course a major step forward, but they are still work in progress and it may very well be that they fail be provide a (mathematically) consistent and (physically) correct theory of quantum gravity.
marcus
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Nov22-11, 03:44 PM
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Quote Quote by tom.stoer View Post
marcus, don't get me wrong: the new models are of course a major step forward, but they are still work in progress and it may very well be that they fail be provide a (mathematically) consistent and (physically) correct theory of quantum gravity.
Just to make sure we understand each other, the new models I've been talking about are primarily the one that first appeared in April 2010 with the "New Look" paper that you quote in your post: 1004.1780. And then got a more thorough presentation in http://arxiv.org/abs/1102.3660 . I also mentioned two new approaches by Eugenio Bianchi that I called "aharo-bohm" and "polytopes". But these two are in very early stages. The main new model is the one that came out last year and is most fully presented in the Zakopane paper 1102.3660.

I think we both understand that this is not the same as what is often referred to as "EPRL" or as "EPRL-FK". It's what I've been calling "zako" for short

I agree that the zako formulation of LQG is a major step forward, as you say, and also fully agree that it is work in progress!

Indeed we do not know how physically correct it will turn out to be! Nature must decide that one. Rovelli, who is the main architect of this formulation says explicitly at the end of the main paper on it (1102.3660) that it may be wrong and he urges the researchers for whom the paper is written to try to show it wrong. But that is normal for him, in every survey talk he emphasizes the theory's tentativeness, and that there is plenty of work to be done on it.

That means that - yes - "... the dynamics of the theory has a very simple and natural definition, largely determined by general physical principles ... and appears to code the full Einstein equations" but that this is by far not sufficient to resolve all conceptual issues and prove that the QG regime itself is described correctly. The Einstein equations are nothing else but a preliminary test for consistency.
Indeed! Derivation from classical theory is no guarantee that a quantum theory is right.
And as you say consistency with the (classical) Einstein equations are no guarantee either!
As you say this is just a preliminary test.
That would also be true, obviously, if one were to formulate a canonical LQG, with hamiltonian, and show that it couid be derived from the classical by "quantizing" general relativity. All these things are merely preliminary tests.

The purpose of a theory is twofold---to give a new better way to think the world (in this case a new conceptual picture of geometry and cosmology) and to predict testable new phenomena. If it does not predict anything it is empty fantasy.

But I think you are not right when you say LQG cannot be tested. You say not by "experiments", but I assume you include cosmological observation on the same footing as ground-based experiment. The whole point of LQG, as far as I am concerned, is to predict future early universe observations as more and better instruments are launched into orbit.
That and of course to have a better way to think about (big bang, black hole and other) geometry--improved concepts.

http://arxiv.org/abs/1102.3660
qsa
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Nov22-11, 04:44 PM
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Quote Quote by tom.stoer View Post
but that this is by far not sufficient to resolve all conceptual issues and prove that the QG regime itself is described correctly. .
first, shouldn't the conceptual issues be an output of the theory. second, how do we know if QG regime is described correctly since there is nothing to compare. I guess you mean something else by those two things.
marcus
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Nov22-11, 06:54 PM
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I mentioned the issue of predicting new observations. One reason that early universe phenomena are a good "LABORATORY" for LQG and quantum relativity more generally is that quantum effects are associated with high energy density and with small scale, while the early universe bang or bounce is a HUGE MICROSCOPE.

Quantum effects, fluctuations, are enormously magnified and spread across the sky.

So one wants a quantum theory of geometry (interacting with matter) which predicts what we see and will see, as new intruments go into orbit.

This is the reason for many of the papers found by this InSpire search:
http://inspirehep.net/search?ln=en&l...100&sc=0&of=hb

Earlier I was using a Spires search, but Spires is being turned off and replaced by the new InSpire service. This search gets papers which appeared or were published in the four years 2008-2011.
In conjunction with LQG/LQC it uses the OR of categories "gravitational radiation", "inflation", "power spectrum", "cosmic background radiation", "primordial".
The papers are ranked by citation count.

I want to stress the Empiricism aspect. It is the final criterion. Of course we are happy that LQG seems able to reproduce predictions from the Einstein equation of GR---but ultimately this is of value only because the Einstein equation agrees with observations over a wide range of scales.
qsa
#27
Nov22-11, 07:21 PM
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So what does lqg predict exactly that the new missions should be looking for.
marcus
#28
Nov22-11, 08:33 PM
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Quote Quote by qsa View Post
So what does lqg predict exactly that the new missions should be looking for.
It doesn't have precise killer predictions on record yet! but it is getting there.
To see what some phenomenologists (not LQG people themselves but the uncommitted people whose business is figuring out how to test theories) have come up with, look at the most highly cited papers in that list that are by phenomenologists like Barrau, Grain, Wen Zhao, and their co-authors.

Do you remember what the next ESA CMB mission (after the current Planck mission) is called? I saw it discussed recently and lost the link.
[EDIT: It may have been canceled. I looked and could only find this:
http://sci.esa.int/science-e/www/obj...objectid=42839
There is no mission name attached. Just the bare study of a concept.]

Wen Zhao's paper refers to a proposed NASA mission tentatively called CMBpol, which as far as I know has not been funded. But Zhao et al also use data that has already been gathered (e.g. by WMAP) to see what constraints they can derive.

I'll suggest five sample papers, but these are not the most recent you can find using the InSpire search. Ranked by cite-count, these are #1, #7, #11, #12, and #21. Some I've read and some just barely glanced at and thought might interest you.

#1 (cited 43 times) http://inspirehep.net/record/812301?ln=en
Cosmological footprints of loop quantum gravity.
#7 (cited 21 times) http://inspirehep.net/record/798154
The gravitational wave background from super-inflation in Loop Quantum Cosmology.
#11 (cited 18 times) http://inspirehep.net/record/830146
Observational constraints on a power spectrum from super-inflation in Loop Quantum Cosmology.
#12 (cited 18 times) http://inspirehep.net/record/813856
Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation.
#21 (cited 8 times) http://inspirehep.net/record/861191
Constraints on standard and non-standard early Universe models from CMB B-mode polarization.

BTW one robust prediction of Loop cosmology is a bounce with a period of faster-than-exponential growth called "superinflation" during which the Hubble parameter actually increases very quickly, rather than (as in ordinary inflation) remaining approximately steady or gradually declining. You find this discussed authoritatively in Ashtekar papers. It does not require an inflaton or any exotic physics, it is just built in to the Loop bounce. So that is kind of distinctive and I see that a couple of the papers on the list explictly study the possible observational consequences of that superinflation bounce feature.
tom.stoer
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Nov23-11, 01:20 AM
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Quote Quote by marcus View Post
Just to make sure we understand each other, the new models I've been talking about are primarily the one that first appeared in April 2010 with the "New Look" paper ...
OK

Quote Quote by marcus View Post
Indeed! Derivation from classical theory is no guarantee that a quantum theory is right.
And as you say consistency with the (classical) Einstein equations are no guarantee either!
As you say this is just a preliminary test.
OK

Quote Quote by marcus View Post
That would also be true, obviously, if one were to formulate a canonical LQG, with hamiltonian, ...
A second, independent derivation of the dynamics + formal proof of equivalence would be more than a preliminary test, it would be a breakthrough.

Quote Quote by marcus View Post
But I think you are not right when you say LQG cannot be tested. You say not by "experiments", but I assume you include cosmological observation ...
The problem is that most cosmological observation will not address the deep QG regime but the semiclassical one which cannot serve as a litmus test. But this is a generic problem for QG and indicates somehow a paradigm shift away from close interaction between theory and experiment towards predominantly mathematical considerations. This is a major problem in (certain domains of) modern physics and - as far as I can see - there is absolurely no way out!
tom.stoer
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Nov23-11, 01:30 AM
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Quote Quote by qsa View Post
So what does lqg predict exactly that the new missions should be looking for.
Afaik - nothing!

- for high-energy cosmic radiation (GZK cutoff) there is no unambiguous, indisputable prediction (*)
- for energy dependent speed of light there is no unambiguous, indisputable prediction, either (*)
- for effects on light polarization there is no unambiguous, indisputable prediction, either
- LQG footprint in CMB due to primordial gravitational waves is only be derived within LQC (**)
- everything else (black holes, big bang) is neither fully understood nor directly testable

(* there were attempts to derive such effects but afaik the old models suffered from physically incorrect approximations, e.g. weave states which were not exactly in the kernel of the - largely unknwon - Hamiltonian)

(** this sems to be the most promising research area, but afaik it is unclear if full LQG will reproduce the LQC predictions)
marcus
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Nov23-11, 01:53 AM
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Quote Quote by tom.stoer View Post
...
- LQG footprint in CMB due to primordial gravitational waves is only be derived within LQC (**)
...
...

(** this sems to be the most promising research area, but afaik it is unclear if full LQG will reproduce the LQC predictions)
I agree that it is the most promising. It sounds to me like the big issue for you is whether full LQG will reproduce the LQC predictions.

I keep seeing research in that direction which seems to be making progress. So to satisfy you that LQG is as testable as LQC I need to start keeping better track of those particular papers.
==================================

BTW I should report that, contrary to my expectations and perhaps prejudices, when I had a look in the literature just now the FIRST author I found working on Lqg --> Lqc
was a guy working for Steve Carlip at UC Davis. Carlip is an excellent quantum relativist who has PhD students working in several QG including LQG, "shape dynamics", and CDT.

I heard Carlip talk on QG spontaneous dimensional reduction here at Berkeley and hold him in high regard. He has this student Chun-yen Lin.
PhD thesis --- http://arxiv.org/abs/0912.0554 (revised March 2011)
November 2011 followup --- http://arxiv.org/abs/1111.1766
Emergence of Loop Quantum Cosmology from Loop Quantum Gravity: Lowest Order in h
I don't know if the work is good, but I was surprised to see it uses the
canonical Lqg approach. You have to figure that Carlip (who is world class) is guiding this guy. He seems to be still at UC Davis even though probably now post-doc. Here is Chun-yen Lin's conclusion paragraph:
==quote 1111.1766==
This paper starts from the kinematical Hilbert space of loop quantum gravity, which describes the matter fields living in the dynamical quantum geometry of space. Using the model with a modified Hamiltonian constraint operator, we see that the dynamics of such a system reproduces FRW cosmology in the large scale limit. Further, the O(h0) corrections of the model for FRW cosmology conform with loop quantum cosmology in a specific scheme. Such a result is valuable, since it attributes the predictions of loop quantum cosmology to the fundamental principles in loop quantum gravity.
The result serves as a starting point to many possible future projects. First, one may explicitly construct the coherent states in the model to evaluate the emergent cosmology beyond O(h0), to get the quantum fluctuation corrections in the emergent cosmology. Second, one may try to derive more of the implications of loop quantum cosmology by applying the model to more realistic cosmological settings. Third, one may try to improve the model by incorporating the graph-topology changing feature in the Hamiltonian constraint operator, in the hope of deriving loop quantum cosmological models with μ = μ ̄.
==endquote==
Well nobody is saying that the job is finished! But I see he has made a little progress. He gets a bounce with his Lqg model and estimates the matter density and it higher than the density at bounce that Ashtekar gets in regular Lqc, but at least not grossly lower as one might have feared. Plenty of work left to do here.

And there are also other Lqg --> Lqc papers which I should gather to get an idea of how the research is going on this front.
tom.stoer
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Nov23-11, 05:26 AM
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Quote Quote by marcus View Post
I agree that it is the most promising. It sounds to me like the big issue for you is whether full LQG will reproduce the LQC predictions.
Well, the issue is whether "LGQ: first quantize - then reduce symmetry" is (in a certain approximation) equivalent to "LQC: first reduce symmetry - then quantize".
marcus
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Nov23-11, 12:26 PM
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Quote Quote by tom.stoer View Post
...
- LQG footprint in CMB due to primordial gravitational waves is only be derived within LQC (**)
...

(** this sems to be the most promising research area, but afaik it is unclear if full LQG will reproduce the LQC predictions)
Quote Quote by marcus View Post
I agree that it is the most promising. It sounds to me like the big issue for you is whether full LQG will reproduce the LQC predictions.

I keep seeing research in that direction which seems to be making progress...

...papers which I should gather to get an idea of how the research is going on this front.
Quote Quote by tom.stoer View Post
Well, the issue is whether "LGQ: first quantize - then reduce symmetry" is (in a certain approximation) equivalent to "LQC: first reduce symmetry - then quantize".
I'm not sure what you mean by "the" issue. There are probably several issues, some of greater importance. I think of vintage-2006 LQC as an heuristic--eventually to be replaced by full-LQG cosmology (or retained as an approximation if it can be shown useful in that role.)

I see that beginning to happen in a number of papers from the Ashtekar and Marseille groups. They already have some preliminary results indicating a bounce which is LIKE the usual LQC bounce (using spin foam or other LQG with some restrictions which one then tries to progressively relax.)

One does not have to symmetrize first! The assumptions of homogeneity and isotropy can be weakened, gradually. This is a common theme in current research as I expect you know. Various means are used to make the problem tractable.

I judge that it is a "done deal" that the full theory will yield bounce predictions which are, in any case, LIKE, those obtained from the usual LQC. I would not necessarily expect them to be precisely the same, just similar. The Loop bounce is robust. So then the phenomenologists can work with full-LQG cosmology and work out observational tests.

The restrictive version, LQC, would then be relegated to a secondary role---it might continue as a useful approximation or it might not---such details are hard to foresee.

But on conceptual grounds I would say that the "symmetrize first" issue you mention is of only passing or temporary importance. What I consider of prime importance are cosmological tests of the full theory. This involves ongoing work that a number of people are involved with where they use the full theory under restrictions which are (if all continues to go well) progressively relaxed.

In any case that's how I view the main conceptual issues here. I should gather some links to the work on spin foam cosmology and perhaps some of the other papers that relax the traditional uniformity assumptions (iso and homog).
tom.stoer
#34
Nov23-11, 01:22 PM
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With "LQC: first reduce symmetry - then quantize" I mean that in LQC you first constrain the system from infinitly many to finitly many degrees of freedom which you then quantize. It is by no means clear whether the LQG approach where you have to study a symmetric subsector of the full theory containing infinitly many variables will lead to the same predictions.
marcus
#35
Nov23-11, 02:13 PM
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Quote Quote by tom.stoer View Post
With "LQC: first reduce symmetry - then quantize" I mean that in LQC you first constrain the system from infinitly many to finitly many degrees of freedom which you then quantize..
Of course I understand that, but it's good you mention it in case someone is reading who is new to the subject.

==quote continued==
It is by no means clear whether the LQG approach where you have to study a symmetric subsector of the full theory containing infinitly many variables will lead to the same predictions
==endquote==

Well the trend in LQG/spinfoam cosmology is to relax the symmetry requirement. They get away from string isotropy and homogeneity, and see whether they continue to see a bounce.

I'm not sure why you say you would have to study a "symmetric subsector" of the theory.
That would be if you thought it was important to imitate LQC with the full theory.
As I see it, the main thing is not to imitate or show equivalence to other versions, but to get definite testable predictions from some formulation (like Zako) of the full theory. The most obvious being if you get a bounce. That seems to be the way the research is going.
tom.stoer
#36
Nov23-11, 02:45 PM
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I agree that in the end a symmetry reduction in LQG is not what you really want, but perhaps it's easier to motivate LQC by some clever trick than to derive a bounce in full LQG. If this is the case than the symmetry reduction in LQG can at least provide some hint that the bounce in LQC is reasonable.

A simple example why I think this is important: in QED applied to a hollow sphere you find a casimir force. In QM with a finite number of degrees of freedom no similar effect is known..


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