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- Thread starter tom.stoer
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- #77

atyy

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The figure on p21 of http://arxiv.org/abs/1102.3660. "Continuous limit" is not the classical limit.To which sentence or equation are you referring to?

In http://arxiv.org/abs/1108.2258v1 it seems that they know how to define the classical limit.

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- #78

atyy

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I think the idea is that if the "continuous limit", as Rovelli calls it in the figure on p21 of his Zakopane lectures, exists, then the theory is triangulation independent and unique in that sense. As I understand, the existence of such a limit is unknown at the moment.

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- #79

atyy

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In asymptotic safety, theories which have a continuum limit lie on a critical manifold, and are attracted to a fixed point on that manifold. Parameters must be tuned so that the theory is one which is on the critical manifold. The predictivity of the theory depends on the dimension of the critical manifold. As http://www.percacci.it/roberto/physics/as/faq.html" [Broken] explains "we want to use the condition of having a good UV limit as a way of selecting physically acceptable trajectories. From this point of view the ideal case would be that in which a single trajectory reached the fixed point. This would pin down the theory uniquely."

However, http://arxiv.org/abs/1107.2310" [Broken] envisages that his notion of a continuum limit is different and "does not require tuning a parameter in the action to a critical value".

However, http://arxiv.org/abs/1107.2310" [Broken] envisages that his notion of a continuum limit is different and "does not require tuning a parameter in the action to a critical value".

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That's a conjecture! Another one of many.In conventional QG, the continuum limit is asymptotic safety.

- #81

atyy

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Yes, of course (ie. the existence of asymptotic safety is unknown).That's a conjecture! Another one of many.

- #82

atyy

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Hmm, Rovelli seems to make different conjectures in the figure of of p21 of http://arxiv.org/abs/1102.3660 and in http://arxiv.org/abs/1107.2310. In the Zakopane lectures, it seems that the continuum and classical limits must commute, but in Ditt-invariance, maybe not, at least not for recovering some regime of GR.

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- #83

marcus

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Atyy I think you are over-straining yourself in putting your own interpretations on the figure on page 21. At that point there little or no substantive discussion of the figure to support any interpretation. Discussion of the results on limits are found elsewhere in the paper.Hmm, Rovelli seems to make different conjectures in the figure of of p21 of http://arxiv.org/abs/1102.3660 and in http://arxiv.org/abs/1107.2310. In the Zakopane lectures, it seems that the continuum and classical limits must commute, but in Ditt-invariance, maybe not, at least not for recovering some regime of GR.

As you point out, the same diagram occurs in 1107.2310. And it is accompanied there by a bit more discussion, however I woud not call that conclusive either.

The same illustration occurs with considerably more discussion on page 5 of a new August 2011 paper. I would suggest you have a look.

http://arxiv.org/abs/1108.0832

Carlo Rovelli

(Submitted on 3 Aug 2011)

The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions amplitudes and their truncations.

7 pages

The caption there is:"TABLE II. Continuous and classical limits in quantum gravity."

A diagrammatic framework or table like that does not say anything by itself, it serves as a focus for investigation and topic of discussion. A nucleus around which ideas and understanding develop.

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- #84

atyy

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Don't Eq 7,8,9 require the limits commute?Atyy I think you are over-straining yourself in putting your own interpretations on the figure on page 21. At that point there little or no substantive discussion of the figure to support any interpretation. Discussion of the results on limits are found elsewhere in the paper.

The same figure occurs in 1107.2310, as you point out, with more discussion, however I woud not call that conclusive either.

The same figure occurs as "Table II" with considerably more discussion on page 5 of a new August 2011 paper. I would suggest you have a look.

http://arxiv.org/abs/1108.0832

On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit

Carlo Rovelli

(Submitted on 3 Aug 2011)

The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions amplitudes and their truncations.

7 pages

A diagrammatic framework or table like that does not say anything by itself, it serves as a focus for investigation and topic of discussion. A nucleus around which ideas and understanding develop.

- #85

marcus

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It's risky for you (or anybody) to put your own non-expert spin on stuff when it is not actually spelled out. You are pointing our attention at this diagram on page 21 of Zako Lectures.Don't Eq 7,8,9 require the limits commute?

Equations 7,8,9 are somewhere else, page 4, so 17 pages away, with other discussion. If you mean Equations 7,8,9 in Zako. But they don't have anything to do with the topic.

Or maybe you mean equations 7,8,9 in the new paper that goes into much more detailed discussion of that topic, with that picture of the continuous and classical limits.

It would make sense to be focusing on the new paper http://arxiv.org/abs/1108.0832

But if you mean the new paper, then equations 7,8,9 do not refer to Table II at all!

So I am left without the slightest idea of what you are talking about.

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atyy

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"I have given a tentative overall picture of the structure of the theory, the observables, and the form of the continuous and classical limits."

"Finally, not much is known about the effect of the radiative corrections on this structure (for partial results, see [31, 54–56]). These are finite in the deformed version of (27) [17, 18] but this does not make them irrelevant. The main open problem in quantum gravity, I think, is to study their effect on the convergence of the continuous limit."

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marcus

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Yes! I was just about to quote that myself. I think it is a good explicit indicator of where the program is at present on the important issue of continuous limit.

"I have given a tentative overall picture of the structure of the theory, the observables, and the form of the continuous and classical limits."

"Finally, not much is known about the effect of the radiative corrections on this structure (for partial results, see [31, 54–56]). These are finite in the deformed version of (27) [17, 18] but this does not make them irrelevant. The main open problem in quantum gravity, I think, is to study their effect on the convergence of the continuous limit."

I think we have to add this August paper "On the structure" to our list. I hate to increase the number of pages of the "review of current status" but it is only 7 pages so here we are

That would make the combined essential "current status" review be

1102.3660 + 1108.2258 +1105.2212 + 1108.0832

Zakopane lectures+Emergence of gravity+Cosmological constant + On the structure

Rovelli + Magliaro Perini + Han + Rovelli

33 pages +6 pages +6 pages + 7 pages

That brings us up to 52 pages. I have been thinking for some time that I should include "On the structure" in our current status review. But Tom said at the outset that he did not want a LIST of papers, he wanted something like a single review paper compact package. So I was reluctant to include this one. Four papers begins to look like a list

But maybe we are forced to include this because it is the up to date discussion of work in progress on understanding and defining the continuum limit (considerable evidence now supporting the conclusion that the classical limit is right.)

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Don't Eq 7,8,9 require the limits commute?

Istarted to skim that paper lat night but only got a some of pages before I fell asleep, but IMHO, what Rovelli has done is converting the conceptual problem (that he IMHO previously ignored) into technical issue where in the end the same problem comes back.Rovelli:

...

The main open problem in quantum gravity, I think, is to study their effect on the convergence of the continuous limit."

It's easy to get the feeling reading rovelli's paper, looking at "classical limits" and "continuum limit" of refinement as a technical or mathematical problems. But I don't think it is just that.

For the discussion, to add my personal conceptual interpretation of those limits, from my own biased view:

The continuum limit corresponds to the infinite observer mass limit (ready also asymptotic observables). Because in my logic, no finite observer, can count infinitely many "possibilities". This is why I think that the "continuum limit" corresponds just to a limiting case of observables. The reason is that Rovelli transformed the "complexity of an observer" into a technical think where treat it just as a mathematics with no physical meaning.

The classical limit OTOH, corresponds also to the system complexity (ie. the Observed) going to infinitiy.

Conceptually, then both the observer and the observed are increasing in complexity. From the point of view of counting, it seems the results is entirely dependent on exactly how the limit is taken. And the way rovelli presents this (as a technical issue) there seems to be no physics in this choice.

I'd rather like to see a reworking here, where the complexity of the observer imposes truncation of C, that is physical. If you want to study C -> infinity, fine, but then it means that you are looking from a large and larger observer. But I'd say the more interesting perspective is to see if from the perspective of a finite observer.

Somehow, I have a decent feeling that the problem Rovelli ends up with isn't much difference from the original one that I got the impression he ignored?

/Fredrik

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Isn't it already clear, given how LQG is constructed (as finding a specific stance to GR, where it's easier to defined the PI without running into infinites) that the way limits are taken do matter? Isn't that somehow the whole point?

If so, shouldn't there in fact be physics in the choice of ordering the coupling of the theory?

And if this ordering of couplings, is made dependend on the observers complexity, then it seems we have a quite intersting candicate for explaning interactions since the coupling between A-B intercating seen from C, naturally depends on te mass of A and B as well as C.

I think some of the things that looks like technical issues here, due to the analysis of choice here, might better be understood as having physical significance.

Edit: A hunch from this perspective is that the above limiting procedures can't be understood properly without seeing it together with theory scaling and mass generation. Scaling the observer and the system up, IMO corresponds to considering how their masses are scaled up; and how that affects their interactions. In there, I think there is interesting physics having to do with mass generation.

/Fredrik

If so, shouldn't there in fact be physics in the choice of ordering the coupling of the theory?

And if this ordering of couplings, is made dependend on the observers complexity, then it seems we have a quite intersting candicate for explaning interactions since the coupling between A-B intercating seen from C, naturally depends on te mass of A and B as well as C.

I think some of the things that looks like technical issues here, due to the analysis of choice here, might better be understood as having physical significance.

Edit: A hunch from this perspective is that the above limiting procedures can't be understood properly without seeing it together with theory scaling and mass generation. Scaling the observer and the system up, IMO corresponds to considering how their masses are scaled up; and how that affects their interactions. In there, I think there is interesting physics having to do with mass generation.

/Fredrik

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- #90

atyy

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I think Rovelli's http://arxiv.org/abs/1108.0832 is a good concise summary of the present position of LQG. Two things that I think are important are also noted by him. First, the Immirzi to zero for recovery of GR is a kludge, although certainly reasonable (footnote 7). Second, the existence of the continuum limit, or the full theory in fig 2 is now the key question (Section VI).Yes! I was just about to quote that myself. I think it is a good explicit indicator of where the program is at present on the important issue of continuous limit.

I think we have to add this August paper "On the structure" to our list. I hate to increase the number of pages of the "review of current status" but it is only 7 pages so here we are

That would make the combined essential "current status" review be

1102.3660 + 1108.2258 +1105.2212 + 1108.0832

Zakopane lectures+Emergence of gravity+Cosmological constant + On the structure

Rovelli + Magliaro Perini + Han + Rovelli

33 pages +6 pages +6 pages + 7 pages

That brings us up to 52 pages. I have been thinking for some time that I should include "On the structure" in our current status review. But Tom said at the outset that he did not want a LIST of papers, he wanted something like a single review paper compact package. So I was reluctant to include this one. Four papers begins to look like a list

But maybe we are forced to include this because it is the up to date discussion of work in progress on understanding and defining the continuum limit (considerable evidence now supporting the conclusion that the classical limit is right.)

Personally, I'd say the continuum limit is even more important than getting GR, since string theory shows we don't need gravity to get gravity.

Also, I believe the key points in this latest review were in remarks made 3 years ago by Conrady and Freidel. I think the key advance since then is the proposal for the continuum limit made by Rovelli, and further expanded on by Rovelli and Smerlak. I'm also very partial to the work from Lewandowksi and colleagues, but I don't know how that relates to Rovelli and Smerlak's proposal. Tantalizingly, Lewandowski says in his latest paper that he thinks someone (not necessarily himself) knows the answer!

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- #91

marcus

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Here's another index we've been tracking:

LOOP RESEARCH BY YEAR (loop quantum gravity, loop quantum cosmology, spin foam)

2005 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2005&d2d=&d2m=&d2y=2005&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (42 found)

2006 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2006&d2d=&d2m=&d2y=2006&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (77 found)

2007 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2007&d2d=&d2m=&d2y=2007&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (120 found)

2008 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2008&d2d=&d2m=&d2y=2008&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (142 found)

2009 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2009&d2d=&d2m=&d2y=2009&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (145 found)

2010 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2010&d2d=&d2m=&d2y=2010&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (152 found)

2011 http://inspirebeta.net/search?ln=en&as=1&m1=e&p1=quantum+cosmology:+loop+space&f1=keyword&op1=o&m2=e&p2=quantum+gravity:+loop+space&f2=keyword&op2=o&m3=e&p3=spin:+foam&f3=keyword&action_search=Search&dt=&d1d=&d1m=&d1y=2011&d2d=&d2m=&d2y=2011&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (139 as of 26 Sept, annualized > 180)

To illustrate, http://howlonguntil.net/ 268 days, so in this case annualized rate is 139*365/268 = 189

- #92

marcus

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In September two more papers appeared which significantly advance the current status. Now we have a problem. Are there any of the original four that we can drop because now superseded? How to keep this current status picture compact?...

I think we have to add this August paper "On the structure" to our list. I hate to increase the number of pages of the "review of current status" but it is only 7 pages so here we are

That would make the combined essential "current status" review be

1102.3660 + 1108.2258 +1105.2212 + 1108.0832

Zakopane lectures+Emergence of gravity+Cosmological constant + On the structure

Rovelli + Magliaro Perini + Han + Rovelli

33 pages +6 pages +6 pages + 7 pages

That brings us up to 52 pages. I have been thinking for some time that I should include "On the structure" in our current status review. But Tom said at the outset that he did not want a LIST of papers, he wanted something like a single review paper compact package. So I was reluctant to include this one. Four papers begins to look like a list

...

The two important new papers are by Dittrich et al and by Bianchi Ding.

Bianchi Ding seems to pretty much take care of the Regge limit of LQG. Could it maybe replace the Magliaro Perini "Emergence of gravity" 1108.2258 that we have here? Let's not do that. Let's include ALL these papers for the time being and then maybe edit the list down later.

Dittrich et al pursues the ideas of coarse-graining and numerical analysis---basically understanding how to do extensive lattice computations with spin nets and foams.

http://arxiv.org/abs/1109.4927" [Broken]

It is a beautiful paper: thoughtful and lucid, and at the same time driving forward. Or so I think anyway---just a bystander's impression.

First let's look at Bianchi Ding http://arxiv.org/abs/1109.6538" [Broken]

"Our main result is the following. We consider the limit, introduced in [13] and discussed in [9, 10], where the Barbero-Immirzi parameter is taken to zero γ → 0, and the spin of the boundary state is taken to infinity j → ∞, keeping the size of the quantum geometry A ∼ γj finite and fixed. This limit corresponds to neglecting Planck scale discreteness and twisting effects, at large finite distances. In this limit, the two-point function we obtain exactly matches the one obtained from Lorentzian Regge calculus [38]. We therefore extend to Lorentzian signature the results of [13]."

Reference [13] is a 2009 paper by Bianchi Magliaro Perini.

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- #93

marcus

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For the moment I'm finding it hard to cover the current LQG status in a concise compact way. Given the potential importance of the September paper by Eugenio Bianchi and You Ding, I want to add it to our short list of papers. We may be able to edit the list down later but at present I do not see how.

That makes the combined essential "current status" review consist of:

1102.3660 + 1108.2258 + 1109.6538 + 1105.2212 + 1108.0832

http://arxiv.org/abs/1102.3660" [Broken]

Rovelli + Magliaro Perini + Bianchi Ding + Han + Rovelli

33 pages +6 pages +13 pages +6 pages +7 pages

and brings us up to 65 pages.

That makes the combined essential "current status" review consist of:

1102.3660 + 1108.2258 + 1109.6538 + 1105.2212 + 1108.0832

http://arxiv.org/abs/1102.3660" [Broken]

Rovelli + Magliaro Perini + Bianchi Ding + Han + Rovelli

33 pages +6 pages +13 pages +6 pages +7 pages

and brings us up to 65 pages.

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- #94

tom.stoer

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You are right, when looking at you September poll it becomes clear that it's hard to vote for one specific LQG paper (in the past it was hard to vote for one single QG paper, now even for one specific approach there are many interesting new aspects).

Besides the papers you already have in your list I would add

And of course Han's paper on the cc - especially b/c it shows that even the basic algebraic structure to be used is still under discussion.

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marcus

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tom.stoer

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marcus, honestly: do you really think that this is the *Current status of LQG*? It seems that it is a very active research program, but at the same time the big picture is (partially) missing. I think we don't know (yet) how to fit these puzzle pieces together:

- canonical and covariant formulation

- renormalization in the canonical approach (what is H?), renormalization a la Kadanoff, ...

- asymptotic safety

- cc as running parameter in the asymptotic safety approach, cc as a quantum deformation

- matter on top of LQG vs. emerging braided matter ...

- ...

I am afraid that the situation becomes comparable to string theory: plenty of indications, little hard evidence, no experimental facts. Maybe we are simpy not able to do physics w/o experiments!

- canonical and covariant formulation

- renormalization in the canonical approach (what is H?), renormalization a la Kadanoff, ...

- asymptotic safety

- cc as running parameter in the asymptotic safety approach, cc as a quantum deformation

- matter on top of LQG vs. emerging braided matter ...

- ...

I am afraid that the situation becomes comparable to string theory: plenty of indications, little hard evidence, no experimental facts. Maybe we are simpy not able to do physics w/o experiments!

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- #97

atyy

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I think there has to be an exploration of language so that when new data does come we'll be more ready to describe it.I am afraid that the situation becomes comparable to string theory: plenty of indications, little hard evidence, no experimental facts. Maybe we are simpy not able to do physics w/o experiments!

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atyy

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http://arxiv.org/abs/1109.4927" [Broken] which describes the link between the two: "We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement." Dittrich et al explicitly say "In this work we will therefore apply the Migdal-Kadanoff scheme [59, 60] and the tensor network renormalization (TNR) method [61, 62]."

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- #99

marcus

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You are right, when looking at you September poll it becomes clear that it's hard to vote for one specific LQG paper (in the past it was hard to vote for one single QG paper, now even for one specific approach there are many interesting new aspects).

Besides the papers you already have in your list I would addCoarse graining methods(which is the first attempt towards Kadanoff's block spin approach in the LQG context; I was waiting for something like that for years),Emergent Braided Matter(which is still an active but unfortunately small and slow research project) and of courseThiemann's paperstrying to link spin foams and the canonical approach.

And of course Han's paper on the cc - especially b/c it shows that even the basic algebraic structure to be used is still under discussion.

There is a lot of truth in what you say. First of all, as you indicate, LQG is a research program. When we try to describe the current status of LQG we are talking about themarcus, honestly: do you really think that this is theCurrent status of LQG? It seems that it is a very active research program, but at the same time the big picture is (partially) missing. I think we don't know (yet) how to fit these puzzle pieces together:

- canonical and covariant formulation

- renormalization in the canonical approach (what is H?), renormalization a la Kadanoff, ...

- asymptotic safety

- cc as running parameter in the asymptotic safety approach, cc as a quantum deformation

- matter on top of LQG vs. emerging braided matter ...

- ...

I am afraid that the situation becomes comparable to string theory: plenty of indications, little hard evidence, no experimental facts. Maybe we are simpy not able to do physics w/o experiments!

That covers a number of different initiatives, some more active than others. Some approaches can drop out of sight for a while---seem hardly to exist---and then regain prominence and importance.

For me, the picture goes through periods when it looks focussed and coherent, and then other times when it seems more fragmented and in flux.

I can't serve as anything more than an onlooker with my own personal impressions, so you mustn't take it too seriously when I say that I don't see much future for some things that both you and other smart informed people see as interesting. But I see OTHER new formulations that I think could challenge the dominant "Zakopane" version.

I think the expression is "dark horse"----the contender nobody noticed was even in the race.

This alternative formulation intrigues me right now: http://arxiv.org/abs/0907.4388 . it may be something that you noticed and commented on two years ago, but I did not realize at the time was interesting.

What sparked my interest in this alternative Lqg formulation is this recent talk:

http://pirsa.org/11090125

given 21 September, titled

...Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the [prospect] of formulating the Spin Foam dynamics as the local interaction of topological defects.

This talk is based on 0907.4388 and has 24 very good slides (in fact my computer cannot get the Flash video so all I can see are the slides!) Slide 22 has an interesting point:

Appealing scenario for Quantum Gravity

No trans-Planckian d.o.f. because topological (and therefore finite) at small scales

at larger scales, finitely many d.o.f. which can be described effectively in terms of a local quantum field theory.

In the Perimeter pdf, slides are repeated so there are 48 pdf pages and this slide #22 does not appear until page 41. So you have to scroll down a lot to get there.No trans-Planckian d.o.f. because topological (and therefore finite) at small scales

at larger scales, finitely many d.o.f. which can be described effectively in terms of a local quantum field theory.

I suppose that this Topological Defect approach is not automatically unfriendly to braids. But one could also see them as two rival approaches, both very much on the periphery with only a few people currently attending to them. Bad luck that PIRSA, out of all its great collection of video lectures, just managed to lose or spoil this one, or that it just happens to be the one that my computer cannot read.

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marcus

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I think there has to be an exploration of language so that when new data does come we'll be more ready to describe it.

I think you are right about being more ready. It does not matter if the LQG program has several different approaches being worked on. Not all the pieces need to be connected all times. What matters is that somebody has an approach which they are willing to say "This is the theory." and which they can calculate with and confront with observation.http://arxiv.org/abs/1109.4927" [Broken] are in the spirit of Kadanoff's "block spin renormalization"...

In the case of Loop Gravity, I expect modeling of the cosmological bounce, calculating features of the CMB ancient light, and confrontation with polarization data from whatever mission comes after Planck. (Or possibly even with data from the current Planck mission.)

I know that Dittrich et al is largely about Migdal-Kadanoff method and they say a lot about the ability to calculate. What I am curious about is calculating WHAT? Can you or anyone help me imagine what kind of massive lattice calculation might be in view? Can you see how this might connect up with CMB observations, for instance, or with some other data?

Maybe it could lead to simulations of the bounce? Or or of black hole collapse?

I'm convinced that Dittrich's work will play a critical role, I just wonder what that role might be, more specifically. How do you picture it?

BTW Atyy, Eugenio Bianchi in his 21 September PIRSA talk referred to something of XG Wen.

It is on one of those slides. I checked: slide 23/24 on page 46/48 of the PDF

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