Clear concise Loop survey as of January 2012

[tom.stoer]

... and I'm curious to know what you think is incorrect about this particular version of Loop gravity.

To say that clearly: I don't simply say that the model is wrong; what I am saying is that the derivation of the model has some serious flaws (*), therefore I believe that the resulting model is physically wrong, i.e. has a dynamics which cannot be related to 'quantization of GR'. For some toy models where the correct quantization i.e. construction of H, PI and a map between them it is exactly known, one knows that repeating the flaws (*) leads to physically unacceptable PIs. This is a strong hint that EPRL is not correct.

Most of the problems are discussed in http://arxiv.org/abs/1112.1961v2
Some alternatives are discussed in http://arxiv.org/abs/1201.4247v1

If you ignore the construction and take EPRL as god-given, then there seems to be no problem; it's a consistent definition of model; the question why it should be the correct model is still open.

 

[atyy]

What exactly is the problem with Thiemann's constraint? Is it inconsistent? Or is it consistent but not known to give the Einstein equations in the classical limit?

 

[tom.stoer]

Do you mean Thiemann's "old approach" or his new work?

Regarding the old approach it is clear that the action of H on physical states creates only trivial new vertices carrying zero volume. This ensures consistency of the constraint algebra but is physically not acceptable.

Regarding the new papers I have to admit that I haven't studied them in detail, unfortunately.

 

[atyy]

Yes, his old work.

Is the old Thiemann constraint unphysical because it doesn't implement the Dirac quantization? Or is it possible to implement the Dirac quatization and still be unphysical?

 

[tom.stoer]

The old constraint does not obiously violate the Dirac quantization; the algebra closes, but non-trivially, i.e. commutators of constraints are linear combinations of constraints but with "constraint dependent structure functions"; that means that operator ordering and regularization will become ambiguous.

The first problem is the step-by-step approach to constraint implementation. Usually you have a set of first class constraints, you quantize and regularize them and then you implement them (all at once) as constraints on physical states. Doing it that way guarantuees that you can check the consistency of the regularization and operator ordering with the constraint algebar in each step.

Doing it like Thiemann et al. in a stepwise approach first all constraints but H go away leading to the kinematical Hilbert space of spin networks; what remains is H. The linear combinations of constraints with constraint dependent structure functions calls for a deeper understanding; one may worry that the regularization and operator ordering of H is inconsistent, but this inconsistency doesn't show up on-shell in the kinematical Hilbert space; in addition there is no control on the off-shell closure of the constraint algebra b/c the other constraints have been implemented already.

So the first problem is that inconsistencies in H cannot be checked against the symmetries of the theory. I do not know whether Thiemann's master constraint approach has changed this in a fundamental manner.

The second problem is that the last constraint to be implemented is H; when you regularize it a la Thiemann you find that its quantum version suffers from being unphysical; of course one may suspect that it is related to the first problem.

The general problem is that there are many different inequivalent constructions of H, all of them can be motivated somehow (Rovelli found one that 'creates volume' and therefore could be physically acceptable), but all suffer from the stepwise approach (all of them act in the same kinematical Hilbert space) which means that the first problem is never addressed.

I do not even know if there is consensus whether the first problem is a problem at all. It's like the EPRL model: you have something that has some strange features (physically) and a rather weird construction (mathematically). Therefore you may suspect that both are related, but the theory doesn't provide tools via which you can double-check.

 

[atyy]

Ok, I'm confused - Thiemann's old approach isn't his master constraint?

 

[marcus]

To say that clearly: I don't simply say that the model is wrong; what I am saying is that the derivation...

Thanks for the reply. The Zako spinfoam QG theory whose definition I just now quoted is not derived. As I recall this point was made explicitly up front in the Lectures. Maybe we should carefully distinguish between this and the pre-2010 EPRL.

Most of the problems are discussed in http://arxiv.org/abs/1112.1961v2
Some alternatives are discussed in http://arxiv.org/abs/1201.4247v1
​

But neither paper addresses the Zako spinfoam QG theory I was talking about. I can only find citation to previous EPRL and stuff like that. It does not seem relevant.

If you ignore the construction and take EPRL as god-given, then there seems to be no problem; it's a consistent definition of model; the question why it should be the correct model is still open.​

I assume that by "construction" you mean derivation. But the theory I'm asking you about is not derived. It has no derivation. So there is no "construction" to be ignored. Of course like any man-made theory it has a mathematical construction (basically due to Eugenio B, or completed by him, it is said) and it's a rather nice one I think. But that comes under the "consistent definition" you talk about.

I am not sure what exactly you mean when you say EPRL, since the references you give never seem to cite or discuss the spinfoam theory I am asking you about.

Maybe we should use a different abbreviation for post-2010 spinfoam as in Zakopane Lectures---from which I quoted the definition in post #35. Should we say ZQG?
Or ZLQG? Z for Zakopane.

I'm really interested in your thoughts and impressions about ZQG, not about EPRL. Like e.g. the fact that there is nothing in the model called "simplicity conditions" (but surely the same effect must essentially be achieved by a different route. Or no?)

That's an interesting question and I wonder what your take on it is. Is the effect of the pre-2010 EPRL "simplicity" requirement achieved in ZQG even though not imposed as such?
========================
For handy reference I'll copy your full post:

To say that clearly: I don't simply say that the model is wrong; what I am saying is that the derivation of the model has some serious flaws (*), therefore I believe that the resulting model is physically wrong, i.e. has a dynamics which cannot be related to 'quantization of GR'. For some toy models where the correct quantization i.e. construction of H, PI and a map between them it is exactly known, one knows that repeating the flaws (*) leads to physically unacceptable PIs. This is a strong hint that EPRL is not correct.

Most of the problems are discussed in http://arxiv.org/abs/1112.1961v2
Some alternatives are discussed in http://arxiv.org/abs/1201.4247v1

If you ignore the construction and take EPRL as god-given, then there seems to be no problem; it's a consistent definition of model; the question why it should be the correct model is still open.

==========================

BTW one nice thing about Ashtekar's historical/overview survey here is that it was the opening talk at Zakopane and will serve as the introductory chapter of the book of Proceedings. So among other things, Ashtekar's intro repeatedly refers to Rovelli's Z Lectures which are to be bound in the same volume, as well as to chapters/talks by others at the Zakopane QG school. Whenever Ashtekar is talking about spinfoam he naturally refers to the ("ZQG") chapter by Rovelli. So Ashtekar is pointing the reader at what I'm called ZQG to distinguish it from earlier spinfoam models often called EPRL.
I hope they do go ahead and, as Ashtekar indicates, prepare a bound volume of proceedings. It could turn out to be a useful book.

BTW this talk Eugenio gave in January 2010 at Sophia-Antipolis may help clarify the history or make the connections. The f_γ notation appears around slides 23, 24. But it seems not yet to denote quite what it came to stand for later that year: a mapping from FUNCTIONS on SU(2) to functions on SL(2,C).
http://wwnpqft.inln.cnrs.fr/pdf/Bianchi.pdf

 

[tom.stoer]

The Zako spinfoam QG theory whose definition I just now quoted is not derived. As I recall this point was made explicitly up front in the Lectures.

Yes, Rovelli was rather clear about that point, but of course he is wrong ;-)
- his model is not derived in all details, but inspired in many ways by several related derivations
- I strongly believe that the steps where a derivation is missing are the most problematic ones

Maybe we should carefully distinguish between this and the pre-2010 EPRL.

Perhaps I miss something, so let me ask you: what is the major difference between the "pre2010 EPRL" and the Zako-EPRL? My impression always was that Zako-EPRL does not address the fundamental issues of EPRL (and FK).

But the theory I'm asking you about is not derived. It has no derivation.

As I said: I don't think that there is not any (partial) derivation; and I don't think that the missing (complete) derivation is a benefit - it's a drawback.

I'm really interested in your thoughts and impressions about ZQG, not about EPRL. Like e.g. the fact that there is nothing in the model called "simplicity conditions"

w/o derivation that's difficult to say b/c the simplicity constraints would show up in delta functions and the PI measure.

 

[marcus]

- his model is not derived in all details, but inspired in many ways by several related derivations
- I strongly believe that the steps where a derivation is missing are the most problematic ones​

As he says, it is inspired by several derivations.
There are no isolated "steps" or "details" apart from which it is derived.

Perhaps I miss something, so let me ask you: what is the major difference between the "pre2010 EPRL" and the Zako-EPRL? My impression always was that Zako-EPRL does not address the fundamental issues of EPRL (and FK).
​

No explicit equation called "simplicity constraint" is needed. That is a big difference. In an earlier post I already called your attention to the f_γ mapping from functions on SU(2) to functions on SL(2,C).

 

[tom.stoer]

marcus, please have a careful look at Rovelli's paper:

http://arxiv.org/abs/1102.3660
Zakopane lectures on loop gravity

On page 3 he presents the definiton for Z (eq. 3); then he writes

"The expression (3) was found independently and developed
during the last few years by a number of research
groups [15-21], using dierent path and different
formalisms (and a variety of notations). Different definitions
have later been recognized to be equivalent. The
resulting theory is variously denoted as EPRL model,
EPRL-FK model, EPRL-FK-KKL model, new BC
model ... in the literature. I call it here simply the partition
function of LQG. The presentation I give below does
not follow any of the original derivations."

So based on this I can't see anything that is new compared to

[15] arXiv:gr-qc/9709028.
[16] arXiv:0705.2388.
[17] arXiv:0705.0674.
[18] arXiv:0708.1236.
[19] arXiv:0708.1595.
[20] arXiv:0711.0146.
[21] arXiv:0909.0939.

On page 14 he writes

"general relativity is BF theory plus the simplicity constraints."

So again he stresses the importance of these auxiliary condition introduced by hand to break the symmetry of the topological BF theory.

In (135) he explicitly introduces the constraint K+γL=0 and refers to its kernel or "subspace".

You will see that (135) is core to the whole construction, but that compatibility of constraints, second-class constraints etc. are never discussed. So this Zako-EPRL has the same weak-points as all prior references [15-21].

Regarding his map f_γ: I don't see how this map changes the situation for consistency of (135). On page 14 he writes

"The map f_γ implements the simplicity
conditions, since it maps the states to the space where
the simplicity conditions (51) hold;"

This is true w/o doubt.

The problem is not the implementation of (51) itself, but the consistency of (135) with other constraints. This issue is simply not discussed, nowhere!

It should be clear that adding a new constraint changes the symplectic structure of the theory. Studying the the algebra of (135) with other constraints (G,D and H) one finds that (135) is second class and must be implemented a la Dirac which explicitly changes the symplectic structure. Rovellis et al. ignore this procedure completely, they quantize the unmodified symplectic structure of the BF theory instead, and impose (135) after quantization.

So basically what is wrong with the EPRL model (in all its variants) is the following: in the presence of second-class constraints we know from Dirac that one must first solve the second-class constraints consistently in the classical phase space and then quantize the system on the reduced phase space.

Dirac:
(1) derive or introduce all constraints
(2) calculate the Dirac brackets or solve second class constraints explicitly
(3) quantize

'Babel':
(1) derive some constraints
(2) calculate the Poisson brackets
(3) quantize
(4) introduce new constraints

For all models where one can solve the theory explicitly it is known that 'Babel' is wrong, whereas 'Dirac' is right (in the physical sense); unfortunately the quantization procedure of EPRL corresponds to 'Babel'! Here 'wrong' referes to a wide range of possibilities; there can be quantization anomalies which render the resutung quantum theory inconsistent - or it can simply mean that 'Dirac' and 'Babel' result in physically different theory with different dynamics, different degrees of freedom etc. In a situation w/o any good foundation for a different (consistent) constraint quantization procedure but Dirac (EPRL never mentions something like that) I am still with Dirac.

 

[marcus]

The last section of Zako Lectures before the "conclusions" is a 4-page "Section V" which could be called "Several Heuristic Not-Quite Derivations".
It's included for didactic, motivational purposes and for historical continuity. The theory is presented NOT as derived and none of the derivations from other areas of theory reaches it although I would say they converge towards it.

This is explained clearly at the start of Section V in a warning not to treat these (quasi-)derivations as if they presented as a way of straightforwardly deriving the QG theory itself as formulated earlier.

(But see Tom's post #45 where he makes repeated references to equation 135 and other stuff from this 4-page section at the end.)

But this historical heuristic discussion is, I think, quite interesting! Section V starts at the bottom of page 23 and it has 4 parts
A. Dynamics (quantization from BF theory using a simplicity constraint, see eqn. 135)
B. Kinematics (mentions that we don't yet have a conjoined hamiltonian approach)
C. Covariant lattice quantization (yet another quasi-derivation, explains how eqn. 135 can be viewed as a reality condition.)
D. Polyhedral quantum geometry (interesting new approach to formulating the theory)

 

[marcus]

Ashtekar's Loop survey was the opening talk at the Zakopane QG school which was predominantly about the post-2010 (not derived) formulation of Loop gravity which I've sometimes called ZQG to distinguish it from pre-2010 "EPRL" and such, that many people seem very attached to.

This version of Loop gravity is clear and can be presented definitively in a couple of pages. The essentials in a single paragraph, as I quoted.

Google "Rovelli Zakopane" and you get http://arxiv.org/abs/1102.3660, see page 13.

So what's the outcome of this development? Where is the community going from here?

One very interesting new development, I think, is that Laurent Freidel with the help of some smart new people has begun to develop LOOP CLASSICAL GRAVITY. You can see this as a reaction to ZQG, even as in a sense taking off from Zakopane as a point of departure.

I urge anyone at all interested in QG to watch at least the first 28 minutes of Jon Ziprick's recent PIRSA video.

Google "Ziprick PIRSA" and you get http://pirsa.org/12020096. The last 35 minutes is Lee Smolin and Laurent Freidel and Bianca Dittrich (who is great) arguing about what Ziprick said in the first 28 minutes. Do watch at least the first part!

Here's what I think is the essential. Relativity has infinite degrees of freedom. What if we use the partial ordering of graphs to truncate GR to a partial ordered crowd of finite DoF theories, and then get continuum GR as a projective limit?

The finite DoF version of GR, based on a graph, is still classical. Suggestively, we can call it Loop Classical Gravity. Or loop classical geometry if you like that better. LCG anyway.

Then it will be straightforward to quantize LCG and so to actually derive LQG. In essence that is the plan, as I see it.

Eugenio Bianchi is also involved in that intense discussion following Ziprick's presentation (of the Loop Classical Gravity approach) around minute 49. Bianca comes in around minute 37 and again around minute 50. There is someone sitting next to her, guy in a red shirt I don't recognize. He joins the discussion around minute 45. Laurent talks a lot, it is a serious discussion with quite provocative ideas.

 

[atyy]

Here's what I think is the essential. Relativity has infinite degrees of freedom. What if we use the partial ordering of graphs to truncate GR to a partial ordered crowd of finite DoF theories, and then get continuum GR as a projective limit?

What, what? Really? That is the anti-Rovelli view - his Zakopane lectures clearly do not take this approach. It seems very much like a Dittrich view. I'll definitely watch the video when I have time, sounds great. In the Rovelli view, there should be a continuum "upwards", which you can also get by going "downwards" see the figure on p21 of the Zakopane lectures. Dittrich has for quite some time been contemplating that you can only get the continuum by going "downwards". (Well, to be fair, she's also contemplated the relationship to Asymptotic Safety, which is a continuum "upwards" philosophy.)

Why does Rovelli want the "upwards" limit to also hold? I think this is because he wants to get the full match to the canonical LQG states. I think the only sense in which the Zakopane lectures go beyond EPRL is that they incorporate KKL's generalization to get a full match to canonical LQG states. In this sense, I think tom.stoer is right that Rovelli is still quite concerned with the relationship between canonical LQG and EPRL.

Other places in the Zakopane lectures that emphasize the continuum upwards, and KKL's extension of EPRL are:
p14: "The resulting expression naturally generalized to an arbitrary number of nodes and vertices, and therefore defines the dynamics in full LQG. The existence of this generalization was emphasized in [21]."
p21: "The theory is given by the formal limit of infinite refinement for transition amplitudes defined on finite two complexes. But we may not need to take the limit to extract approximate predictions from the theory.²¹"

So the Zakopane lectures are really about EPRL, or more properly EPRL-FK-KKL, which is a term Rovelli mentions on p3.

 

[marcus]

In this sense, I think tom.stoer is right that Rovelli is still quite concerned with the relationship between canonical LQG and EPRL.

Of course he is concerned with the relation between (as yet not formulated) canonical and the spinfoam formulation! You can see that in the recent Alesci Rovelli proposal for a Hamiltonian that (finally) can increase volume! One that uses tets rather than triangles. No one has said not concerned.

My point is about the correctness of the Zakopane "ZQG" spinfoam formulation, which is explicitly presented as not derived by quantization (and the reasons for this are clearly explained). No one can truthfully say that a physical theory that is clearly predictively formulated like that is not correct until it has been tested. We do not know the future. It is consistent with past observation as far as we know.

So the Zakopane lectures are really about EPRL, or more properly EPRL-FK-KKL, which is a term Rovelli mentions on p3.

What they are "really about" is a matter of individual interpretation. They mainly feature the new "ZQG" formulation which is superior in many ways to the pre-2010 "EPRL-FK-KKL".
But of course when you make a new formulation, one that is far more concise, you want to go back and show the connections and the historical continuity. So if you like you can say that any new formulation is "really about" the antecedents and motivation that gave rise to it.
=======================
It is superstition to believe that a new physical theory is not correct unless it is derived by some established procedure from past theory which has been successful in the past. At times physics has advanced by a smart/lucky guess, or in other ways.

The big thing that I am looking for now are the repercussions. The reaction by Laurent Freidel, for example. If possible he will try to show that Rovelli's message about "probably no straightforward derivation from GR is possible" to be wrong.
There is always a Hegelish dialectic of thesis-antithesis-synthesis going on.
Now Freidel will study how you "really" should quantize GR, by first FINITIZING it into a kind of "Loop Classical Gravity" based on finite graph states of geometry. And then the finite LCG will be quantizable in a straightforward way.

And in the process this will again transform Loop gravity. It could even nullify it (according to Jon Ziprick) if one can show that it is impossible to finitize classical GR with finite graph-based (holonomyflux) dynamics. This comes out around minute 27-28 of the talk and sets off the serious discussion by Smolin Freidel Dittrich Bianchi and the guy in the red shirt with the french? accent.

Rovelli's conjecture is plausible enough, and Freidel will work hard to show it wrong or partially wrong and partially right in the sense I have described. It is plausible because no straight quantization of GR has appeared in over 60 years of trying. If there were one it probably would have appeared. And it has happened in physics in the past that sometimes one has to make a guess and formulate something in a radically new way. It is plausible, then, but not necessarily right. We have to see.
===================

For newcomers who want to look at what is being discussed:

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660
Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf
Google "jonathan ziprick pirsa" and get the video http://pirsa.org/12020096 - Continuous Formulation of the Loop Quantum Gravity Phase Space--watch first 28 minutes

 

[atyy]

It is superstition to believe that a new physical theory is not correct unless it is derived by some established procedure from past theory which has been successful in the past. At times physics has advanced by a smart/lucky guess, or in other ways.

Yes, of course. I was actually trying to be as uninterpretive in what I wrote. My interpretation is that Rovelli is still too close to canonical LQG in trying to interpret EPRL.

 

[marcus]

Yes, of course. I was actually trying to be as uninterpretive in what I wrote. My interpretation is that Rovelli is still too close to canonical LQG in trying to interpret EPRL.

Right, I wasn't replying to you when I mentioned superstition (based on fixed idea of what procedure has worked in past). I didn't mean to suggest that you were involved in that. It was more of a general observation.

I do have trouble understanding it when you or others say "EPRL". Do you mean the pre-2010 spinfoam formulations Rovelli refers to as "EPRL-FK-KKL"? Or do you mean what I'm calling "ZQG" for zako loop quantum gravity? A theory is nothing apart from its formulation and the formulation is very different.

Do you think Rovelli is "still too close to canonical LQG" when he is proposing to radically change it by having the Hamiltonian feel the six-edge tetrahedra basket-work rather than just run around triangles. Shouldn't the Loop community be trying to get very close to the the problem of canonical formulation and wrestle with it until they get something they like better?

I'm going to take another look at the 2010 Alesci Rovelli hamiltonian proposal:
Google "hamiltonian compatible spinfoam" and get http://arxiv.org/abs/1005.0817

 

[tom.stoer]

marcus, you continuously try to avoid the discussion regarding quantization; I am with you that the theory may be correct physically even w/o derivation, but nevertheless its (theoretical) foundations are relevant; LQG is a mch broader field of research than Rovelli's view on EPRL.

 

[marcus]

A propos QG quantization, who here has watched Jon Ziprick's talk?

"Google "jonathan ziprick pirsa" and get the video http://pirsa.org/12020096 - Continuous Formulation of the Loop Quantum Gravity Phase Space--watch first 28 minutes"

I'm curious to know, and others of us may be also, so please say.

 

[genneth]

I think Marcus and Tom should stop arguing on this point; I think the argument is being done in good faith, but fundamentally you're going to disagree. I think (but probably wrong) that Tom is concerned with the intellectual aesthetics of the theory, which is pretty much defined by how it connects with other known theoretical ideas; marcus is solely focusing on the question of "correctness" with respect to nature --- these points of view both have merit, but I think it's going to be bizarre if some people on a forum will hash it out rather than, say, Rovelli et al.

In an attempt to bring the conversation back to the original point a little: marcus has been impressed by the loop *classical* gravity work; personally I was impressed too, until I thought a little harder about it --- now I'm not so sure; it may have bearing on the issue of a Hamiltonian. The problem is the lack of dynamics as proposed by Friedel et al. I'm satisfied that they have a good formulation of discretised gravity degrees of freedom, but I'm not sure that they have the correct *phase space*, since phase space is by definition the space of trajectories. For instance, I'm not sure how they will deal with inevitable graph changing operations --- I can't think of any way to make that consistent purely classically. In other words, I'm not sure (and in fact am very sceptical) that one can simply commute "discretisation" and "quantisation".

 

[marcus]

... The problem is the lack of dynamics as proposed by Friedel et al. ...

They talk about dynamics in the discussion following Ziprick's talk. Freidel holds forth quite a bit. It emerges that it is a decisive question whether a discretized version of classical GR dynamics can be implemented in the holonomy flux variables.

Freidel thought it would be bad for loop if it could not, and he had a backandforth with Bianca Dittrich, as I recall. I tried to listen to the whole Q and A but it was hard to follow. I may have misunderstood the gist and be giving you an inaccurate paraphrase of what the key question about dynamics was.

We will get another go at this in the ILQGS (international Lqg seminar) which is like a conference call. Ashtekar and Rovelli often join in the discussion. It will be later this month and this time Marc Geiller will be presenting the FGZ paper.

Anyway thanks for your comment Genneth!

 

[atyy]

I do have trouble understanding it when you or others say "EPRL". Do you mean the pre-2010 spinfoam formulations Rovelli refers to as "EPRL-FK-KKL"? Or do you mean what I'm calling "ZQG" for zako loop quantum gravity? A theory is nothing apart from its formulation and the formulation is very different.

I do think EPRL-FK-KKL is the same as ZQG - ie. the formulation is the same. The only difference between ZQG and EPRL is that ZQG incorporates KKL, but KKL is a "straightforward" extension of EPRL, so EPRL-FK-KKL is the same as ZQG.

Rovelli's Zakopane lectures, p3: "The resulting theory is variously denoted as "EPRL model", "EPRL-FK model", "EPRL-FK-KKL model", "new BC model"... in the literature. I call it here simply the partition function of LQG."

 

[marcus]

I do think EPRL-FK-KKL is the same as ZQG - ie. the formulation is the same. The only difference between ZQG and EPRL is that ZQG incorporates KKL, but KKL is a "straightforward" extension of EPRL, so EPRL-FK-KKL is the same as ZQG.
...

I've never seen a proof of equivalence, Atyy. The proof would turn on understanding the mapping between function spaces on SU(2) and SL(2,C). f_γ... I've seen kind of halfway handwave descriptions of how it might go.

So perhaps MORALLY equivalent but rigorously in a math sense? I remain skeptical that the different formulations are equivalent, and in some cases I don't know what equivalence would even mean, where for example the pre-2010 version deals with embedded spin networks and spinfoams, and employs a quite different sort of Hilbertspace.

Of course ZQG is purely combinatorial, no embedding, and the formulation is in terms of graph Hilbert spaces H which look like the group field theory hilbertspaces, functions defined on finite cartesian powers of a group.

Do you have a link for KKL? Maybe KKL has formulation that is more akin to Zako, and I'm missing something. That would be nice.

 

[atyy]

I've never seen a proof of equivalence, Atyy. The proof would turn on understanding the mapping between function spaces on SU(2) and SL(2,C). f_γ... I've seen kind of halfway handwave descriptions of how it might go.

So perhaps MORALLY equivalent but rigorously in a math sense? I remain skeptical that the different formulations are equivalent, and in some cases I don't know what equivalence would even mean, where for example the pre-2010 version deals with embedded spin networks and spinfoams, and employs a quite different sort of Hilbertspace.

Of course ZQG is purely combinatorial, no embedding, and the formulation is in terms of graph Hilbert spaces H which look like the group field theory hilbertspaces, functions defined on finite cartesian powers of a group.

Do you have a link for KKL? Maybe KKL has formulation that is more akin to Zako, and I'm missing something. That would be nice.

Well, that's what Rovelli claims. I was just as surprised as you to read it. I'm still trying to figure out how this works. But I'm pretty sure Rovelli claims it. Honest, this is not my interpretation - it's what I think Rovelli wrote.

If you search for all the references to KKL in the Zakopane lectures, it should be clear that Rovelli thinks that KKL is incorporated into the Zakopane framework. What is different in the Zakopane framework is the "derivation". But he says that the formulation is the same. Interestingly, he also seems to indicate that neither he nor KKL knew at first that the formulation was the same (p3): "The expression (3) was found independently and developed during the last few years by a number of research groups [15-21], using different path and different formalisms (and a variety of notations). Different definitions have later been recognized to be equivalent."

 

[marcus]

Well, that's what Rovelli claims. I was just as surprised as you to read it.

Maybe he should just have said "loosely speaking equivalent". or "surprisingly similar". I think KKL is explicitly different from several of the others.As you know people use the term EPRL to refer to all sorts of things. Rovelli's post-2010 theory is probably referred to in the literature as EPRL! That is all his very general page 3 statement (that you quoted) needs to mean.

There is a bunch of theory, referred to by various acronyms, by writers who are NOT consistent. To know what they mean you have to look at their arxiv or journal references.

And this bunch of theory contains many different separate theories which have NOT been proven to be all equivalent one to the other.

And he says that HIS formulation can have been referred to by various acronyms, but that he is going to call his theory "LQG partition function".

I think you overinterpreted the significance of the sentence on page 3 that you read. He doesn't want to waste time talking about everybody's different pre-2010 formulations and the different names they (inconsistently) call them. He's just saying he is going to call his theory "LQG partition function"

Morally that is what it is because it replaces all the previous formulations and it is different from all of them. So call it something and get going, don't waste time in the introduction when you want to teach something.

 

[atyy]

No, he is clear.

The video is funny! At 56:30 - Smolin explains to Freidel - one of the formulators of the current path integral formulation - why "most of us" work on the path integral formulation!

The last slide is really very provocative. It's too short, and Smolin has to ask lots of questions to figure out what they mean - he thinks the answer is obviously "yes", and it is - but Freidel clarifies that the question on the slide isn't the full question, and goes on to say something about whether the truncation is also consistent.

 

[marcus]

...indicate that neither he nor KKL knew at first that the formulation was the same (p3): "The expression (3) was found independently and developed during the last few years by a number of research groups [15-21], using different path and different formalisms (and a variety of notations). Different definitions have later been recognized to be equivalent."

I just got back from supper and saw your post. This is pretty persuasive. I'll have to think about it.
Probably in the introduction to Zako Lectures Rovelli should have used some modifier. All the formulations are closely related and certainly one could say "essentially equivalent"
or "effectively the same but formulated in a variety of ways." I don't understand the actual situation well enough to guess what a more careful wording might have been.

 

[tom.stoer]

I think Marcus and Tom should stop arguing on this point; I think the argument is being done in good faith, but fundamentally you're going to disagree. I think (but probably wrong) that Tom is concerned with the intellectual aesthetics of the theory, which is pretty much defined by how it connects with other known theoretical ideas; marcus is solely focusing on the question of "correctness" with respect to nature --- these points of view both have merit, but I think it's going to be bizarre if some people on a forum will hash it out rather than, say, Rovelli et al.

In an attempt to bring the conversation back to the original point a little: marcus has been impressed by the loop *classical* gravity work; personally I was impressed too, until I thought a little harder about it --- now I'm not so sure; it may have bearing on the issue of a Hamiltonian. The problem is the lack of dynamics as proposed by Friedel et al. I'm satisfied that they have a good formulation of discretised gravity degrees of freedom, but I'm not sure that they have the correct *phase space*, since phase space is by definition the space of trajectories. For instance, I'm not sure how they will deal with inevitable graph changing operations --- I can't think of any way to make that consistent purely classically. In other words, I'm not sure (and in fact am very sceptical) that one can simply commute "discretisation" and "quantisation".

Good points!

I agree with you
a) technically b/c you seem to be inline with my reasoning regarding dynamics, Hamiltonian, phase space, interchaging discretisation and quantisation, ...
b) the rather bizarre case here in this Forum; I am convinced that we can trust in all the real experts who are not only clever enough to realize the weak points of the theory, but who are certainly smart enough to figure out the answers ...
c) regarding stopping the discussion b/c everything has been expressed and explained many times

 

[atyy]

In other words, I'm not sure (and in fact am very sceptical) that one can simply commute "discretisation" and "quantisation".

I agree with you
a) technically b/c you seem to be inline with my reasoning regarding dynamics, Hamiltonian, phase space, interchaging discretisation and quantisation, ...

Is the issue of interchanging discretization and quantization the same as asking whether in Rovelli's Zakopane lectures, the figure on p21 exists? There he indicates one should get from full QG to classical GR by j→∞, or by first discretization, then j→∞, then a continuum limit.

This seems to be the issue on the last slides of Ziprick's talk, and that Freidel makes in the long discussion following. Ziprick's last slide is too terse, and one has to listen to the conversation between Smolin and Freidel at 42:46 - 44:00 to understand the slide.

 

[marcus]

The FGZ paper ("loop classical gravity") and Ziprick's online video presentation of it are definitely key things for us to assimilate. Atyy it's great to have your reactions, to Ziprick's talk! (And the remarkable discussion following it. )

Freidel already has a followup paper, or one that I at least found to be exploring in the same groove. It focuses on the alternative ways to formulate classical GR. In particular the thinking surrounding BF theory and the different ways to get GR out of it (Plebanski, McDowell-Mansouri, Peldan-Jacobson-Bengtsson, Krasnov...)

This is by Freidel and Speziale
http://arxiv.org/abs/1201.4247
On the relations between gravity and BF theories
Laurent Freidel, Simone Speziale
(Submitted on 20 Jan 2012)
We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.
Comments: 16 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

SIGMA is an online refereed journal which is gradually assembling a "special issue" or collection of articles on Loop gravity. Freidel Speziale and a number of other articles have appeared that have not yet been reviewed and formatted by the editors, so are not yet included in the "special issue" collection. But it's potentially a useful source.
Here is the SIGMA special collection of articles on Loop gravity/cosmology:
http://www.emis.de/journals/SIGMA/LQGC.html (Berlin site)
http://www.emis.ams.org/journals/SIGMA/LQGC.html (American Mathematical Society site)

 

[marcus]

Remember that the FGZ paper came out four months ago, in October. Freidel has been very productive in the days since then--three papers in January 2012 alone.
The Freidel Speziale paper I mentioned can supplement the discussion at Ziprick's talk and help to give us a handle on current thinking.

Here is the summary or "outlook" section at the end:

6 Outlook
One of the key difficulties with general relativity is the high non-linearity of its field equations. This complexity is enhanced further in the Einstein-Hilbert action principle, which is non-polynomial in the fundamental field, the metric. To obtain a polynomial action, one has to expand the metric around a fixed background. Then the perturbations can be quantized, but the theory is not renormalizable. An important line of research in quantum gravity imputes this failure to the background-dependent, perturbative methods, and seeks a background-independent formulation. When seeking for alternative approaches, the use of different fundamental variables with simpler actions is a useful guiding principle. In this respect, the relation of general relativity with BF theory appears very promising. The work appeared so far in the literature has unraveled the deepest level of such a classical relation, and introduced new tools and ideas to push forward the investigation of gravity in these variables. These results can be of benefit to approaches such as loop quantum gravity and spin foam models.​

In this thread we're trying to get an up-to-the minute picture of where Loop gravity research is and where it's going.

For newcomers who want to look at what is being discussed:

Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660

Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833

Google "jonathan ziprick pirsa" and get video http://pirsa.org/12020096

Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247