Clear concise Loop survey as of January 2012

[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