The Future of LQG - Oldey's Perspective

[julian]

This is what an oldey in LQG thinks: http://arxiv.org/pdf/1201.4598.pdfs - page 27.

It's great to see such confidence expressed in something that has for so long been put to the side because of the popularity in string theory.

What most interests you and why? Do you have a different opinion to Ashtekar?

 

[marcus]

http://arxiv.org/abs/1201.4598
http://arxiv.org/pdf/1201.4598.pdf

This is what an oldey in LQG thinks: http://arxiv.org/pdf/1201.4598.pdf - page 27.

The cumulative results in the main stream development of loop quantum gravity now carry sufficient weight for us to take the basic ideas seriously and continue to develop them by attacking the hard conceptual and technical open issues. Examples of such issues are: Finding principles and strategies to significantly narrow the ambiguities in the definition of the Hamiltonian constraint; exploring the role of supersymmetry; sharpening the set of quantum geometries to sum over, and addressing the problem of convergence in spin foam models; analyzing the renormalization group flows in group field theory; understanding the dependence of the n-point functions on the choice of the boundary state; developing approximation methods to calculate S-matrix from spin foams and pin-pointing why the standard perturbative treatments fail; fully incorporating matter fields in spin foams, particularly scalar fields; constructing effective field theories to adequately describe low energy physics; finding the detailed relation between loop quantum gravity and loop quantum cosmology; constructing a detailed completion of the inflationary paradigm in the Planck regime; exploring its observable consequences in the very early universe; ... The list is long enough to keep young researchers busy and happy for quite a while!

It's great to see such confidence expressed in something that has for so long been put to the side because of the popularity in string theory.

What do you think is most important direction?

I think those are wise words. Loop is currently moving into the limelight and getting a larger share of researchers' attention (probably for good reason).
The blue text is what you quoted in your original post. Amen to that, I say! Good advice for the young people. He's an elder statesman in the gravity and quantum geometry research community, and was giving the opening talk at last year's Zakopane school, primarily for young researchers just getting into LQG.

 

[marcus]

If I put together Ashtekar's words and what you said in your post what I get is 3 main points:

1. LQG now carries sufficient weight for us to "take the basic ideas seriously and continue to develop them by attacking the hard conceptual and technical open issues."

2. The list of these conceptual/technical issues "is long enough to keep young researchers busy and happy for quite a while!"

3. As you originally asked, but I would put in the plural: What do you think are the most important directions?

 

[julian]

Having a background in condensed matter so I'm especially interested in deriving an effective field theory and whether it would contain emergent degrees of freedom that could correspond to matter coupled to classical GR. I know that Smolin et al have been working on a preon type model based on q-deformed LQG type theory in which micro causality is made explicit...I have been wondering whether unification could arise in general LQG.

Plus I like how Smolin gives an explanation for dark energy in terms a small amount on non-local contaminate to semi-classical states. One question I have is how to incorporate this into the effective dynamics of LQC or extensions of.

Off course there is the huge hurdle of proving your model has the correct semiclassical limit. This not only involves a verification of the dynamical laws in their quasi differential form but also the construction of a suitable complete set of observables that have small quantum fluctionas with respect to specific semi-classical states. This latter problem - according to Thiemann - is on a same footing as proving confinement in QCD from first principles - now there is something for youngsters to work on!.

 

[julian]

Plural. What are the most important questions is better.

 

[julian]

Something else I'm interested in is Rovelli's attempts to formulate statistical thermal physics in a timeless context.

Relating to this, how to understand our usual experience of time and it's flow, coming from not having a complete knowledge of the system.

 

[marcus]

Julian, i noticed that on the "Our picks" MIP poll both you and Nonlinearity voted for this paper of Gielen and Wise:


http://arxiv.org/abs/1206.0658
Linking Covariant and Canonical General Relativity via Local Observers
Steffen Gielen, Derek K. Wise
(Submitted on 4 Jun 2012)
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables. The key is viewing dynamical fields from the perspective of a field of observers -- a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the 'space of observers' is fundamental, and spacetime geometry itself may be observer-dependent.
8 pages

I didn't vote for it but I think it's a very interesting idea.

I think you voted for two or three other things, out of the 20, and I can see a degree of correspondence between what you suggest here are good directions for research to go in and your choices in the poll.

 

[julian]

I am quite interested in covariance formulation and spin foams. Espicially those derived using the Master constraint. I've written up some of the calculations.

 

[atyy]

"But it would be a mistake if a significant fraction of the community focuses on constructing new models every few months, making a first stab and then passing on to the next model."

Yet this is what the mainstream seems to be. EPRL seems already dead.

"Thus there is ample evidence that the subject is now sufficiently mature to have applications to other areas. In these explorations, it is important to focus on problems that other communities consider as important in their areas. In my view, this ‘outward bound’ spirit is the second pillar on which further development of the field will rest."

I believe this is a better line of thought - that pure LQG will fail - but the mathematics of LQG will be relevant to string theory.

 

[marcus]

EPRL I would say started one of the most vital lines of development. It seems totally wacky to call it "dead"
Two of the papers on the MIP poll (one by Engle one by Rovelli) have directly to do with that line of development.
Of course it is steadily evolving, that is what a live theory does. When people discuss it they need to address the current version, which last year was characterized by the Zakopane Lectures (which this paper by Ashtekar was in effect introducing).
Next year it will almost certainly have been slightly modified*. It's an evolutionary process.

*See the papers by Engle and by Rovelli for ideas of how that might go.

 

[atyy]

EPRL I would say is one of the most vital lines of development. It seems totally wacky to call it "dead"
Two of the papers on the MIP poll (one by Engle one by Rovelli) have directly to do with that line of development.

It's those two papers that I think make EPRL dead. It's fair to consider them lines of development, but at the same time they seem to be proposals for new models, because the old model was unsatisfactory. The new models appear unsatisfactory too, so they may be pointing towards a profusion of new models that Ashtekar was hoping against.

 

[julian]

I think it was Ashtekar who stated that the Master constraint is the most promising way to derive the corect spinfoam formulism. So even if EPRL were wrong the Master constraint might still provide correction away from it. I don't know?

 

[atyy]

I think it was Ashtekar who stated that the Master constraint is the most promising way to derive the corect spinfoam formulism. So even if EPRL were wrong the Master constraint might still provide correction away from it. I don't know?

I'm not sure about the Master constraint, but one thing that is nice about the new Rovelli and Wilson-Ewing paper is that the new models are due to trying to make contact with the canonical formalism, eg. where they note "The corresponding conjugate momentum is the Ashtekar electric field ... but (confusingly) one finds two different expressions for this field in the literature [7, 8] ... The two expressions differ by the sign s and can be derived from S′ and S′′, respectively."

Another paper that goes in the direction of profusion of models to the point where I think maybe they are really stuck is the Giesel and Thiemann paper where even basics like the physical and kinematical Hilbert spaces being different are up in the air!

BTW, since you have a condensed matter background, have you seen http://arxiv.org/abs/0907.2994 and http://arxiv.org/abs/1106.1082 which note links between LQG, condensed matter and string theory?

 

[tom.stoer]

EPRL is not dead, but wrong. That means it sufferes from wrong constraint structure, phase space and therefore wrong quantization. That does not mean that SFs are dead. One has to find a consistent coinstraint algebra and its quantization.

Canonical LQG is not dead, either, but it is still inknown how to quantize the Hamiltonian constraint. There is a related issue, namely the step-by-step implementation of the constraints: Gauss - Diff - Hamiltonian; maybe it's this stepwise approach which is wrong. If one can fix Diff + H at once this may be a way out, but if it's even the very first step i.e. Gauss (which results in the kinematical Hilbert space) then we are really in trouble.

 

[marcus]

EPRL is not dead, but wrong. That means it sufferes from wrong constraint structure, phase space and therefore wrong quantization. That does not mean that SFs are dead. One has to find a consistent coinstraint algebra and its quantization.
...

In line with what you are saying I would also extend the idea to General Rel and Quantum Mechanics. GR and QM are not dead either, but simply wrong. They have their obvious problems and one has to find improved formulation. That is how physics goes.

 

[atyy]

In line with what you are saying I would also extend the idea to General Rel and Quantum Mechanics. GR and QM are not dead either, but simply wrong. They have their obvious problems and one has to find improved formulation. That is how physics goes.

But they make correct predictions. LQG must make a correct prediction beyond GR as an effective QFT. At this stage, I would certainly say that is not even the goal. The more limited goal is to be a UV completion for GR. There may be more than one possible completion, and experiment would have to decide between them. At this stage, LQG is not even a candidate completion, and on grounds decided by the LQG programme itself.

 

[tom.stoer]

In line with what you are saying I would also extend the idea to General Rel and Quantum Mechanics. GR and QM are not dead either, but simply wrong. They have their obvious problems and one has to find improved formulation. That is how physics goes.

No!



Think about QM with wrong commutators, e.g. by using non-cartesian coordinates and not taking into account the Jacobians; or think about the PI of QCD with ∂_αA^α=0 and 'neglecting' the Fadeev-Popov ghosts; that's the type of error they currently make in SF models ... The problem is not that they make unreasonable physical assumptions but that they do not solve / impose all constraints correctly. In QCD w/o Fadeev-Popov ghosts you get wrong amplitudes w/o.

 

[marcus]

I want to recall the initial ideas that Julian started us off with in the first post. This is how I boiled them down---into 3 main points.

If I put together Ashtekar's words and what you said in your post what I get is 3 main points:

1. LQG now carries sufficient weight for us to "take the basic ideas seriously and continue to develop them by attacking the hard conceptual and technical open issues."

2. The list of these conceptual/technical issues "is long enough to keep young researchers busy and happy for quite a while!"

3. As you originally asked, but I would put in the plural: What do you think are the most important directions?

I don't think we need to waste time venting our personal attitudes---good-mouthing, bad-mouthing, cherrypicking and interpreting Ashtekar etc.
The thing is HOW DO YOU SEE THE FUTURE of the Loop program?

I don't think any of us can accurately envision the future of an active research program but I will tell you my guesses.

Right now I'm looking thru Hartle-QM glasses (explain that later) and I see Thiemann and the Erlangen group all going in the direction of DUST. That is what his "matter reference system" means and what Gielen Wise "field of observers" means and it makes sense from a Hartle-QM perspective.

Hartle and friends propose a reformulation of Quantum theory we can call "Histories" QM which basically says that the machinery of Dirac quantization does not exist--it is merely emergent at low energies, a convenient workable approximation to reality over a limited range. The spacelike 3D manifold does not exist in reality. To formulate QM, you need three things:
A. Histories
B. Partitions of histories (grouping, classifying, "coarsegraining" them)
C. a Decoherence functional that tells you when a given partition is bettable.

A given partition is bettable when you can assign fair odds (approximate conventional probabilities) to it, make predictions, settle bets, in other words make honest book on it.
The Decoherence functional tells you when a partition of the histories is sufficiently uncorrelated that the probabilities will be additive---interference is small enough to be considered negligible.

Hartle Histories QM is, I believe gaining acceptance. So it makes sense to me, in that light, that the Erlangen group should be moving away from a strict Dirac quantization and in the direction of DUST.

None of this has to do with "right" or "wrong". It has to do with Sociology. That is, watching the glacier-slow shifts of the research community, which is basically all we can know. IMHO it is naive to pretend that we can declare what is "right" or "wrong" (except to admit that all living human theories are wrong and subject to revision). All we can do is watch the community and see where their blind instinct leads them. It is an awesome and wonderful process, but it does not obey set rules

 

[tom.stoer]

I see different directions:
- technical: reformulation in terms of spinors, twistors, group field theory, ...
- technical: fixing the issues with quantization (both canonical and PI/SF) + their equivalence
- dynamics! (once the SF and H are rigorously constructed)
- boundary Hilbert spaces and holographic principle (get rid of the bulk)
- coarse-graining / Kadanoff's renormalization group approach / certain other related limits
- matter d.o.f., unification, possibly the Sundance Bilson-Thompson approach
- exotic smoothness, PL manifolds, 'non-diffeomorphic defect-structure', ... relation to Asselmeyer's work

 

[marcus]

Thanks for telling us about all these directions you see, Tom. Some look real to me---major going concerns. Others seem based on your own ingrained preconceptions of what "ought" to happen, others just distractions, or where almost no work is being done. But who knows? Some of them might suddenly jump up in importance.
==quote==
I see different directions:
- technical: reformulation in terms of spinors, twistors, group field theory, ...
- technical: fixing the issues with quantization (both canonical and PI/SF) + their equivalence
- dynamics! (once the SF and H are rigorously constructed)
- boundary Hilbert spaces and holographic principle (get rid of the bulk)
- coarse-graining / Kadanoff's renormalization group approach / certain other related limits
- matter d.o.f., unification, possibly the Sundance Bilson-Thompson approach
- exotic smoothness, PL manifolds, 'non-diffeomorphic defect-structure', ... relation to Asselmeyer's work
==endquote==

Basically my perception is guided by people "in the business" like Lewandowski and Pullin and I'd say to anybody look at the lineup of Loop talks at Stockholm this week.
The MG13 organizers gave Lewandowski nearly 10 hours of parallel session, and Pullin over 9 hours.
A total of 19 hours designated for Loop gravity. These guys know the field, what's active, what their colleagues are interested in hearing about.

It's certainly not a perfect indicator, but it can give one something outside oneself to balance one's subjective favorites and preconceptions.

 

[marcus]

In case anyone else might be interested in this way of looking at the future of LQG (thru the eyes of an expert organizing the Loop session of an international conference) here are some links:

The Marcel Grossmann triennial conference being held this week in Stockholm (MG13). There are 1021 registered participants.
http://www.icra.it/mg/mg13/parallel_sessions.htm
Here is an over 5 hour session organized by Lewandowski (the first of his two sessions). Click on talk titles to see brief summaries of the talks.
QG!A http://ntsrvg9-5.icra.it/mg13/FMPro...tField=order2&-SortOrder=ascend&-Max=50&-Find
Here are two roughly 4 and 1/2 hour sessions organized and chaired by Jorge Pullin (with Param Singh)
QG4A http://ntsrvg9-5.icra.it/mg13/FMPro...tField=order2&-SortOrder=ascend&-Max=50&-Find
QG4B http://ntsrvg9-5.icra.it/mg13/FMPro...tField=order2&-SortOrder=ascend&-Max=50&-Find

The Stockholm MG13 conference covers a wide range, not just Quantum Gravity but also EXPERIMENTAL, NUMERICAL, OBSERVATIONAL, AND THEORETICAL General Relativity and extensions, Extreme Gravity, Astrophysics, Cosmology, Fields on curved, and including several kinds of alternate approaches and modifications of standard theory that researchers are currently trying. BTW there is also a 4 and 1/2 hour parallel session explicitly devoted to String papers! Chaired by Henningson--here's a link:
http://ntsrvg9-5.icra.it/mg13/FMPro...tField=order2&-SortOrder=ascend&-Max=50&-Find

The next big international meeting focused on these topics will be the General Relativity and Gravitation triennial conference (GR 20) which will be held in Warsaw July 8 - 13, 2013. Lewandowski will be the lead organizer. He is also handling the Loop lectures at the Erlangen QG School this October. So we will get several opportunities to see how he views the future of LQG.

 

[audioloop]

well, a bit of optimism is not bad

...Calculating these constants for the EPRL/FK vertex amplitude appears
to be a difficult problem, but the solution must exist...
http://arxiv.org/pdf/1101.3294v4.pdf

 

[marcus]

well, a bit of optimism is not bad

...Calculating these constants for the EPRL/FK vertex amplitude appears
to be a difficult problem, but the solution must exist...
http://arxiv.org/pdf/1101.3294v4.pdf

It certainly is not bad!
And Jerzy Lewandowski seems to confirm your interest in the work of Aleksandar Mikovic.
Mikovic is giving a 20 minute talk in Lewandowski's second session (Thursday 5 July) at the MG13 conference:
http://ntsrvg9-5.icra.it/mg13/FMPro...tField=order2&-SortOrder=ascend&-Max=50&-Find

Jerzy's two sessions are both titled "Loop Quantum Gravity, Quantum Geometry, Spin Foams". I posted the link to the first one in my previous post. You might be interested to see what he has chosen for the lineup of talks. Click on the talk titles to get an abstract summary of any that are of interest.

BTW I think the business of simply calculating the vertex amplitudes (with the existing vertex formulas) has been taken care of. There are still outstanding questions to work on, though, having to do with the "asymptotics" of the vertex amplitudes---their limiting behavior for large quantum numbers j---their large scale limit behavior. It's one of many topics newcomers to the field can choose from, to work on.

 

[tom.stoer]

Please let me know where you think that ...

Some look real to me---major going concerns.

... I am right ...

...and where you think that ...

Others seem based on your own ingrained preconceptions ..., others just distractions, ...

... I am wrong

 

[atyy]

I see different directions:
- technical: reformulation in terms of spinors, twistors, group field theory, ...
- technical: fixing the issues with quantization (both canonical and PI/SF) + their equivalence
- dynamics! (once the SF and H are rigorously constructed)
- boundary Hilbert spaces and holographic principle (get rid of the bulk)
- coarse-graining / Kadanoff's renormalization group approach / certain other related limits
- matter d.o.f., unification, possibly the Sundance Bilson-Thompson approach
- exotic smoothness, PL manifolds, 'non-diffeomorphic defect-structure', ... relation to Asselmeyer's work

How do you see the holographic principle? I too think it must factor in, but the way it occurs in string theory, it seems also to be tied up with unification, whereas canonical LQG seems anti-unification. Because of string theory, I tend to think that maybe the holographic principle is more fundamental, and so I tend to think canonical LQG will not work out. Do you think there's a way for holography and canonical LQG to work together?

 

[marcus]

Hi Tom, all I want to do is characterize our different viewpoints at the level of generality. I don't think you consider me an expert so my detailed comment wouldn't be useful to you.
I see the suggested directions you offer as a "mixed bag".

As I said: "...But who knows? Some of them might suddenly jump up in importance.
==quote==
I see different directions:
- technical: reformulation in terms of spinors, twistors, group field theory, ...
- technical: fixing the issues with quantization (both canonical and PI/SF) + their equivalence
- dynamics! (once the SF and H are rigorously constructed)
- boundary Hilbert spaces and holographic principle (get rid of the bulk)
- coarse-graining / Kadanoff's renormalization group approach / certain other related limits
- matter d.o.f., unification, possibly the Sundance Bilson-Thompson approach
- exotic smoothness, PL manifolds, 'non-diffeomorphic defect-structure', ... relation to Asselmeyer's work
==endquote==

That could apply to Sundance approach or Asselmeyer approach. Not much going on with them now, just a few people--but either could "suddenly jump up in importance."
I don't think we can know the future and I DON'T MAKE BETS. Basically I just watch the professional research community.

Where my perspective differs markedly from yours, and where I possibly might benefit you by giving an alternate point of view, is IF AND WHEN I notice a trend that you might have overlooked.

I've noticed that Thiemann and the Erlangen group seem to be getting away from strict Dirac quantization. And I think that fits with Hartle "Decoherent Histories" reformulation of standard QM. Which I think has a lot going for it. Fundamentally more valid than the split version of QM that prevailed in Dirac's day.

So I think your use of language above is questionable where you say "their equivalence" and "H rigorously constructed". This is just IMHO but I suspect you may eventually have to give up on the strict Dirac canonical, just as I already see happening in the Erlangen group. If Hartle DH is right, it's not valid in a fundamental sense, just "effective" or "emergent" in certain regimes.

To recapitulate:
==quote==
Basically my perception is guided by people "in the business" like Lewandowski and Pullin and I'd say to anybody look at the lineup of Loop talks at Stockholm this week.
The MG13 organizers gave Lewandowski nearly 10 hours of parallel session, and Pullin over 9 hours. A total of 19 hours designated for Loop gravity. These guys know the field, what's active, what their colleagues are interested in hearing about.

It's certainly not a perfect indicator, but it can give one something outside oneself to balance one's subjective favorites and preconceptions.
==endquote==

 

[atyy]

So I think your use of language above is questionable where you say "their equivalence" and "H rigorously constructed". This is just IMHO but I suspect you may eventually have to give up on the strict Dirac canonical, just as I already see happening in the Erlangen group. If Hartle DH is right, it's not valid in a fundamental sense, just "effective" or "emergent" in certain regimes.

It is still strict canonical - just not Dirac quantization of a gauge theory via constraints. And it is not new.

http://arxiv.org/abs/0711.0119: "There are two major approaches to the canonical quantisation of such theories. ... The advantage of the Dirac apporoach is that the unreduced phase space of non observables is typically a smooth (Banach) manifold so that the algebra of non – observables is sufficiently simple and representations thereof are easy to construct. Its disadvantage is that one has to deal with spurious degrees of freedom which is the possible source of ambiguities and anomalies in the gauge symmetry algebra. The advantage of the reduced phase space approach is that one never has to care about kinematical Hilbert space representations. However, its disadvantage is that the reduced phase space typically no longer is a smooth manifold turning the induced algebra of observables so difficult that representations thereof are hard to find."

 

[tom.stoer]

Marcus, let me comment on some of my ideas:

technical: reformulation in terms of spinors, twistors, group field theory, ...
These are certainly no new directions, but simply ways to reformulate the theory in order to make it more tractable; some approaches may apply to LQG In general, some to certain limits only, ...; I don't expect too many conceptual surprises here. The maths must be worked out; this is often quite boring (have you tried to do 2-loop calculations in QCD?) but mandatory.

fixing the issues with quantization (both canonical and PI/SF) + their equivalence
I am not sure about the details. It's correct that reduced phase space, Dirac, ... all have their shortcomings, but eventually a consistent quantization procedure taking all constraints into account correctly (i.e. w/ correct d.o.f., w/o anomalies etc.) must be found. In addition the two approaches "canonical" and PI/SF must be shown to be equivalent to a certain extent (or it has to be be proven where and why one approach necessarily fails; otherwise you simply do not have a physical theory but only a collection of formulas where you never know whether they are consistent or not).
Note that these issues may not show up in any semiclassical limit!

dynamics! (once the SF and H are rigorously constructed)
Up to know most of LQG is about kinematical structures (except for some n-point functions which are not really relevant in the deep QG domain); we have a discrete area spectrum - but the area operator is not a Dirac observable; we have black hole state counting - but we cannot explain non-stationary effects; we have LQC with its dynamics - but we cannot rigorously establish the link from LQG w/ correct H to LQC.

boundary Hilbert spaces and holographic principle (get rid of the bulk)
This idea is based on the black hole state counting. Inside the BH there may be a collection of vertices, or there may be only one huge vertex carrying the whole volume. To some extent these different pictures are equivalent; the difference is unobservable due to the event horizon.
I think that the holographic principle will provide something as follows: a theory consisting of a collection ob boundary Hilbert spaces w/o bulk d.o.f. plus dynamical relations between these boundary Hilbert spaces. After all this is what we always do: we observe a certain volume "from outside" so there should be no conceptual obstacle to get rid of the detailed picture of the interior i.e. the bulk.

coarse-graining / Kadanoff's renormalization group approach / certain other related limits
I think some work has already been started into that direction

matter d.o.f., unification, possibly the Sundance Bilson-Thompson approach
Even if we do not end up with matter d.o.f. emerging from spacetime itself, we have to understand the topological structures of (braided) spin networks; up to know everybody focusses either on the microscopic picture or on the macroscopic one (semiclassical limit); I bet that there will be some surprises on intermediate length scales!

exotic smoothness, PL manifolds, 'non-diffeomorphic defect-structure', ...
Perhaps I should not mention Asselmeyer. My feeling is that with LQG we overlook two essential things: The construction relies on diff. inv.; we know that there are (infinitly) many non-diffeomorphic smoothness structures in 4-dim., but we never explore how they may affect the construction of LQG. Then we know that in 4-dim. the relation between smoothness structures and piecewise linear structures on manifolds is much more complicated than in all other dimensions. In LQG we use both (smoothness an PL), but we never care about their relationship and we simply ignore the fact that there are manifolds which are equivalent in one sense but not in the other. There are two poerspectives: you can start with the construction of the theory (from smoothness to PL, i.e. to spin networks or SFs) or you can try to derive the semiclassical limit (from PL to smoothness); in both cases nobody cares about the relationship between smoothness and PL structures.
In addition we do not know what to count in a QG PI using fields: equivalence classes regarding homeomorphisms or regarding diffeomorphisms - which is by no means the same.
The last problem is that in the construction of LQG we use global spacelike foliations which restricts the manifold not only topologically but even w.r.t. its smoothness structures. That means that in (canonical) LQG we may lose physics and that this is the reason why (canonical) LQG may essentially fail!

 

[marcus]

Thanks! This is a thoughtful and constructive outline that should help guide a discussion of "future of LQG". Unfortunately for me, it is after 11PM here (23:00 h.) and I am falling asleep!
But I have to compliment you on the clear careful wording, before I head off for bed.

I'm especially interested in what Thiemann's group (Erlangen) is doing now. Kristina Giesel just taking a professorship there and co-authoring a recent paper with Thiemann. Have you read some of it?

Also, just some incidental information: Antonia Zipfel is Thiemann's PhD student and Emanuele Alesci and Francesco Cianfrani are his postdocs. All three are giving papers this week at the MG13. The first two in the Tuesday session chaired by Lewandowski, the other in Pullin's Friday session. If you click on the titles of the talks you get the abstracts.
It is too late for me to be hunting for links. I will get the links tomorrow morning. In any case you can find them easily if you share my interest in what the Erlangen folks are up to.

======EDIT======
Adding some links in case others are interested:

http://arxiv.org/abs/1206.3807
Scalar Material Reference Systems and Loop Quantum Gravity
Kristina Giesel, Thomas Thiemann
[clear and explicit about antecedents and motivation for non-Dirac quantization. "physical" Hamiltonian instead of "constraint". explicit about what they do that is new. See conclusions.]

Since Alesci and Zipfel and Cianfrani are in the Erlangen group it's interesting to check out what they are presenting at Stockholm MG13 conference this week.
Alesci:
http://ntsrvg9-5.icra.it/mg13/FMPro...s&talk_accept=yes&-max=50&-recid=42195&-find=

Zipfel:
http://ntsrvg9-5.icra.it/mg13/FMPro...s&talk_accept=yes&-max=50&-recid=42000&-find=

Cianfrani:
http://ntsrvg9-5.icra.it/mg13/FMPro...&-max=1200&-recid=35350&-token.0=19&-findall=

Thiemann's postdocs:
Enrique Fernandez Borja
Emanuele Alesci (MG 13)
Derek Wise (non-Dirac quantization, paper with Gielen on MIP poll}
Maïté Dupuis (see your point about "spinors, twistors, group field theory" and her paper on MIP poll)
Francesco Cianfrani (MG 13)

 

[julian]

Hello tom - you make very interesting points. But can I just mention one thing, to do with your comment on the area operator and it's spectrum not corresponding to an observable ...(http://arxiv.org/pdf/gr-qc/9806079.pdf):

"The operator A (\Sigma) is invariant under SU(2) gauge transformations, but not under three or four dimensional diffeomorphisms. Therefore, strictly speaking it is not an observable of the theory, and we cannot directly give its spectrum physical meaning. The failure of A (\Sigma) to be diff-invariant is a consequence of the fact that the area of an abstract surface defined in terms of coordinates is not a diff invariant concept. In fact, physical measurable areas in general relativity correspond to surfaces defined by physical degrees of freedom, for instance matter (the area of the surface this table) or the gravitational field itself (the area of an event horizon). However, it is reasonable to expect that the fully gauge invariant operator corresponding to a physically defined area (say defined by matter) has precisely the same mathematical form as the non gauge invariant operator studied here. The reason is that one can use matter degrees of freedom to gauge-fix the diffeomorphisms – so that a non-diff-invariant quantity in pure gravity corresponds to a diff-invariant quantity in a gravity+matter theory. This expectation has been confirmed explicitly in a number of cases [see refs]"...I don't know how many people on the forum are from the UK, but there is this BBC pop science programme called "Horizon". There is this physicist called Brian Cox and he has presented a couple of these programmes (Bizarrely he was also a member of the pop band called D'ream who had a hit with the song "things can only get better" which may have relevance here). Horizon did a programme called "how long is a piece of string" in which they ended saying you can't measure the length to aribrary accurancy b/c the photons required would induce a black hole. LQG gets around this cus the backreaction of matter on the grav field is taken into account - I kinda understand this. Anyway I wrote an email to Rovelli (c.c. Brian Cox) saying this might be a good strting point for another programme introducing LQG to the general public. Rovelli wrote back saying he would be very interested in this. Brian Cox just ingored me. I don't like Brian Cox - and other physicists have agreed with me ;).