Prospects of the canonical formalism in loop quantum gravity

[tom.stoer]

There are still unsettled questions in loop quantum gravity, especially regarding uniqueness of the Hamiltonian constraint, constraint algebra, on-shell vs. off-shell closure, operator norm and convergence, ultra-locality, possibly quantization anomalies. These questions have been asked in Nicolai's "an outside view" paper more then five years ago, they are been adressed by Alexandrov, Thiemann ist still working on these issues, ...

So it seems that besides the reformulation of LQG in terms of spin foamns which makes the theory more tractable for practical purposes there still seems to be the question of the consistent definition of loop quantum gravity and the relation between its different formulations. It seems that not only are these formulations considered incomplete by themselves, but that both their fundamental formulations and their relation is still unclear.

I am currently studying the paper

http://arxiv.org/abs/1110.2157v1
Lessons from toy-models for the dynamics of loop quantum gravity
Authors: Valentin Bonzom, Alok Laddha
(Submitted on 10 Oct 2011)
Abstract: We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.

Even if the toy models considered in this paper do not teach us anything new, its worth reading the first sections b/c the authors summarize the issues listed above, they present a rather comprehensive overview plus relevant references.

I do not want to disparage the new SF perspective developed over the last few years, but it should be stressed that there is more than one perspective ...

 

[genneth]

Perhaps I'm naive, but I find it hard to morally believe in the canonical formulation. Again, perhaps because I'm not well-versed in it, I don't see any reason to believe that such a method can work in principle. "Quantization" is, after all, not well-defined, and one must put in more information to complete the procedure; the only benefit is that after completing the program one can trivially see that the relevant *-bracket structures are preserved --- so the reduction to classical GR is should then be obvious.

The covariant/SF approach seem to have trouble showing for sure that GR is recovered (though I'm optimistically hopeful that it will work out), but at least the definition of the theory as a quantum theory seems clear. There is a well-defined sequence of calculations for various things, and like lattice QCD the "only" difficulty is to actually do them.

I guess my personal flavour is to prefer well-defined, computable (though not really effectively) things over ill-defined but potentially very elegant models.

 

[atyy]

How about LQC? That seems to be working out, even though LQG is going nowhere, and I am skeptical of the Rovellian view of spin foams.

 

[suprised]

There is a well-defined sequence of calculations for various things, and like lattice QCD the "only" difficulty is to actually do them.

Actually there _is_ a major difference as compared to lattice QCD. As said before, the latter is UV complete, ie renormalizable and unitary, and there are reasons of universality that, roughly speaking, no matter where you start in the right universality class, you end up with the same theory in the IR.

As for gravity, which is not UV complete (at least in the traditional sense if we neglect a possible self-unitarization by classicalization or something like that), there is no reason why any such notion of universality should hold and this may well be the inherent reason why there seems to be an infinite amount of ambiguities to even define such theories. No matter what, the discussion is bound to always come back to this or related points.

Many people in this field have the feeling that starting with some classical gravity theory and then canonically quantizing it, is a very wrong starting point in the first place.

 

[marcus]

There are still unsettled...

I do not want to disparage the new SF perspective developed over the last few years, but it should be stressed that there is more than one perspective ...

There certainly are a lot of open questions to be worked on in QG! The field is in active ferment and going through a creative period of growth.

I want to note that Eugenio Bianchi has promoted a third perspective to stand beside the two main others (abstract SF and canonical).
http://pirsa.org/11090125/

For what seems a long time we have been hearing suggestions about this---but I have the impression always as a side remark or footnote or lowerdimension toy illustration. I never saw it so clearly developed as in Eugenio's talk. So I think of it as his project.

I think there was even a paragraph or two about it in the Zako lectures 1102.3660. But as a side comment: the main line of development there was abstract SF (with abstract SN boundary).

http://pirsa.org/11090125/
Loop Gravity as the Dynamics of Topological Defects
Eugenio Bianchi
A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the prospect of formulating the Spin Foam dynamics as the local interaction of topological defects.
21 September 2011

Who knows if this will succeed? Progress is made by branching out and trying new ways.

 

[tom.stoer]

Perhaps I'm naive, but I find it hard to morally believe in the canonical formulation. ... I don't see any reason to believe that such a method can work in principle

In principle or in QG only? It is well-define in QM; it works well in QED and QCD; the PI formalism was derived via the canonical one, so where's the principle problem?

The covariant/SF approach seem to have trouble showing for sure that GR is recovered

It's more difficult in the canonical formalism.

 

[tom.stoer]

How about LQC? ... even though LQG is going nowhere ...

Why? b/c it's too restrictive?

and I am skeptical of the Rovellian view of spin foams.

It's the "shut-up-and-calculate" approach. Other's are still working on the fundamental problems.

 

[atyy]

Why? b/c it's too restrictive?

But it works! Isn't that a clue to make it less restrictive? (I have no idea what the clue means, but someone else like Ashtekar, Thiemann, Lewandowski or Bahr should?)

It's the "shut-up-and-calculate" approach. Other's are still working on the fundamental problems.

I'm skeptical of the calculations which take the Immirzi parameter to zero and appear to be consistent with Einstein gravity. The reason is that we do expect Einstein gravity to be recovered in some limit, after all, the theory is a discretization of the Holst action. What's important is that it is recovered in the correct limit. Even more important, given that the problem of non-renormalizability is one of uniqueness, not finiteness, is that the theory is not triangulation independent, unless the Rovelli-Smerlak limit exists. Actually, that proposal is the one thing I like about Rovelli's work. I hope it exists, and that Einstein gravity is not recovered in the IP→0 limit, and that we end up with something like AdS/CFT or better.

 

[tom.stoer]

But it works! Isn't that a clue to make it less restrictive? (I have no idea what the clue means, but someone else like Ashtekar, Thiemann, Lewandowski or Bahr should?)

I would say that removing all restrictions from LQC you end up with LGQ; and it works only in a very restricted sense. Most of he semiclassical limit of LQC is already present as input or as restriction. But I agree that one can learn something about LQG in general.

I'm skeptical of the calculations which take the Immirzi parameter to zero ...

This limit (or something else) should become a "dynamical" or "scaling" limit produced by renormalization, not by hand; there are some preliminary attempts ...

To make one thing clear: I still think that LQG is a very promising approch, but this is not necessarily due to its phenomenological success (which we do not see yet) but due to mathematical rigor (which certainly plays a very important role in the deep QG regime). If the issues I listed in post #1 cannot be resolved, I am afraid the whole effort is in vain!

 

[Fra]

Many people in this field have the feeling that starting with some classical gravity theory and then canonically quantizing it, is a very wrong starting point in the first place.

I symphatize with this view.

I think it is not the right starting point for unification either, but I think the "symptom" for applying the scheme is different in the two cases.

What do you think about the informal suggestion that ambigousness of the hamiltonian constraint, is somehow one thing they face instead of a landscape problem? Does that make sense to you? or is it just me thinking so

/Fredrik

 

[qsa]

lets say LQG does manage the classical limit. and string reproduces the standard model. Are they really telling us about THE UNIFYING concept of gravity with other forces, I think even the most naive physicists should know better. Let alone the million( well maybe only ten) other questions.

 

[suprised]

@ Fra
If we talk about pure gravity, any theory better reproduces the landscape of solutions to the Einstein eqs, to lowest order. If this theory is not unambigously defined, then there might be an arbitraryness on top of it, perhaps in the infinitely many counter terms added to the Einstein action, which play no big role at low energies/curvatures but become important at high energies/curvatures. Perhaps requiring the theory to be unitary would fix some or many or all such terms; perhaps unitary can never be achieved in this framework, god knows!

 

[tom.stoer]

Many people in this field have the feeling that starting with some classical gravity theory and then canonically quantizing it, is a very wrong starting point in the first place.

I agree that quantization of a classical theory seems strange b/c it tries to "invert the limit h = 0" ... and canonical quantization may be dangerous due to loss of large diffeomorphisms and things like that ... nevertheless it works in many cases. So let me ask why gravity is fundamentally different. I mean not simply more complicated in practice but really conceptionally different! In LQG it seems that it's harder than usual but that the naive approach might work. In string theory you essentially do the same (OK, you do not take gravity, but you take a classical theory and quantize it). If you want to address a REALLY fundamental issue then you should ask about an alternative to quantization i.e. a concept to define a theory w/o knowing its classical limit.

 

[marcus]

lets say LQG does manage the classical limit. and string reproduces the standard model. Are they really telling us about THE UNIFYING concept of gravity with other forces,..

Does "unification" always mean "unification of forces" for you?

I think gravity is a theory of geometry (not just another force.) So trying to unify it with the three forces is the wrong goal.

I see the program as connecting GR with QM. GR is about dynamic geometry. To connect it with QM means to find out how to do quantum geometry.

In other words, forget about "unification of forces". Find out how to represent quantum states of geometry. A hilbert space of quantum states of the geometry of the universe. Geometric operators, corresponding to making geometric measurements (of area angle volume etc.). Quantum dynamics governing geometry.

Then once you have a quantum geometry, put matter and forces into it.

To me this seems like the logical unification program. "Unification of forces" does not seem logically well-founded.

What do you think? Do you actually believe that unification means unification of forces?
Should that be the aim of QG, then?

 

[marcus]

I agree that quantization of a classical theory seems strange b/c it tries to "invert the limit h = 0" ... and canonical quantization may be dangerous due to loss of large diffeomorphisms and things like that ... nevertheless it works in many cases. So let me ask why gravity is fundamentally different. I mean not simply more complicated in practice but really conceptionally different! In LQG it seems that it's harder than usual but that the naive approach might work. In string theory you essentially do the same (OK, you do not take gravity, but you take a classical theory and quantize it). If you want to address a REALLY fundamental issue then you should ask about an alternative to quantization i.e. a concept to define a theory w/o knowing its classical limit.

It seems to me that for a couple of years now, Rovelli has been regularly making explicit that he does not think starting with classical GR and quantizing is the right way to go. He pointedly prefers the other direction. Formulate a definite quantum theory of geometry. Check that it has the right limits. See if phenomenologists can figure out practical ways to test it.

IIRC he gives arguments for this approach in 1102.3660. Including incomplete but suggestive convergence of several GR quantization programs which all point towards this theory, increasing the likelihood of its working out.

To believe Suprised, MANY people would agree with Rovelli that quantizing classical GR is not the way to go. Apparently many people believe it is better to do as he does, namely start with a quantum theory and check/test.
================================

Tom, you ask why GR is fundamentally different. I think you have already reflected on this and have some tentative answers in mind. But I will venture an obvious one. GR is fundamentally different because it is a theory of GEOMETRY in which other things occur and other fields are located.

Therefore it must be fundamentally different.

A quantum theory of geometry is a theory of the framework for fields and events. A quantum state must specify such a framework---in which other things can happen. So it is quite a different problem from, say, "grand unification" of 2 or 3 particle forces.

I am intrigued by Eugenio Bianchi's proposal because it uses a manifold---where I imagine all the usual particle stuff can be defined---and the manifold is uniformly flat except on a web of defects. These defects run through the manifold and are where the curvature lives. The idea is neither altogether novel nor certain to work, but interesting nevertheless.

 

[atyy]

Well, here's Ashtekar and Singh's latest review. The last section does have the things I hoped they'd speculate about - lessons of LQC for canonical LQG and spin foams. http://arxiv.org/abs/1108.0893

 

[tom.stoer]

It seems to me that for a couple of years now, Rovelli has been regularly making explicit that he does not think starting with classical GR and quantizing is the right approach.

...

MANY people would agree with Rovelli that quantizing classical GR is not the way to go. Apparently many people believe it is better to do as he does, namely start with a quantum theory and check/test.

marcus! this is not true!

Rovelli says that quantizing a classical theory is not relevant once you have a quantum theory; therefore he concludes that it may be time to look at the quantum theories we have at hand (LQG/SF is rather a class of models, not a single theory) and to see where they take us (instead of studying their derivation). But of course these theories HAVE been created via quantization, so classical GR seems NOT to be the wrong starting point (Rovelli is not suffering from amnesia, is he?) But this program has not yet been completed. I agree that these theories seem to be consistent quantum theories, but a proof is still missing. In addition it is not clear if and how canonical LQG and SFs are related. If they are equivalent it would be nice to see why; if not it is of major importance to learn exactly why this equivalence fails!

Rovelli is promoting one way of doing quantum gravity - and his way is certainly OK. But there are other ways to attack this problem, and these are not wrong, either. They support each other, definitly.

I think we agree to try to falsify a theory of QG based on experiments solely could be a very long-term and therefore risky strategy. If there are doubts regarding the correctness of a physical theory one must try to find the the root of evil - and especially in QG it might very well be that you are able to find a serious flaw in the construction / quantization / consistency whereas it will take eons to find the error in the data :-)

 

[marcus]

...(Rovelli is not suffering from amnesia, is he?) ...

I did not say R. was suffering from amnesia Each time he has said this he has referred to the several past attempts to quantize, which have pointed towards but not precisely arrived at the current abstract SF formulation of LQG. These attempts at quantizing have been helpful heuristics. As he says in http://arxiv.org/abs/1102.3660 section on "Derivations".

==quote Zako lectures page 23 and following==

V. DERIVATIONS
I have presented the theory without deriving it from classical general relativity. There are a number of distinct derivations that converge to* the theory. In this last section, I sketch some basic ideas in these derivations. A word of caution is however needed.
Quantum-gravity research has often focused on setting up and following “quantization paths” from classical general relativity to a quantum theory. These are very useful to provide heuristic indications for constructing the quantum theory, but they are neither sufficient nor necessary for taking us to quantum gravity. If there was a straightforward quantization route, the quantum theory of gravity would have been found long ago. Any generalization requires a certain amount of guesswork. The “quantization paths” sketched below must be seen as nothing more than heuristics, which have given suggestions useful for construction of the theory, and shed light on aspects of the definitions.
The theory itself should not be evaluated on the basis of whether or not quantization procedures have been “properly followed” in setting it up. It must be judged on the basis of two criteria. The first is whether it provides a coherent scheme consistent with what we know about Nature, namely with quantum mechanics and, in an appropriate limit, with classical general relativity. The second is to predict new physics that agrees with future empirical observations. This is all we demand of a quantum theory of gravity.


Since for the moment we do not have so many useful empirical observations, it might sound that the considerations above give us far to much freedom. How then to choose between different quantum gravity theories, or different ways of constructing the theory? This question is asked often. I think it is a misleading question, for the following reason. At present, we do not have several consistent, complete and predictive theories of quantum gravity. In fact, we are near to have none at all. Most of the quantum gravity approaches lead to very incomplete theories where predictions are impossible. Therefore the scientifically sound problem, today, is whether any complete and consistent quantum theory of gravity can be set up at all. If we can solve this problem, it is already a great success, after decades of search. The issue of checking whether this is the right theory, namely the theory that agrees with experiments, comes after.
==endquote==

*"to the theory" here is to be understood in the sense of "towards". None of the several quantizations arrive exactly at the present formulation---they all point towards it from different directions.

 

[Fra]

If you want to address a REALLY fundamental issue then you should ask about an alternative to quantization i.e. a concept to define a theory w/o knowing its classical limit.

I agree, this was what I meant too with not thinking it's right starting point for unification of the other forces either (I mean even w/o gravity).

/Fredrik

 

[tom.stoer]

@marcus: first of all I think we agree that Rovelli does not say that classical GR with its quantization is a wrong starting point! He talks about "useful ... heuristic indications" - but means that this is of of limited relevance. And he makes clear why it's of limited relevance, namely b/c "distinct derivations ... converge to the theory" - or perhaps they don't - we don't know yet - b/c "we do not have several consistent, complete and predictive theories of quantum gravity ... we are near to have none at all". So it's about the relevance or the weight of different approaches and different interpretations and ratings of "quantization" or "construction" - and that's that's pretty subjective.

I don't think that everybody in the community agrees with him. Think about Ashtekar's point of view - you'll find it in the LQC review paper http://arxiv.org/abs/1108.0893 - or think about Thiemann's research program; or Nicolai's "outside view" to which - after 6 years - there still seems to be no fully satisfactory reply; or think about the overview presented in the paper I cited in the first post of this thread.

Let me stress some of my recent statement:
If the issues I listed ... cannot be resolved, ... the whole effort is in vain.
If there are doubts regarding the correctness of a physical theory one must try to find the the root of evil.
If they (SF and canonical LQG) are equivalent it would be nice to see why; if not it is of major importance to learn exactly why this equivalence fails.

We do not know why quantization works at all, we do not know why "inverting the singular limit h=0" together with some heuristics works at all. But we know that it does work very well in many successfull theories - and therefore it is of major importance to understand whether it works in QG as well - and if not - why it fails.

If Rovelli thinks that this is of little relevance than I totally disagree.

 

[Fra]

So it's about the relevance or the weight of different approaches and different interpretations and ratings of "quantization" or "construction" - and that's that's pretty subjective.
...
and therefore it is of major importance to understand whether it works in QG as well - and if not - why it fails.

I assume were talking about to what extent it makes sense to apply the quantum formalism as we know it, to the gravitational field as a whole.

I have only read a little on Rovelli's reason and doesn't know much about others LQG people, but I've seen Rovelli avoid several key questions on the grounds that he doesn't want to "speculate" in wether QM applies or not.

AFAIC QM is only known and tested on small subsystems. This is a point Smolin has made repeatedly in different places. IMO the reason for this is that the observer that looks at a subsystem, is effectively classical - this is why it works IMO. This also IMHO explains conceptually why one might strongly suspect that it is the wrong approach to gravity in particular (the argument can be made also to other forces but it's much more subtle).

With gravity it's more obvious since that's the dominating force at large scale, and the observer-observed environment-subsystem assymetry fails.

This is the simple reason why I think the approach are unlikely to work out.

However the root of problem is common to String theory as well, although in a more subtle way. Which is probably yet anohter reason why no one cares since it's a problem "everbody has": which is a good excuse to not do anything about it

/Fredrik

 

[atyy]

Bonzom & Laddha: "It has been put to a rigorous mathematical status, which makes clear that it is a generic way to quantize background independent theories. ... A key theorem asserts the uniqueness of the quantization map when diffeomorphism invariance is required [5]."

So it could be the non-perturbative completion of string theory, which is supposed to be background independent? Would AdS/CFT which presumably contains gravity in the bulk be background independent enough to fall within this framework?

 

[tom.stoer]

Bonzom & Laddha: "It has been put to a rigorous mathematical status, which makes clear that it is a generic way to quantize background independent theories. ... A key theorem asserts the uniqueness of the quantization map when diffeomorphism invariance is required [5]."

This is the celebrated LOST theorem. But it only refers to the kinematical framework and does not say anything regarding dynamics, anomalies, off-shell closure etc.

btw.: I don't like 'theorems' in theoretical physics b/c in many cases it turns out that they are just 'physical theorems' - whatever this means - but not mathematical ones; too many hidden assumptions etc; I haven't seen a physically viable theory relying on such theorems; and I haven't seen such theorems leading to physically viable theories :-(

 

[suprised]

It is hard to stay focused in such a discussions since many key words (like background independence, the issue of quantizing a classical theory, etc) are not sharply defined, and different people associate different things with them.

Eg there are two different points related to the issue of "quantizing a classical theory".

1) Essentially the question whether gravity is an effective (or "emerging") theory of some underlying theory (a), or a fundamental theory (b).

If (a) applies, then it would not make much sense to attempt to quantize classical GR, in a similar way as it does not much sense to try to quantize a hydrodynamical system. The idea is that the theory needs to be embedded into a larger one, with different degrees of freedom. This is the point of view of many modern approaches, like string theory.

The opposite view (b), namely that the theory can be defined within from itself, by somehow regularizing it, is taken eg by canonical quantization and UV fixed point approaches, lattice models (dynamical triangulations etc), and classicalization models.

I am not sure in what category modern SF approaches fit here, actually when talking to different people, I keep on hearing both a) and b).

2) There is another, different issue of "quantizing a classical theory". When given an abstract given quantum theory, then to define and extract a classical limit can be very hard. Normally we do not perceive this as a big issue, as long as the strategy "quantize a classical theory" works. But we should not forget that actually the logic is the other way around. The correspondence principle is in a sense one of the biggest miracles ;-)

I say this because it becomes more and more evident that in order to understand QG, this issue seems a crucial one. And I don't mean how to extract a classical limit from LQG or a lattice model. I rather talk of holography and black holes. Here it seems that massive non-locality plays an important role at the quantum level. If anything is true in Mathur's fuzzball approach, then there would be quantum effects acting all the way up to the horizon, ie, of macroscopically large distances. The "miracle" is then how the classicsal BH geometry arises from the coherent superposition of all those quantum states.

Obviously, starting from quantizing a classical theory, would then be the completely wrong way to think about these problems. And that's probably why the problem of black hole violation of unitary took such a long time to resolve.

 

[tom.stoer]

suprised, thanks for the clarification.

To make a clear distinction (a - emergent) and (b - fundamental) is fundamental. It's so to speak the very first step. And in that sense quantizing GR could simply be wrong.

Regarding the truth in the fuzzball approach and the viability of the (canonical) quantization of a classical theory: I do not completely agree. It will definately be harder to identify the fundamental formulation, d.o.f etc., but it will not be impossible. Why shouldn't LQG being able to produce a 'large quantum fuzzball'? I mean we still do not have a classical limit which allows us to describe dynamical objects like BHs in LQG, but I see no principle obstacle (we did the same thing for QCD and hadrons).

I see no techical or conceptual reason why LQG should fail except for the open issues mentioned in the begining. But I clearly see that it will fail if gravity is not a fundamental theory.

 

[tom.stoer]

Regarding quantization; I like Wittgenstein's statement (of course in a different context and with a different meaning): He must so to speak throw away the ladder, after he has climbed up on it

 

[suprised]

Tom,

I guess it again boils down to the same question as always: can LQG or any other given theory, in principle, provide the correct of degrees of freedom in order to make BH work and in order to restore unitarity for high energy scattering, or not. In other words, do we need to add extra stuff (embed gravity in a larger theory) or not.

 

[Fra]

1) Essentially the question whether gravity is an effective (or "emerging") theory of some underlying theory (a), or a fundamental theory (b).

Since I symphatize to this general direction(a), but not with ST, I'd like to add a distinction since "emergent" is also used in different ways.

(a1) As you say, emergence can mean originating from a bigger more complex theory behind which there is some fixed objective degrees of freedom. But then the problem IMO seems to be that again of uniqueness of this bigger theory and the new theory space just gets larger here unless it's complemented with some additional selection principles. It's not either clear if this "selection" is a physical choice or just existing in some abstract mathematical realm.

(a2) By emergence one can also refer too a kind of algorithmic type of emergence where we are talking about evolving theories, and here the emergent theories corresponds to a kind of stationary state or local equilibrium between theories, but without global or objective characteriztion. And without "fundamental degrees of freedom". In this picture the focus is on classifying and understanding the components of the evolution.

A similar distinction exists between objective and subjective bayesian interpretation to conditional probability. a1 is more like hte objective bayesian, but a2 refers to the subjective view in which the EFFECTIVE objectivity that is undeniable is just the result of tuning of subjects.

The main difference is that a2 potentially provides the selection mechanism missing in a1. In a1 the arbitrariness is the choice of the non-observables master theory. In a2 the arbitrarieness is the choice of subject=observer, but if one adds the idea that the "emergence" refers to that the population of subjects is interacting and exters selection pressurs on each other - a "tuning" naturally takes place. But the catch is that since there is no external "description" in which this tunig process can be "embedded" there is only one way to learn and that is to enter the game.

So there is an apparent circularity in a2, that is the constructive key(rather than problem) and leads to evolutoion. Somehow the laws of nature are determined by the properties of matter system populating it, similarly the evolution of hte matter systems themselves are guided by the collectively established laws in the random walking sense.

I find it striking that note the FORM of this is very much like the constructing principles behind GR, BUT applied to inferences by general observers rather than just observers pictureed as "reference frames". There is a lot of qualities of an observer that doesn't possible encode into a reference frame. For example information capacity.

Something like that would be IMO a more in line with what maybe GR would have been if it was constructed today, rather than 100 years ago.

I like how Jaynes put it when he first read up on Shannons papers...

"the essential content of both statistical mechanics and communication theory, of course, does not lie in the equations; it lies in the ideas that lead to those equations."
-- "Probability Theory in Science and Engineering", 1956

The same statement can IMO be applied to GR. We can keep most of it's original constructing principles, without bringning the classical *result* (equations) out of context. It's out of context IMO because the structures of classilca GR simply aren't targets for a measurement theory in the first place. I can't help but having a distinct feeling that it's an misapplication.

/Fredrik

 

[marcus]

@marcus: first of all I think we agree that Rovelli does not say that classical GR with its quantization is a wrong starting point! He talks about "useful ... heuristic indications" - but means that this is of of limited relevance. And he makes clear why it's of limited relevance, namely b/c "distinct derivations ... converge to the theory" - or perhaps they don't - we don't know yet - b/c "we do not have several consistent, complete and predictive theories of quantum gravity ... we are near to have none at all". So it's about the relevance or the weight of different approaches and different interpretations and ratings of "quantization" or "construction" - and that's that's pretty subjective.

I don't think that everybody in the community agrees with him...

I think we can agree on some of what you say here. I would go further and say quantization of classical GR was the right starting point. And it was right to work on it for quite many years and try try different ways and get lots of "heuristic indications".

Only NOW this is of limited relevance, the message is, and it is NOT the way to go now, in your research. That is how I hear it anyway.

Nobody is disparaging the PAST work on quantizing the classical. Nor should one disparage the work of the handful of people who may still be exploring quantization. It's useful heuristic guidance and interesting that so many different quantizations seem to point towards the current version.

But yes, as you say, "limited relevance". It is not essential NOW to go back and determine why this or that specific quantization did not give exactly the same theory as some other specific quantization. I think that is the practical meaning of "limited relevance", is it not?
==========================

So I think we agree on some of this. However we may differ as to the importance we attribute to this:
==quote Zako lectures page 24==
... The “quantization paths” sketched below must be seen as nothing more than heuristics, which have given suggestions useful for construction of the theory, and shed light on aspects of the definitions.
The theory itself should not be evaluated on the basis of whether or not quantization procedures have been “properly followed” in setting it up. It must be judged on the basis of two criteria. The first is whether it provides a coherent scheme consistent with what we know about Nature, namely with quantum mechanics and, in an appropriate limit, with classical general relativity. The second is to predict new physics that agrees with future empirical observations. This is all we demand of a quantum theory of gravity.
==endquote==

As far as I can tell, the Loop community is rather focused. There are perhaps two or three main approaches being worked on by substantial numbers of people. I don't see a "landscape". If any variant being worked on should turn out to meet those two criteria, I would be dubious of anyone claiming that the effort was "in vain".

 

[tom.stoer]

marcus, we agree on nearly everything excpet for

... "limited relevance". It is not essential NOW to go back and determine why this or that specific quantization did not give exactly the same theory as some other specific quantization.

...

The “quantization paths” sketched below must be seen as nothing more than heuristics, which have given suggestions useful for construction of the theory ...

Let me explain via I totally disagree.

A) Suppose you construct gauge theories based on SU(N); you can have SU(M)*SU(N), you can have different generations of fermions, maybe adjoint fermions, perhaps SUSY, whatever. To check the viability of the theory the construction procedure is irrelevant (it is well-established), all what counts is whether the theory fits to experiment.

B) Now suppose you construct a chiral gauge theory with different gauge groups and different generations. To check the viability you have to ask for anomaly cancellation, you have to review the construction of your theory. It's a waste of time to construct LHC++ over the next decades and to rule out a theory which fails due to anomalies; you could have killed the theory with a few pages of calculations!

Suppose you quantize gravity using spin foams; you can have different gauge groups, different intertwiners, quantum deformation etc. This lokes somehow like case A. Now you know that usually the PI and the canonical formalism are related - but for some reason the family of theories you have constructed does not fit into a canonical framework. It is quite close, but ... In addition there is a canonical theory which is quite close, but again not fully identical; or it may be but you can't prove it. Still case A ?

Now somebody tells you that the canonical theory to which you SFs seem to be equivalent
- misses off-shell closure
- has no well-defined Hamiltonian; the "natural' one is "ultra-local"
- has been constructed via a non-separable Hilbert space
- has a constraint algebra with structure functions (instead of constants)
- ...
Still case A ?

So the conclusion is that the theory may suffer from fundamental inconsistencies.

Still case A ?

 

[suprised]

I guess it's quite obvious that LQG and SF/GFT should be viewed as program or framework, rather than anything close to a definite theory. Eg just have a look at Oriti's lectures at
http://ph-dep-th.web.cern.ch/ph-dep-th/content2/THInstitutes/2011/QG11/talks/Oriti.pdf
which gives an extensive overview of the many different models being investigated.

The big Q is whether this whole program will eventually converge onto some concrete theory or not - anybody's guess!

 

[qsa]

Does "unification" always mean "unification of forces" for you?

I think gravity is a theory of geometry (not just another force.) So trying to unify it with the three forces is the wrong goal.

I see the program as connecting GR with QM. GR is about dynamic geometry. To connect it with QM means to find out how to do quantum geometry.

In other words, forget about "unification of forces". Find out how to represent quantum states of geometry. A hilbert space of quantum states of the geometry of the universe. Geometric operators, corresponding to making geometric measurements (of area angle volume etc.). Quantum dynamics governing geometry.

Then once you have a quantum geometry, put matter and forces into it.

To me this seems like the logical unification program. "Unification of forces" does not seem logically well-founded.

What do you think? Do you actually believe that unification means unification of forces?
Should that be the aim of QG, then?

The whole idea of QUANTUM gravity is just that to take GR away from geometry (in the metric sense) and show its quantum origin which should have united it with other forces. and to finally show us how all these forces arise naturally together with matter being the center of it all. none of the QG theories has come to anything close, without going into details. But I admit that both opened some windows of opportunities, like dualities in string and finding matter in LQG.

 

[marcus]

I guess it's quite obvious that LQG and SF/GFT should be viewed as program or framework, rather than anything close to a definite theory. Eg just have a look at Oriti's lectures at
http://ph-dep-th.web.cern.ch/ph-dep-th/content2/THInstitutes/2011/QG11/talks/Oriti.pdf
which gives an extensive overview of the many different models being investigated.

The big Q is whether this whole program will eventually converge onto some concrete theory or not - anybody's guess!

That's a curious attitude!
We are not talking about Group Field Theory but about LQG. LQG is indeed a program (containing both canonical and spinfoam approaches as well as other lines of investigation).
And there is also a definite LQG theory. The person normally asked to review the LQG program is Rovelli. But I see he was not at your CERN workshop.

The majority of the work in LQG nowadays is spinfoam. That is beginning to include Loop cosmology, which has moved in that direction.

A good review for non-specialists would be "Loop Quantum Gravity: the first 25 years"
http://arxiv.org/abs/1012.4707

It is confusing for someone who is a non-specialist to make up their own terminology like "SF/GFT" and interject their own perspective. Better to align terminology with the prevailing review papers of leading experts in the field.

Oriti does GFT, which is a very general line of research connecting with a great variety of stuff, not necessarily even limited to quantum gravity. There certainly is no one definite theory that stands out in the GFT program.

But as I said, we are talking about LQG in this thread, which is now formulated primarily with spinfoam in most Loop research. In that case there is one unique definite LQG theory which stands out, and which even is concisely formulated. One page..."This is the theory."

So LQG is both a program and a definite theory.

It now remains to check if that theory meets two criteria. A. the right limit. B. predicting new phenomena to be confirmed or disconfirmed by future observation.

Regarding the definite LQG theory, nothing else matters.

 

[tom.stoer]

And there is also a definite LQG theory.

Canonical and SF approach have not been shown to be equivalent, so there are at least two :-) In addition there are quantization and regularization ambiguities in H.

... LQG ... which is now formulated primarily with spinfoam ... In that case there is one unique definite LQG theory which stands out

It is unclear whether the different IP-limits are allowed and how they are related; renormalization group flow and parameter space has not yet been studied; different intertwiners can be used. So it's a single approach but not a single theory in the classical sense.

But uniqueness it not the issue; conistency is!

 

[genneth]

I haven't check this thread for a while and it seems to have exploded. Let me write down some thoughts, in no particular order:

@tom: the issue of anomaly cancellation shouldn't be a problem here because anomaly issues are fundamentally a perturbative problem. In the current Rovellian view he simply defines a manifestly finite theory (on finite graphs) and takes the limit. I agree that the existence of this limit is problematic, but as a condensed matter theorist I've seen and done much worse without too much problem, so :shrug:? My intuition says that the limit is probably fine as long as the admitted graphs are not too "wild", which probably means that one has to restrict the structure, which I believe is indeed an open question currently anyway, and actively investigated.

@atyy: At the same time, I don't think being only an effective theory is a problem. Again, from a condensed matter point of view, one can certain go ahead and quantise non-microscopic degrees of freedom and hope to get something reasonable.

As a matter of terminology: I think of the canonical approach as trying to perform promotion of a Poisson algebra to a quantum one, whilst satisfying the requirements of consistency as laid out by Dirac so many years ago. It is my understanding that this program did not really work out, in ways which the infamous Nicolai paper points out, to do with a failure of closure of the constraint algebra. The benefit of this program is that upon successful completion it would automatically give the (functorial) classical correspondence and immediately reproduce GR in the classical limit.

I thought that the covariant or Spin-Foam approach (which is what I think of Rovelli as being behind these days) as trying to side-step the entire issue. Here, one sets up an obviously well-defined quantum theory, which is motivated but not derived in any sense from GR, and then the difficulty is to show that GR is given in the right limits. Clearly, one of the issues which has only recently become apparent is what that limit actually is --- and it seems to involve the IP. This theoretical structure also has the benefit that one feels free to play around with the basic constructs, and e.g. come up with entirely different intertwiner structures, q-deformations, etc. and just go ahead and compute the outcome and see if it's interesting or relevant.

Finally, Fra's persistent issue of observer/system dichotomy is, as always, a good issue and it's unclear how any of the existing ideas deals with or side-steps the issue. Fra usually phrases it in an information-theoretic point of view, but a more physical one (which certainly helped me to understand the sharp end of the question) is simply the observation that in usual field theories one has measurement equipment which has infinite mass and no charge so that there is a stable background and one can measure things like recoils precisely; clearly for gravitation this completely breaks down because mass is charge.