Current status of LQG

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  • #26
marcus
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Tom particularly asked for papers he could print out, mark up, and read on the train. In other words, the video of Madrid conference talks don't suffice. This makes sense to me (I like to mark up printout, write in the margins etc.)

When this thread was started I did not know of a satisfactory bunch of papers that would give a summary of the current status. But now the situation has improved. In the preceding post I gave links to papers that either appeared first in July-August 2011, or if they appeared earlier in 2011 had been substantially revised in July-August. Based thereon I would say briefly:

1. Lqg now has a definitive formulation.

2. Evidence is mounting that this definitive version has the right limits.

3. Considerable effort is directed at seeing how to test loop cosmology with early universe data.

I think the most valuable part of this thread, so far, is the post#1 list of questions to be answered. Tom is right that the Zakopane lectures are not exhaustive---they cover some but not all of these questions---and some, like the meaning of the Immirzi parameter, are the subject of interesting current research! Maybe we can find answers to some of these questions, and indicate ones that involve work in progress. Here is Tom's list:

==quote==

So my question is whether there is a recent review article (or a new book in preparation) covering (some of) the following topics including relevant open issues:
- definition and status of path integral and canonical formalism plus their relation
- open (or solved) issues regarding Hamiltonian, dynamics, regularization, off-shell closure of constraint algebra, ...
- meaning, value, ... of the Immirzi parameter
- different classes of spin networks, different vertices / intertwiners (higher SU(N) and/or higher dimension)
- different graphs w/ and w/o dual triangulation
- quantum deformation, status of the cosmological constant
- matter coupling for fermions and gauge fields, gauge fixing for other gauge fields, SUSY / SUGRA
- renormalization, summing / refining, "block-spin" method
- horizons, surface Hilbert spaces, holographic principle
- definition of observables
- construction of coherent states, semiclassical limit, propagators, ...
- phenomenology
==endquote==
 
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  • #27
marcus
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Tom asked about the current status of LQG and I've pointed mainly to the expanded August version of the current review of loop gravity: http://arxiv.org/abs/1102.3660
and mentioned some shorter auxiliary "helper" papers that go along with that review. (the Magliaro Perini is just 9 pages.)

I'd like to add another suggested auxiliary resource. This is in two parts. Winston Fairbairn's talk at the ILQGS about the quantum group introduction of the cosmo constant.
The interesting and timely thing is that Hanno Sahlmann just posted a essay on the work of Fairbairn and Meusburger this month (3 August) at the ILQGS blog. It gives some extra intuition about what is an important recent development. (finiteness, convergence as well as incorporating the cosmological constant.)

Here is the page that has both Hanno's essay and links to the AUDIO and SLIDES PDF for Winston's talk:
Quantum Deformation of 4D Spin Foam Models
http://ilqgs.blogspot.com/2011/08/quantum-deformations-of-4d-spin-foam.html

The Fairbairn Meusburger paper this talk is based on is Rovelli's reference [11] in his current review of loop gravity:
http://arxiv.org/abs/1012.4784
Quantum deformation of two four-dimensional spin foam models
Reference [12] is to subsequent work by Muxin Han in the same area:
http://arxiv.org/abs/1105.2212
Cosmological Constant in LQG Vertex Amplitude
==quote Muxin Han conclusions==
To summarize, in this paper we propose a new q-deformation of the Euclidean EPRL/FK spinfoam vertex amplitude. The concrete construction uses the evaluation of the Vassiliev invariant from 4-simplex graph. We also show that the asymptotics of the q-deformed vertex amplitude gives the Regge gravity with a cosmological constant (from Regge calculus using flat 4-simplices) in the regime that the physical scale of the 4-simplex is much greater than the Planck scale lp but much smaller than the cosmological length lc.
==endquote==
For anyone not familiar with it, the cosmological length lc, given by Λ = 1/lc2, is the length scale associated with the cosmo constant Λ.

Like the Magliaro Perini paper just published in EPL, that I mentioned in post #25, Muxin Han's paper is only 6 pages, so maybe we'll take those as our add-on helpers to the main review 1102.3660. I want to keep any additional material brief.

That would make the combined essential "current status" review be
1102.3660+1108.2258+1105.2212
Zakopane lectures+Emergence of gravity+Cosmological constant
Rovelli +Magliaro Perini + Han
33 pages +6 pages +6 pages
On the basis of this overview, I'd sum up the essentials by saying loop is now a definite theory and evidently finite with the right limits. The loop research community has grown in size and shows an active interest in testing.
 
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  • #28
marcus
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  • #29
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==quote==
So my question is whether there is a recent review article (or a new book in preparation) covering (some of) the following topics including relevant open issues:
- definition and status of path integral and canonical formalism plus their relation
- open (or solved) issues regarding Hamiltonian, dynamics, regularization, off-shell closure of constraint algebra, ...
- meaning, value, ... of the Immirzi parameter
- different classes of spin networks, different vertices / intertwiners (higher SU(N) and/or higher dimension)
- different graphs w/ and w/o dual triangulation
- quantum deformation, status of the cosmological constant
- matter coupling for fermions and gauge fields, gauge fixing for other gauge fields, SUSY / SUGRA
- renormalization, summing / refining, "block-spin" method
- horizons, surface Hilbert spaces, holographic principle
- definition of observables
- construction of coherent states, semiclassical limit, propagators, ...
- phenomenology
==endquote==
What do you guys think about the way the open questions are connected, and which that are more fundamental (and thus might resolve the others as spin offs once solved)?

I find it interesting that all research fields tend to list "open questions" where some of them are reall conditional upon wether you've comitted to the program already. While some "open questions" implicitly may question the program itself.

I'm curious what you guys think are the key questions in LQG? Ie. the ones that is better focused on first?

My own view is that I always get hung up on Rovellis IMO incomplete analysis of the observers role in a theory, and in particular the inferential status of the observer invariants in the context of a scienne. How to define observables not only mathematically, but in a way that is inferrable and computable by an actual inside observer.

Indeed ST and ordinary QFT also has problems with this, but it's different.

I just feel that some questions are of such profound importance, since all the other questions are built upon them that I think more focus should be brought to them.

For example a simple think: What exactly is the observational connection of the transition amplitudes between spin network states in LQG? More specifically, how is the probability and probability space encoded by the observing system? It seems, it isn't. And I recall that Rovelli for some reason thinks this isn't important. But I really don't understand how one can be comfortable in that position. It freaks me out.

/Fredrik
 
  • #30
marcus
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Hi Fra,
I just posted this at N.E.W.
The issue is that so far LHC sees no sign of susy or extra dimensions and one could say that this is good news for loop gravity because the current version of the theory is distinctly 4D and not-sugra. Does that make sense to you?

Here is what I posted, in response to a comments by Shantanu and Giotis:

==quote==
Shantanu: So Marcus, how then does LQG address the dark matter problem? or is the dark matter have nothing to do with electroweak scale according to LQG?
==========================
Giotis: It is widely accepted that LQG is not incompatible with SUSY/SUGRA and the papers you mentioned just prove this point…
LQG has nothing to say about physics at LHC; it can’t even derive GR at the classical limit.
==========================
There is now a kind of standard formulation, by far the most prevalent in terms of the number of researchers using it. This has developed since 2007. Thiemann’s “Towards LQSG” papers (towards loop sugra and extra dimensions) are along a different line and are preliminary.
I merely watch the field and don’t speak with authority. All I can say is that LHC seeing extra dimensions (and I think also supersymmetry) would be a severe setback for the program—equivalent to losing 4 or 5 years of work.

I’m talking about the current *prevailing version* of LQG summarized here:
1102.3660+1108.2258+1105.2212
Zakopane lectures+Emergence of gravity+Cosmological constant
Rovelli +Magliaro Perini + Han
33 pages +6 pages +6 pages
On the basis of this I’d say this version of loop is now a definite theory and much evidence points to it being finite with the right limits.

Current loop gravity has a definitive concise (one-page) formulation which is explicitly 4D and which is not sugra. If it had to include extraD and sugra it would probably have to be drastically modified. That is why Thiemann’s 2011 series of a half dozen papers says “towards”. I would accept that the basic ideas and philosophy of loop gravity could be be adapted in a new formulation. That’s credible. But it would mean throwing out the current version that a lot of people have worked on developing over the past 4 or 5 years.

Shantanu, thanks for asking about Dark Matter. I haven’t heard anything conjectured about DM from the loop gravity researchers—the people whose research is actually focused primarily on loop—that I can recall. You can see the progress that has been made in including fermions and Yang-Mills fields if you look at the August update of 1102.3660, the current review paper. Maybe the approach could accommodate susy matter but not sugra! I don’t know how that would be resolved. I think from a loop standpoint DM is simply somebody else’s problem. But I just watch from the sidelines. If I’m missing something (and DM is being addressed within loop context) please let me know.

If I were doing loop gravity research I would be feeling relieved and happy that LHC is not seeing either susy or extra-D. It increases the chances that the current approach is on the right track.
==endquote==
 
  • #31
Dear Marcus,

I was about to post on NEW to reply to you. Often I am sympathetic to your comments, but this time I am afraid I agree with the others. Supersymmetry and supergravity are very easily included in LQG and spin foam models and were a long time ago. N=1 supersymmetry and supergravity are completely straightforward, there is no difficulty, nor does there seem to be any new result that requires N=1 supersymmetry. This is why the topic has not been much pursued. The literature on the inclusion of supergravity into LQG began with an early paper of Jacobson extending our action for the Ashtekar variables to supergravity. There are papers by Pullin and collaborators which were followed by several papers around 2000 by Yi Ling and myself extending spin networks to N=1 supergravity. We also made progress on 11 dimensional supergravity. I don't right now recall who wrote the several papers on extending spin foam models to supergravity.

Historically LQG has roots in supergravity. The Ashtekar-Sen form of the constraints was first found by Sen studying supergravity. An early very significant use of the Ashtekar connection is in Witten's proof of positive energy in general relativity, which was partly inspired by arguments of Deser and others (if I recall right) on the positivity of the hamiltonian in supergravity.

The really interesting question would be extending LQG and spin foam models to extended supersymmetry,and supergravity ie N=2 and higher, where the algebras are much more interesting and more constraining. This would be necessary to compare directly results on black hole entropy with string theory. The only one I know who has worked on this is Yi Ling, but his results remained unpublished.

There are several ideas which have been studied to incorporate the standard model in some interesting way in LQG and spin foam models. To my knowledge none of them so far make any predictions for the LHC.

Thanks, Lee
 
  • #32
Fra
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The issue is that so far LHC sees no sign of susy or extra dimensions and one could say that this is good news for loop gravity because the current version of the theory is distinctly 4D and not-sugra. Does that make sense to you?
I suppose it does but from my perspective those issue while certainly unimportant still comes out as problems built on questionable stances to deeper questions - this is what disturb me. And I'm not even sure these questions would appear once the deeper stances are made. This is why I am more motivated to start with what I think are core problems.

From a pure inference point, it seems dimensionality should be explained. After all, all it is, is an index for abstract distinguishable events. But I don't think starting at 10 or 11 and compactify to 4 is the way. I rather think that we should start from 0, let the continuum emerge and then dimensions. Sometime like causal set style starting points.

/Fredrik
 
  • #33
Fra
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Dear Smolin, it's very nice to see you post here!

I've very much enjoyed some directions you engaged in, I'm thinking about your thinking wrt evolving law and your cooperation with R. Unger. Your two perimeer talks on the subject I'm aware of have been extremely thought provocing in a good way.

I must say I find alot of that, and in particular alot of Ungers points to be at face with alot of the structural realism in LQG.

Since you worked in both, how do you merge this two apparently diverging research directions? I find this somewhat paradoxal. Are they simply two diverging views that you like to entertain, or is there hidden connection I haven't understood?

/Fredrik
 
  • #34
tom.stoer
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Dear Lee!

it's a pleasure to see you here in the 'beyond forum'!

Just a short note: the guy recently working on n-dim. SFs and LQG with SUGRA is Thiemann from Erlangen, Germany.

Tom
 
  • #35
marcus
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Since you mentioned Thiemann's current work on D+1>4 Spinfoams, let me quote from the abstract of http://arxiv.org/abs/1105.3703
"Loop Quantum Gravity heavily relies on ... Unfortunately, this method is restricted to D+1 = 4 spacetime dimensions".

And from page 2:
"... Of course, a connection formulation is also forced on us if we want to treat fermionic matter as well. A connection formulation for gravity in D + 1 > 4 that can be satisfactorily quantised, even in the vacuum case, has not been given so far. For the case D + 1 = 4, it was only in 1986 that Ashtekar..."

And from page 3.
"In this paper, we will derive a connection formulation for higher dimensional General Relativity by using a different extension of the ADM phase space than the one employed in [13, 25] and which generalises to arbitrary spacetime dimension D + 1 for D > 1. It is based in part on Peldan’s seminal work [26] on the possibility of using higher dimensional gauge groups for gravity as well as on his concept of a hybrid spin connection..."

Setting the question of SUSY aside, what I was saying in my previous post #20 was Yes LQG could be adapted to higher D if we did see evidence of extra dimensions, but it would be a SETBACK---I guessed it would be like losing the last 4 or 5 years of work.
(see my post https://www.physicsforums.com/showthread.php?p=3476917#post3476917 )
So loop researchers can express LEGITIMATE SATISFACTION that evidence of extraD has not shown up.

Now I may be wrong when I make a similar guess about SUSY! But I am skeptical of any suggestion that incorporating supersymmetry in the current version of spinfoam LQG would be automatic.

If I remember right I've seen papers from before 2005 that stated that LQG, as the author conceived of it then, would accept supersymmetry. But the theory has changed remarkably in the past 4 years of so, and has reached a definitive formulation (1102.3660) with considerable evidence indicating it has the right limits.
I have to allow for the possibility that the present formulation, representing some 4 years of work, would have some catch or present some stumbling block to SUSYfication.

So absent some published research to the contrary, I have to remain skeptical of what I think Lee is saying. LQG has not stayed the same. Just because somebody back before 2005, say, thought there would be no problem formulating LQG (as he imagined it then) with arbitrary D and with supersymmetry, does not mean that you could do that with the version which has developed over the years 2007-2011.

So I can understand how, despite what Lee says, a currently active loop researcher could find encouragement in the fact that there are no signs of SUSY yet. That was basically my point at NEW.
 
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  • #36
marcus
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Dear Lee!

it's a pleasure to see you here in the 'beyond forum'!

Tom
A pleasure it certainly is!

Just a short note: the guy recently working on n-dim. SFs and LQG with SUGRA is Thiemann from Erlangen, Germany.
Since both Lee and he gave invited talks at the May loops conference at Madrid, where Thiemann and collaborators presented it, Lee must be well aware of the recent Erlangen work. I'd love to hear if he has any thoughts about it.
 
  • #37
Fra
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So Marcus and Tom, to get back to the simple question I asked.

Do you actually consider this issue of supersymmetry (wether it "exists" or not in some sense, and wether it can be consisntely combined with LQG or not) the most important question for LQG?

/Fredrik
 
  • #38
tom.stoer
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As Rovelli and Lee said, LQG is consistent with various approaches of adding matter (I haven't seen adding gauge fields with complete gauge fixing and regularization which is non-trivial in continuum theories; perhaps LQG is a way not to gauge-fix but to integrate over gauge degrees of freedom keeping the matrix elements finite). Usually adding matter is nothing else but an additional coloring of graphs. Regarding SUGRA there will exist certain restrictions regarding this coloring.

The question is where SUSY / SUGRA really comes from and which problems it tries to solve. There are several lines of reasoning.

SUSY like the MSSM tries to solve certain problems in elementary particle physics (infinities) - which may be absent in LQG based approaches. So we don't need SUSY in LQG. In addition SUSY claims to explain the convergence of the strong and electro-weak coupling constants. But w/o experimental indications for SUSY we don't need SUSY for that reason, either.

SUGRA tries to solve similar issues when gravity is taken into account. But b/c these issues are absent in LQG, again we don't need SUGRA. In addition SUGRA as derived from string theory can be formulated in various dimensions (with various restrictions). As the world we see is 4-dim., there seems tobe no reason to introduce higher-dim SUGRA models outside the string theory research domain. So we need SUGRA iff we try to harmonize LQG and strings or if we want to quantize SUGRA (inspired by strings) using LQG methods.
 
  • #39
tom.stoer
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There is an interesting fact regarding dimension of spacetime in LQG: LQG is constructed from SL(2,C) which is rooted in SO(1,3) or Spin(4). But the dimensionality of spacetime is lost when looking at the defining graphs which need not be dual to any spacetime triangulation. Therefore at the fundamental level LQG has no build-in dimension (a graph has no "dimenson'"), only a kind of "remnant" which is SL(2,C) or SU(2). That means that somehow dim=4 will emerge dynamically, similar to the dimension in CDT - at least this is my understanding.

But if this is true then why shouldn't we study arbitrary spin networks defined via X(q)(m,n). Here X means any Lie or Kac-Moody algebra from the A,B,C,D,E series, q means that we could possibly introduce a quantum deformation and m,n means that we allow an arbitrary number of time dimensions (in addition we could add grading). It is then interesting to find out if there always is a "long-distance"limit from which a smooth manifold of dimension dim=D does emerge and how this D is related to X.

That would mean that LQG turns into a "general spin network approach" just like "gauge theory". Then of course one would have to answer the question why nature selected a specific X.
 
  • #40
marcus
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So Marcus and Tom, to get back to the simple question I asked.

Do you actually consider this issue of supersymmetry (wether it "exists" or not in some sense, and wether it can be consisntely combined with LQG or not) the most important question for LQG?

/Fredrik
I don't know what gave you that idea, Fra. I commented because of a snarky comment someone made at N.E.W. about a loop researcher "gloating" because SUSY wasn't being found. Gloating sounds mean and malicious. Taking pleasure in the string program's troubles.
Indeed no-signs-of-SUSY is good news for loop, but for different reasons from the one implied.

And admittedly no-signs-of-SUSY is bad news for string, but that is not something loopers would be gloating about. What happens to string is not their concern__ they have their own active growing research program to think about.

I think it is important that we be able to discuss all these matters without belligerence or snark. Time for bed. I'll try to get back to this in the morning.
 
  • #41
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SUSY like the MSSM tries to solve certain problems in elementary particle physics (infinities) - which may be absent in LQG based approaches. So we don't need SUSY in LQG.
The main reason for introducing SUSY is the hierarchy problem. This has little to do with infinities. That is, the problem does not go away if one introduces a cutoff at some high energy scale; it has to do with stability of a small scale under quantum corrections, in the presence of another, large scale. LQG has nothing to say about this.

Indeed, as I have been pointing out somewhere else here, finiteness is not enough for consistency. For example, putting a non-renormalizable theory (like the Fermi theory of weak interactions) on a lattice, thereby regularizing the divergences and removing infinities by brute force, does not make the theory consistent. There are issues such as unitarity. Typically new degrees of freedom need to be added at a certain scale in order to unitarize the quantum theory.

Thus to me it is by no means obvious whether the advertized finiteness of LQG really solves the problems of quantum gravity (assuming for the time being that LQG leads to gravity in the IR at all). If it is just a lattice-like regularization of gravity, it may be analogous to a lattice-regularized Fermi theory; the latter is made consistent by embedding it in a gauge theory with extra degrees of freedom (W-,Z-bosons). String theory seems to teach us that one needs in fact infinitely many degrees of freedom. Right now I simply don't know how to reconcile these two standpoints.
 
  • #42
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The big problem with string is it insists on imposing a background. This is not necessarily wrong, but, remains unproven.
 
  • #43
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The big problem with string is it insists on imposing a background. This is not necessarily wrong, but, remains unproven.
I am not sure what you mean with unproven. At any rate, you refer to the common definition of string theory in terms of a world-sheet embedded in space-time. This old-fashioned approach is however not the end of the story, see AdS/CFT which serves an example of background independence within string theory. Moreover, there are attempts to describe an emergent space-time with matrix mechanics.

Thus the issue of background independenceare is by far not yet settled; in particular it is not clear whether this is even a problem rather than a red herring. At any rate, it's off topic in this thread.
 
  • #44
Fra
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I don't know what gave you that idea, Fra.
The post next in the sequence following my question, starting with Hi Fra :)

/Fredrik
 
  • #45
Fra
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That would mean that LQG turns into a "general spin network approach" just like "gauge theory". Then of course one would have to answer the question why nature selected a specific X.
Yes, I think it's some deeper picture I lack. In particular, my idea was to see LQG (or a generalizeation thereof) as a "general action networks approach". Where action is a more generic than spin (which smells too much space). Action is something that directly relates to transition probabilites in a way that forces us to take more seriously the treatment of observables.

In principle I see how something like that might respawn my interest in LQG.

Since spacetime is loosely speaking a relation in BETWEEN material observers, it somehow (in my picture) represents a negotiated communication channel, which in turn means that spacetime only makes sense at some kind of equilibrium. To then understand what the rules are for building this relations as a network of actions, we probably need to understand the negotiating process between two material observers - which unavoidable introduces the microstructure of matter.

So I personally think that such a generalization of LQG would maybe may MORE sense if matter is introduced. Then maybe we can understand why the equilibrium singles out a certain group for constructing principles. But then it would involve understanding also the off equilibrium scenario.

In this picture, it seem that X is NOT a constructing principle to put in as a starging point, it must be emergent from a picture when you have say "randomly interacting systems" where microstructure of matter and their relations (spacetime) evolve together.

I have hard to see how one can consistently understand one without the other. This is one of the issue with LQG.

/Fredrik
 
  • #46
Fra
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The big problem with string is it insists on imposing a background. This is not necessarily wrong, but, remains unproven.
From my POV imposing a spacetime background is not the same as, but closely related to imposing an observer.

And indeed I insist on imposing an observer. It does sort of render the theory itself observer dependent. But I think this is right. Two differing theories are not a contradiction until they interact, but then the contradiction translates into an interaction.

What bothers me in ST, is not imposing an observer, but that imposing the flat background does actually NOT correspond to imposing a real observer expcet for one special case, and that's where asymptotic observables make sense - such as when you look into a small subystem surrounded by a classical laboratory and you can infer S-matrices. Real observers do not sit at infinity embracing the system in space, and real observer does not have infinite information capacity.

To get back on topic, LQG logic as I read it does not acknowledge that a testable theory needs to impose an observer, and that just thinking in terms of equivalence classes of observers is not a satisfactory treatment of observables as I see it.

The paradox that makes this non-trivial is that any observation and inference is unavoidable observer dependent. Yet we like to think that all observers ought to be able to infer the same laws of physics, or else things are clearly out of control.

But the questions is:

If this is best understood as a constraint (to impose a priori) or as an emergent symmetry at equilibrium?

Please correct me if I'm wrong, but as I understand it LQG logic seems to impose it a priori as a constraint. The laws of physics are observer invariant, but the price you pay is that no real observer can infer this law :) It remains an element of structural realism. Something that IMO is irrational from the point of view of inference.

In ST it is (at best of course, there is plenty of other problems) rather an emergent symmetry. This is one way ot making sense out of the landscape of theories... all apparently "a priori" possible, but once they are allowed to interact, most probably not all of them are stable.The problem is that ST lacks such selection principle as far as I know. I suspect this is related to the treatment of observables as S-matrices only. Sometime that can never capture the inside view of a real observer.

I think the latter view is a more viable point of view.

/Fredrik
 
  • #47
tom.stoer
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The main reason for introducing SUSY is the hierarchy problem. This has little to do with infinities.
I agree, the hierarchy problem is much more interesting here - but only with matter degrees of freedom, not in a pure gravity context.

Indeed, as I have been pointing out somewhere else here, finiteness is not enough for consistency. For example, putting a non-renormalizable theory (like the Fermi theory of weak interactions) on a lattice, thereby regularizing the divergences and removing infinities by brute force, does not make the theory consistent. There are issues such as unitarity.
I agree

Typically new degrees of freedom need to be added at a certain scale in order to unitarize the quantum theory.
Typically? I do't thin so; look at gauge theories like QCD.

If it is just a lattice-like regularization of gravity, ...
It isn't. Spin networks are the very definiton.

String theory seems to teach us that one needs in fact infinitely many degrees of freedom. Right now I simply don't know how to reconcile these two standpoints.
I would say that we have three very different approaches, namely ordinary QFT, ST (from which some QFTs can be derived), LQG. ST tells us how to solve the issues raised by QFTs - namely going beyond the framework of ordinary QFT. But LQG is itself outside this framework; it is formulated differently and tis is a strength, not a weakness. I would say that LQG does not have the same problems as QFT and ST, therefore there is no solution required (using cars we do no longer care where to put the horse manure).
 
  • #48
Fra
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thereby regularizing the divergences and removing infinities by brute force, does not make the theory consistent. There are issues such as unitarity.
I apologize for repeating myself all the time but if we acknowledge that the concept of probability in an inference perspective, is nothing but an interaction tool, that is constantly evolving and isn't static, we are lead to evolving state spaces and thus possible transient violations of unitarity. The transient non-unitarity is even what DRIVES the evolution of the theories. This is something that IMO might even make sense in ST, and be key to a selection principle because non-unitarity kills or forces drift of a theory. This is why a persistent stable non-unitarity makes no sense, but a transient one is in fact necessary to understand evolution.

I think there are highly natural cutoffs, when you - as opposed to observers sitting at infinity and doing S-matrix statistics - are sitting in the bulk, trying to do the same but that due to limited information capacity are constantly truncated. In this picture it's unavoidable to see transient non-unitarity. Loosely speaking beeing related to the observers mass scale. Note that normal renormalization does NOT really scale the inference and infrmation coding system, all it scales is a zooming factor. This means that even current renormalization theory is bound to be a special case of a more general picture.

I think the two problems are related and sometimes people seem to think that non-unitary evolution is somehow a logical inconsistency, when it's not. It just mens that that the state space itself isn't timeless, and it means that we simply can't a priori know the full state space of the future. Unitarity just refers to that the expected changs are confined to the current state space, this is logic, but it's not logic to assume that all changes are expected and decidable. In a general inference pictures the whole point is that it's impossible decide everything.

So it seems to me that transient non-unitarity can be allowed in a consistent way, if combined with an interaction in theory space that effectively imposes selection principles in the population of theories.

/Fredrik
 
  • #49
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Hi Tom,

Typically? I do't thin so; look at gauge theories like QCD.
Well even for the strong interactions, it does not help if one cuts off the effective meson theory to make it finite, by putting it on a lattice or otherwise. Unitarity above the cutoff scale is restored by introducing the correct degrees of freedom, namely those of QCD. So again, finiteness is not the big deal, rather unitarity. AFAIK it is an open problem in LQG whether the degrees of freedom they use, unitarize the theory.

I would say that LQG does not have the same problems as QFT and ST, therefore there is no solution required (using cars we do no longer care where to put the horse manure).
It seems it has its own kind of problems on top....
 
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tom.stoer
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Well even for the strong interactions, it does not help if one cuts off the effective meson theory to make it finite, by putting it on a lattice or otherwise. Unitarity above the cutoff scale is restored by introducing the correct degrees of freedom, namely those of QCD.
But in contrary to string theory the number of degrees of freedom is finte; no infinite tower of states; simply the final theory. And no additional degres of freedom but the correct degrees of freedom (QCD does not contain mesons as degrees of freedom).

AFAIK it is an open problem in LQG whether the degrees of freedom they use, unitarize the theory.
I do not see the problem of unitarity.

It seems it has its own kind of problems on top....
Not on top; it has different problems. Most (technical) problems we know from QFT, SUSY, SUGRA, ST do not apply to LQG as the theory is formulated differently.

As an example: You cannot even ask the question regarding off-shell finiteness (renormalizibility) of scattering amplitudes b/c there is nothing off-shell. "Off-shell" is not a fundametal thing in a theory, it's created by (partiall inappropriate) approximations (chosing a background and doing perturbation theory). So by proving "off-shell finiteness" you do not validate your fundamental theory, you only validate the approximation - which is nice, but not fundametal.

Another example is the "off-shell closure" of the constraint algebra. In the new formulation starting with spin foams (see Rovellli's definition in the Zakopane lectures)there is no such algebra any more (I agree that the unknown H is still a a thorn in the flesh ...). Via implementing the constraints one constructs a physical Hilbert space in which most constraints are strictly zero i.e. in which the corresponding symmetries are reduced to the identity. A similar approach (for the gauge symmetry i.e.the Gauss law, not for the diff. inv.) is known in QCD. There are no constraints anymore, therefore the closure is trivially [1,1]=0.
 

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