What is the Current Status of Loop Quantum Gravity and Its Open Issues?

[Lee Smolin]

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 The only one I know who has worked on this is Yi Ling, but his results remained unpublished.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

 

[Fra]

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

 

[Fra]

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 a lot of that, and in particular a lot of Ungers points to be at face with a lot 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

 

[tom.stoer]

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

 

[marcus]

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.

 

[marcus]

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.

 

[Fra]

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

 

[tom.stoer]

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.

 

[tom.stoer]

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.

 

[marcus]

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.

 

[suprised]

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.

 

[Chronos]

The big problem with string is it insists on imposing a background. This is not necessarily wrong, but, remains unproven.

 

[suprised]

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.

 

[Fra]

I don't know what gave you that idea, Fra.

The post next in the sequence following my question, starting with Hi Fra :)

/Fredrik

 

[Fra]

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

 

[Fra]

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

 

[tom.stoer]

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).

 

[Fra]

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

 

[suprised]

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...

 

[tom.stoer]

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.

 

[suprised]

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).

Well how do you know what the correct degrees of freedom of QG actually are? Strings seem to tell that you need infinitely many in order to have consistent scattering. It also seems that strings do precisely have the necessary number of degrees of freedom in order to reproduce Bekenstein Hawking Entropy etc. So I see it the other way around, namely that LQG still needs to demonstrate that it can be a consistent approximation/realisation of gravity in the first place.

And certainly QCD has mesons as degrees of freedom, in the IR.

I do not see the problem of unitarity.

Well I do, as do my colleages. This problem can be addressed once one is able to describe scattering processes in LQG. We know that for string theory the intricate structure of the (moduli spaces) of Riemann surfaces is crucial for consistency, ie, unitary scattering. I wonder whether and if so, how, LQG would be able to reproduce this. It may well be, I have no opinion, I am just wondering.

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.

eg the hierarchy problem, which in a broader sense includes the cosmological constant, is certainly a problem for LQG as well, on top of its intrinsic problems.

Actually there is more to quantum gravity than UV problems, as certain problems do not depend on the UV completion at all. Moreover it is not even clear whether there are serious UV problems in the first place - due to the phenomenon of classicalization. Some of these issues are going to be discussed here:
http://ph-dep-th.web.cern.ch/ph-dep-th/content2/THInstitutes/2011/QG11/QG11.html

 

[Fra]

"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.

Doesn't this reasoning a priori assume that there is a fixed observer independent theory that moreover does not need to be infered by any observers? Or equivalently a non-manifest set of theories that are related consistently by fixed objectively known transformation rules.

(1) Wherein lies the rationality and necessity of this assumption?

(2) In the quest for finding observer invariant physics, is it really appropriate to label choosing an observer an "approximation"? Isn't that in fact disrespecting the whole essence of measurement theory?

Yes, these are nontechnical but conceptual questions, but it seems quite clear that these things are what is the root cause of several technical issues as well.

/Fredrik

 

[tom.stoer]

And certainly QCD has mesons as degrees of freedom, in the IR.

No, just quarks and gluons as can be seen from lattice gauge theories; nobody forces you introduce mesons.

This problem can be addressed once one is able to describe scattering processes in LQG.

If you try to study scattering based on an approximation that may be the case - but you shouldn't. Again look at QFT: the problem of unitaritry arises in approximations. I would say that this contradicts the basis of LQG, namely background independence. Breaking background independence introduces new problems - so you should avoid it. But I agree that it's too early to answer this question b/c up to now graviton-graviton or graviton-matter scattering hasn't been derived from LQG. So the problem is entirely different: how to describe these scattering processes? It's like scattering in lattice gauge theory: you avoid a lot of problems - but you can't calculate the scattering amplitudes afaik.

eg the hierarchy problem, which in a broader sense includes the cosmological constant, is certainly a problem for LQG as well, on top of its intrinsic problems.

I agree; sooner or later this will arise.

 

[tom.stoer]

Yes, these are nontechnical but conceptual questions, but it seems quite clear that these things are what is the root cause of several technical issues as well.

Yes and no. Your conceptual questions do exist in QM already, but there seems to be no problem with off-shell closure. All I wanted to say is all problems we discuss should be categorized (roughly) as follows:
(1) conceptual problems posed by nature
(2) conceptual and technical problems posed by a specific approach or theory
(3) technical problems posed by a specific approcimation to a specific theory

Problems of category (3) are of no importance in a different theory and we should avoid waisting time to discuss problems (e.g.) raised or fixed in perturbative string theory in LQG.

 

[Fra]

(3) technical problems posed by a specific approcimation to a specific theory

Problems of category (3) are of no importance in a different theory and we should avoid waisting time to discuss

I certainly agree with the generic point.

But my definitive impression from reading both LQG papers and some ST reasoning is that sometimes a real confusion exists between "mathematical perturbation theory" and and inside observer trying to perform an inference on it's environment. There is also confusion between truncation in the context of regularization as mathematical methods, and natural truncation of information that is due to the observers limited information capacity.

In a way, you can think of an observers GUESSING or INFERENCES about it's own environment, as a kind of perturbation of what it KNOWS, to account for what can possibly be true and you can ORDER this in decreasing order of subjective probability. At some point, the expectations accounting for all possibilities (analogous to PI) stops to count possibilities because they are not distinguishable from the inside due to fallwing below some treshold. This kind of issue, does impact to the action of the system, and this is a conceptual and physical problem and different than mathematical perturbation theory.

For example. Given what you know, you form a prior. Then you can expand the possible distinguishable changs, and order them by falling probability (beeing related to information divergence) and any finite observer, neeeding to make a choice will either due to truncation of representation or due to finite time, truncate the possible considerations somewhere, and make a choice based upon incomplete information. And this is the most rational choice that is physically possible given the constraints.

I have a strong feeling that LQG thinking, exemplified by Rovelli', often treats the observer like an arbitrary choice almost like perturbation theory, for the very reason that he considers the observer invariants as what's physical. But this completely dismisses the inference perspective (beeing the essence of QM IMHO).

/Fredrik

 

[Fra]

Your conceptual questions do exist in QM already

Yes.

but there seems to be no problem with off-shell closure.

Yes, but there is IMHO a way to see why.

QM as we know it before we start to talk about gravity, is essentially all about scattering matrices. This mean you have an environment which is effenticely monitoring the very small sub-system you study. The shell notion is defined in the classical environment.

In QG, the above assymmetry does not hold. Scattering matrices in a cosmological theory simply makes no sense, because the observers is the small guy here, and is floating inside the "black box" rather than embracing and controlling it.

This assymmetry is IMO the root cause of why we do get away with things in ordinary QM, that will not do in a cosmological measurement theory.

I think the problem is two-fold.
1) Measurement theory as it stands with fixed hilbert spaces etc, doesn't make sense for a cosmological measurment theory.

2) The understanding of what on-shell or "equilibrium" means, is different in a mesurement theory than in calssical physics. GR is a realist theory, and on-shell is hard elements of reality. Such things is IMO not something we should have in a measuremnet theory. Instead the equilibrium must be infered from the inside.

/Fredrik

 

[tom.stoer]

My impression is that in the LQG field nobody discusses these topics.

My feeling is that one should try to develop a theory based on "boundary Hilbert spaces"only, where the boundary separates the "system" from the "observer" and possibly from the "environment". That would be in-line with the holographic principle.

 

[Fra]

My impression is that in the LQG field nobody discusses these topics.

If I could only figure out why.

My feeling is that one should try to develop a theory based on "boundary Hilbert spaces"only, where the boundary separates the "system" from the "observer" and possibly from the "environment". That would be in-line with the holographic principle.

I too think the boundary or communication channel between observer and the rest of the universe is a central starting point, but we really lack the framework for this. I have never seen anything near what I think is needed, but that's fine because it's a hard problem. What is more worrying is when the questions are avoided. I'd expect any so inclined theoretical physisitcs to wear these quesions on our forehead until we have answered them ;)

Most ideas like AdS/CFT end up with observers at infinity which effectively gives us just the scattering matrices, so there should exists a much more general framework in which these asymptotic observers positions are a special or limiting case.

Interestingly when you ask these questions unification becomes unavoidable, and suggests that the two things are related, contrary to the reasoning of Rovelli that suggests they are two different problems. The reason is that the logic of the action of a small subsystem (where roughly speaking) ordinary QFT works fine (not quite, but almost anyway) seen from the inside, MUST be a cosmological mesurement theory! So if we are ever to get away from "understanding" the SM by means of postulating more or less classical hamiltonians, and instead try to understand from first measurment principles the construction of the SM action (and thus unification) we need the cosmological measurement theory anyway, since this must be the correcty "inside view".

So indeed IR and UV scales are related here in a sense, somehow the "UV action from an IR perspective is the inverse of the IR action from the UV perspective". Not sure if that makes sense but it seems even inconsistent to think that there is no relation.



/Fredrik

 

[marcus]

...
My feeling is that one should try to develop a theory based on "boundary Hilbert spaces"only, where the boundary separates the "system" from the "observer" and possibly from the "environment"...

That reminds me of Robert Oeckl's proposal of a "general boundary" formulation of quantum mechanics.
http://arxiv.org/abs/hep-th/0306025

Where does the formulation in 1102.3660 fall short of what you have in mind? What would you have to do to it to make it fit your idea?
What i mean is, the LQG Hilbert space of states is already entirely concerned with boundary geometry.

It is a projective limit of Hilbert H_Gamma all of which concern the boundary.
The limit is as Gamma -->∞. Gamma a finite graph serves as a truncation to finitely many degrees of freedom. When one computes one fixes a Gamma. So the boundary has only finitely many degrees of freedom.

One can think of the boundary (or the Gamma) as the "box" containing the system. It is however 3D because it persists in time. The experimenter can watch the box for a certain interval, making initial and final observations. There is a transition amplitude associated with the boundary state.

the 4D spin foam formalism is only used as a tool to compute the transition amplitude. What is real, so to speak, is the 3D boundary. And the LQG Hilbertspace is entirely based on that.

This is the theory as presented in 1102.3660. Is this the kind of theory which you say one should try to develop?

should try to develop a theory based on "boundary Hilbert spaces"only, where the boundary separates the "system" from the "observer" ...
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If not, I'm curious to know how should it be different in order to match more closely?

 

[tom.stoer]

The first difference is the topology. My boundary Hilbert spaces would all be compact surfaces.

The second difference is that I would not calculate any transition amplitude between those boundaries as there is only one boundary, not two (as in the SF approach)

The third difference is that I would try to quantize the theory on the boundary, or to "represent" the volume on the boundary i.e. implement the holographic principle. This is similar to the LQG "isolated horizon" approach" for black holes with a topological surface theory.

The fourth difference is that the boundary represents something like "the system" as defined by the observer. That means the boundary is both something physical and something encoding the subjective perspective of an observer.

Now in order to get rid of the latter I think the theory as a whole must not look at one of these boundaries but at the infinite collection of all possible boundaries, i.e. at all splits of the universe into a "system" and an "environment" defined by an "observer".

I guess this could be a framework from which reduced density matrices could emerge, which would be a step forward to solve the measurement program, and to define the observer mathematically. In addition having this infinite collection of surface Hilbert spaces with its reduced density matrices, one could reconstruct the whole complete state from the this collection (at least mathematically, but not practically). That means that w.r.t. one observer there is a partial trace, decoherence, "wave function collaps" etc., but w.r.t. to all observers unitarity is conserved.

But this has nothing to do with the current status of LQG ...