Exploring the Current Status and Open Issues in LQG: A Comprehensive Review

[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" ...
​

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 ...

 

[Fra]

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".

The question is, is it really desirable to "get rid of the observer"?
This is the point where we probalby disagree.

Part of my point is even, I don't think it's POSSIBLE to get rid of the observer even if we wanted, because any attempt to do so is still bound to be confined to an inside view. The THEORY itself, must be observer dependent if we want the theory to be rationally inferred, because there is not way to even make an inference without an observer. And that latter is in my view at least at the cored of a "measurment theory" (give or take technical details such as fixed hilbert spaces).

Thus, while I agree that the boundary observer/environment is a central thing to elaborated around, I think what we a are seeking is interacting theories, but where the mechanism is evolutionary.

So the general concept of landscapes of theories appearing is not totally stupid. It's just that apparently essential ingredients are missing to make sense out of it (selection principles).

/Fredrik

 

[tom.stoer]

OK, let's rephrase this slightly.

We have "global theories", LQG in its current form is one, and we seem, to agree that we need a local theory which allows one to describe things relative to an observer. What I mean is that a "complete collection of local expressions, e.g. boundary Hilbert spaces" is sufficient to reconstruct the global theory. And in addition there should be a mechanism to reduce the global theory to a local one. This could e.g. be something like taking a partial trace in a reduced density matrix formalism.

In that sense we do not get rid of the observer but we are able to relate different observers.

It would be something like a "relativity principle", but not formulated in position space but in Hilbert space language (or in some other framework, I have no idea if Hilbert spaces will be the right stuff). Let's call it "Principle of relativity w.r.t. quantum-obervers" or something like that.

But as quantum theory seems to be the correct theory of nature I doubt that we need something new. It's perhaps only a re-interpretation of the formalism, just like decoherence. If this is correct then Hilbert spaces and LQG are still the correct framework for QG.

I don't think that we need landscapes or something like that.

 

[marcus]

Thanks for your response. It's a way of addressing the "current status" to say how it differs, as you see it, from your ideal. The first sentence might need editing, or a few extra words. I don't see how any Hilbert space can be compact.

The second sentence seems to contain a misconception about LQG.In the SF approach the boundary can consist of a single connected component. It is not necessarily "two" boundaries.

Intuitively the spin network state describes the geometry of a boundary which may be compact, connected, and surround the "system" before, during , and after. A kind of "box interval". I intended to suggest this in the preceding post when I was talking about the experiment being inside a box which has time-duration.

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 ...

It seems to me that your comments have VERY MUCH to do with the current status :-D
In some cases you are saying what you see as missing---to describe the shortcomings is part of a good status report. And also some of what you say is already achieved and so is already part of the current status of LQG.

The third difference is that I would try to quantize the theory on the boundary, or to "represent" the volume* on the boundary...​

*A common word for the spacetime volume inside the boundary is "bulk".

This is what LQG does. The standard formulation of LQG as given in 1102.3660 does, in fact, quantize the state of the boundary.

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.​

Well this is more philosophical and I'm less sure about it, but it seems to me to be "sort of kind of" or "so-wie-so" how I think about the standard formulation as in 1102.3660. The theory is primarily about the boundary. Which corresponds to what can be measured or observed. The H_Gamma hilbert spaces are about the boundary. Its quantum states.

The amplitudes that one calculates refer to the boundary H_Gamma. But in order to calculate them one sets up foams in the bulk. One sets up provisional histories in the bulk. However these are nothing but diagrammatic ways to calculate the boundary amplitudes!

This is how I think of the current status LQG formulation and I am not sure about the philosophical issue you mention. Is this subjective and observer dependent? Does this have to be "gotten rid of"? Remember that the boundary and bulk have no location in a fixed background spacetime. There is no background. Where could the observer be? Perhaps the boundary IS the observer and we just have to live with that. Maybe there is finally no ontology, no mathematical representation of the bulk reality, only a boundary of measurements related to other measurements. Nature is what responds to measurement in the way that she does and we don't know any more. I get dizzy here. don't feel philosophically adequate to discuss this. Provisionally then, I just accept the theory as it is.
As long as it let's us calculate amplitudes and eventually test.

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".
​

Well as I say, my philosophical grip is a bit too weak to proceed with this, but I note that in LQG there is an infinite collection of graphs Gamma, and they have no definite location since there is no background. Perhaps they could represent "all possible boundaries". (I was thinking of them as all possible truncations of a single boundary to finitely many geometrical degrees of freedom, but perhaps there is a better way to think.)

This is just a partial response to your post. I have to leave much unresolved. I am not sure about "getting rid of" observer dependence. Haven't resolved that in my own mind. But if you want to have an infinite collection of boundaries you might have the materials available to formulate that, given the infinite collection of boundary graphs.

Anyway, interesting post. Thanks!

 

[Fra]

Tom, I understand what you say. What you advocated is from my POV, very close to rovelli's view. Your analogy with global, local, "relativity" is well taken. They are good examples of your stance and I see what you mean but I do not agree.

I am not sure if you get my point or if you just disagree with it.

This gets slighltly off topic except to the extent that it "elaborates the logic in LQG" which was my original intention.

To address a single statement to again illustrate my key point.

In that sense we do not get rid of the observer but we are able to relate different observers.

My point is that "we" here is just another observer, infering or abducing the "theory" simply from it's interaction history.

My point would be that it's impossible for an arbitrary observer to DEDUCE from this "complete collection of local expressions" the global theory. It does not physically fit/encode in any part.

There is however possible for an inside observer to make this inference less strongly than a deduction in the sense that the observers is making guesses, and from feedback it can seem to encode more information than it in fact does. Some of the "information" is stored in the evolutionary selection process. But this information is not physically stored in the observer, it's stored in the form of an equilibrium in the ste of observers.

But in this view, your example of the relavitity symmetry, is NOT a hard fact or constraint - it's merely an equilibrium point. And to understand why it is what it is, we need to understand the equilibrium process. Somehow the difference is that symmetries are no longer "classical" they become "inferencial" in the lack of a better world. I wouldn't say quantum mechanical symmetries because QM as it stands is not the full inference I seek.

/Fredrik

 

[marcus]

Tom asked for a review article that sums up LQG current status and at first we couldn't offer anything really up to date. But several new papers have come out and the Zakopane lectures got updated in August 2011. So that makes a fairly compact current status report.

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 l_p but much smaller than the cosmological length l_c.
==endquote==
For anyone not familiar with it, the cosmological length l_c, given by Λ = 1/l_c², is the length scale associated with the cosmo constant Λ.
...
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.

I will fetch the abstract for the Magliaro Perini article.
http://arxiv.org/abs/1108.2258
Emergence of gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 10 Aug 2011)
We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.
6 pages.

So basically, what this thread is about---getting a concise up to date review---boils down to these three papers with a total of 45 pages (33+6+6)

 

[marcus]

I should give some sources for what I said in the previous:

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.​

To show the growth, Inspire search using terms "quantum gravity: loop space" "quantum cosmology: loop space" and "spin:foam".

LOOP RESEARCH BY YEAR (Inspire beta)
2005 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2005&sf=&so=a&rm=&rg=10&sc=0&of=hb (42 found)
2006 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2006&sf=&so=a&rm=&rg=10&sc=0&of=hb (77 found)
2007 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2007&sf=&so=a&rm=&rg=10&sc=0&of=hb (120 found)
2008 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2008&sf=&so=a&rm=&rg=10&sc=0&of=hb (142 found)
2009 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2009&sf=&so=a&rm=&rg=10&sc=0&of=hb (145 found)
2010 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2010&sf=&so=a&rm=&rg=10&sc=0&of=hb (153 found)
2011 http://inspirebeta.net/search?ln=en...=&d2m=&d2y=2011&sf=&so=a&rm=&rg=10&sc=0&of=hb (124 as of 2 sept, annualized 180+)

To show the interest in testing (Lqg phenomenology) a Spires search for phenomenology papers 2009 and later.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+INFLATION+OR+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
Currently it gets 44 papers.
None of these have to do with "fuzziness of distant quasars" produced by "graininess of spacetime foam" or dispersion (energy dependence of speed of light.) AFAICS they all have to do with features of the cosmic background radiaton (power spectrum, polarization.) You can examine the papers--sample them and see for yourself.

As for the definiteness of the theory, see a definitive formulation in the August 2011 version of http://arxiv.org/abs/1102.3660 .
The theory has changed greatly since 2007. It seems curiously similar to what Tom was describing. I talked about that in post #63 of this thread:
https://www.physicsforums.com/showthread.php?p=3481820#post3481820

It is a quantum theory of the 3d boundary surrounding a spacetime region ("bulk") that holds the system or experiment. The boundary represents what the experimenter knows. It can consist of a single connected component encompassing initial-during-final. Or several separate components.
The hilberts of the theory are quantum states of the boundary. H_Gamma where Gamma is a graph. Think of Gamma as the basic graph on which a spin network could live, this being a quantum state of the 3d geometry (potentially with matter as well) of the boundary.

The spinfoams are diagrammatic tools for calculating the amplitude associated with the boundary, more precisely the amplitude associated with a quantum state of the boundary. So the formulation of the theory is very boundary-focused, curiously like what Tom described as desirable!

I think of the boundary as what the observer can control and read, in a sense the boundary IS THE OBSERVER. But this is getting a little philosophical. We should try to stick with the here-and-now.

Probably most people realize how important it is for a theory to be TIMELY. Theory should progress incrementally step-by-step. It concerns what is PRACTICAL and appropriate to theorize and test at any given time. Frank Wilczek made that point several times in his talk at Uppsala.

 

[tom.stoer]

Thanks for your response. It's a way of addressing the "current status" to say how it differs, as you see it, from your ideal. The first sentence might need editing, or a few extra words. I don't see how any Hilbert space can be compact.

I agree; it should read my boundary Hilbert spaces would all life on compact surfaces.

The second sentence seems to contain a misconception about LQG. In the SF approach the boundary can consist of a single connected component. It is not necessarily "two" boundaries.

Please explain!

It seems to me that your comments have VERY MUCH to do with the current status :-D
In some cases you are saying what you see as missing---to describe the shortcomings is part of a good status report. And also some of what you say is already achieved and so is already part of the current status of LQG.

It would be rather nice if LQG is that close to what I have in mind; but my idea goes far beyond the formalism of LQG. It's an idea how to re-interpret quantum mechanics in terms of boundary Hilbert spaces representing "cuts" and "systems" introduced by "observers". It would be the first time since Heisenberg, Schrödinger and Dirac that one can pointing the finger at a mathematical entity and say "this is the oberver!" If LQG is compatible with that idea - fine. But of course it was not the intention of LQG.

This is what LQG does. The standard formulation of LQG as given in 1102.3660 does, in fact, quantize the state of the boundary.

But my intention is to have a theory which relates all boundary Hilbert spaces and which allows to explain "systems", "observers", "collaps of the wave function", i.e.to re-interpret QM. Again: LQG may be compatible with that idea, but it is by means complete in that sense.

This is how I think of the current status LQG formulation and I am not sure about the philosophical issue you mention. Is this subjective and observer dependent? Does this have to be "gotten rid of"? Remember that the boundary and bulk have no location in a fixed background spacetime. There is no background. Where could the observer be? Perhaps the boundary IS the observer and we just have to live with that. Maybe there is finally no ontology, no mathematical representation of the bulk reality, only a boundary of measurements related to other measurements. Nature is what responds to measurement in the way that she does and we don't know any more. I get dizzy here. don't feel philosophically adequate to discuss this. Provisionally then, I just accept the theory as it is.

These are questions to be asked.

As long as it let's us calculate amplitudes and eventually test.

I agree that currently LQG is in the "shut-up-and-calculate" phase and that my ideas are ot really open issues of LQG but of quantum physics in general. So somehow we lost track. Anyway, thanks for the three references.

 

[Fra]

It would be rather nice if LQG is that close to what I have in mind; but my idea goes far beyond the formalism of LQG. It's an idea how to re-interpret quantum mechanics in terms of boundary Hilbert spaces representing "cuts" and "systems" introduced by "observers". It would be the first time since Heisenberg, Schrödinger and Dirac that one can pointing the finger at a mathematical entity and say "this is the oberver!" If LQG is compatible with that idea - fine. But of course it was not the intention of LQG.

But my intention is to have a theory which relates all boundary Hilbert spaces and which allows to explain "systems", "observers", "collaps of the wave function", i.e.to re-interpret QM. Again: LQG may be compatible with that idea, but it is by means complete in that sense.

I am not sure exactly what you mean, but I assume you are well aware of Rovelli's Relational Quantum Mechanics paper (http://arxiv.org/abs/quant-ph/9609002)? Even when I started to read his LQG book, some things of his views was much more cleanly explain in the RQM paper. Rovelli's specific view of QM, does IMO not have much specifically to do with other details of LQG. So to understand his QM interpretation I think the RQM paper might be good to reference. I'm not aware of that he has written any updates on this?

What is interesting, and the reason why I don't just ignore rovelli's reasoning, is that the initial reasonign of Rovelli is also pretty much well in line with what I said. It's so close, this is why the slight difference is the more annoying.

Rovelli's point as per the RQM paper, is that there are no outside observers, all you have are inside observers. Moreover you have relations between difference observers. But again Rovellis acknowledges that there is no "absolute" relation, the only way for observer A or make statemetns of relations between B and C is by interacting with the system.

First of all, one may ask what is the “actual”, “absolute” relation between the description of the world relative to O and the one relative to P. This is a ques tion debated in the context of “perspectival” interpretations of quantum mechanics. I think that the question is ill-posed. The absolute state of affairs of the world is a meaningless notion; asking about the absolute relation between two descriptions is precisely asking about such an absolute state of affairs of the world. Therefore there is no meaning in the “absolute” relation between the views of different observers. In particular, there is no way of deducing the view of one from the view of the other

Does this mean that there is no relation whatsoever between views of different observers? Certainly not

Up until this point, this is exactly my point as well. I think Rovelli phrase this conceptual point clearly.

The big difference lies in what the relations is!

Rovelli goes on to say

it means that the relation itself must be understood quantum mechanically rather than classically. Namely the issue of the relation between views must be addressed within the view of one of the two observers (or of a third one). In other words, we may investigate the view of the world of O, as seen by P. Still in other words: the fact that a certain quantity q has a value with respect to O is a physical fact; as a physical fact, its being true, or not true, must be understood as relative to an observer, say P. Thus, the relation between O’s and P’s views is not absolute either, but it can be described in the framework of, say, P’s view.

There is an important physical reason behind this fact: It is possible to compare different views, but the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature.

Rovelli essentially here says that the relations can only be "communicated" between observers as a physical intreaction, and this is described by QM (which he has no ambition to change). Here I claim that his analysis is insufficient.

I fully agree that the communication is an interaction and that it can be thought of as them performing measurments on each other, the only problem is that THIS "extended" usage of QM really takes ot BEYOND the testable domain of QM. I am convinced that to implement what Rovelli clearly wants here... QM needs revision.

It would be the first time since Heisenberg, Schrödinger and Dirac that one can pointing the finger at a mathematical entity and say "this is the oberver!"

The exten to which I propose to continue Rovellis' reasoning, with a modified QM, means that even the THEORY is observer dependent. Even theories are not absolute. In my view, the theory IS the observer. The structure of the theory should be one to one with an observes "inference machniery".

Which was what I referred to here

In that sense we do not get rid of the observer but we are able to relate different observers.

My point is that "we" here is just another observer, infering or abducing the "theory" simply from it's interaction history.

/Fredrik

 

[Fra]

I fully agree that the communication is an interaction and that it can be thought of as them performing measurments on each other, the only problem is that THIS "extended" usage of QM really takes ot BEYOND the testable domain of QM. I am convinced that to implement what Rovelli clearly wants here... QM needs revision.
...
The exten to which I propose to continue Rovellis' reasoning, with a modified QM, means that even the THEORY is observer dependent. Even theories are not absolute. In my view, the theory IS the observer. The structure of the theory should be one to one with an observes "inference machniery".

If one starts looking at the conceptual problem, from the above reasoning of Rovelli, I can see two modes of critique:

1) Either you can say that, QM as it stands is correct, and that Rovelli is applying QM in the wrong way. Ie. it's wrong to try to apply quantm mechanics to observer-observer relations (in the extension spacetime/gravity). Instead we should try to recover the observer-observer relations from observer dependent quantum mechanics. I think this is closely the critique I would expect from string theorists.

2) You think that Rovellis is essentially correct, up to the point mentioned, Rovelli's is correct that it should be the measurement theory that explains the observer-observer relations, and this would bound to be an intrinsic measurement theory. But the problem is that Rovelli while having the right idea, tires to be also "conservative" and assume that QM as it stands will be this intrinsic measurement theory.

My stance is (2). I think the problem with current QM is exactly that is NOT an intrinsic measujrement theory. IT is an extrinsic measurement theory. This is why it's so hard to make sense out of bulk observables. It seems to only be possible to get S-matrix style observables.

/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 would be in-line with the holographic principle.

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.

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" ...
​

If not, I'm curious to know how should it be different in order to match more closely?

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 second sentence seems to contain a misconception about LQG.In the SF approach the boundary can consist of a single connected component. It is not necessarily "two" boundaries.

Intuitively the spin network state describes the geometry of a boundary which may be compact, connected, and surround the "system" before, during , and after. A kind of "box interval". I intended to suggest this in the preceding post when I was talking about the experiment being inside a box which has time-duration.

... my boundary Hilbert spaces would all live on compact surfaces.

The second sentence seems to contain a misconception about LQG.In the SF approach the boundary can consist of a single connected component. It is not necessarily "two" boundaries.

Please explain!

Page 10 of http://arxiv.org/abs/1102.3660.
Especially Figure 6.

The states in H can be viewed as describing quantum space at some given coordinate time. A more useful interpretation, however, and the one I adopt here, is to take them to describe the quantum space surrounding a given 4-dimensional finite region R of spacetime. This second interpretation is more covariant and will be used below to define the dynamics. That is, a state in H is not interpreted as “state at some time”, but rather as a “boundary state”. See Figure 6.​

Notice that there is a potential confusion on the part of readers connected with the word "transition". The dynamics will be defined by showing how to calculate a "transition" amplitude (there is no other word in general use). But this transition can be the transition within a single compact connected boundary as shown in the figure 6.

We can be talking about the amplitude of transition within and along a boundary, rather than a transition between two disconnected initial and final.

But this is just a confusion due weakness in the English language. We only have one word so we are not able to make the distinction between transition-between two separates and transition-within channeled by the confines of a boundary.