Argument Against LQG

[BenTheMan]

First of all, this is not my argument, it is due to Nima Arkani-Hamed. And I have probably misinterpretted it, or misunderstood it. Either way I will sumarize it as best I remember, and hopefully some of the smart people here can help me understand what is actually going on. I am at a summer school in Princeton this week, and Nima is giving a series of lectures on phenomenology beyond the SM. This argument came up in the recitation section that Nima gave after his first lecture. I have discussed it some with other grad students here, but still have some gaps in my understandings. I want to write it down here, so that I can get everything straight in my head, and maybe have some intelligent discussion with you people.

 

Ok. First take QED at weak coupling. The theory is very well defined---we can compute scattering amplitudes and runnings of beta functions, etc. What one quickly notices is that QED has a Landau pole, at a place where the (inverse) coupling runs to zero. When the inverse coupling runs to one, the theory ceases to have a well-defined perturbative limit. So let's imagine a universe where we actually WANTED a UV completion of QED.

 

The best way we know how to treat a non-perturbative gauge theory is to discretize the space-time, put the theory on a lattice, solve for something, and pray that the answer we get is independant of the lattice spacing. We have had great success in this vein, in the field of Lattice QCD. The problem is that the UV completion of the theory is very ill-defined. UNLIKE in Lattice QCD, we are trying to understand the UV completion of a theory, as opposed to the IR limit of the theory---while there is a unique IR limit of a theory, the UV completion is far from unique.

 

Either way, when we put QED on a lattice, it becomes something that is no longer QED. Indeed, when we look at the IR behavior of the new theory, we have lost all of the predictions of QED, as well as the beautiful IR limit---in short, the IR limit of the theory we found by discretizing QED is not QED.

 

Nima then argues that this is why LQG is bound to fail. While it is quite obvious how to deal with the low energy limit of a well-defined theory in the UV, it is nowhere near as obvious how to extrapolate a well-defined theory in the IR back up to the UV---this is easy to understand, because if it were not true, then we would have no problems understanding the UV completion of the standard model. The only way we could possibly begin to understand the problem is to discretize the path integral in a lattice-like formulation, and search for a theory that is independant of the lattice spacing. But this is exactly what fails in the case of QED, and is exactly what is attempted by the LQG program.

 

Things like ``background independance'' are just our attempts to describe a physical system, and don't have much to do with the actual physics of the situation. (His analogy was gauge invariance, which is more or less a tool we use to calculate things, and not anything physical.)

 

The counterargument is, of course, that gravity is not QED. But I think this argument might be a bit vacuous, because we are trying to understand gravity as a gauge theory, and the theory certainly doesn't care about the way in which it is parameterized.

 

So, I hope that I haven't mangled this argument too much. I will try to think of this some more, and possibly talk to Nima. What do you guys think?

[Martin]

...Nima then argues that this is why LQG is bound to fail. ... The only way we could possibly begin to understand the problem is to discretize the path integral in a lattice-like formulation, and search for a theory that is independant of the lattice spacing. But this is exactly what fails in the case of QED, and is exactly what is attempted by the LQG program.

 

Things like 'background independance' are just our attempts to describe a physical system, and don't have much to do with the actual physics of the situation. (His analogy was gauge invariance, which is more or less a tool we use to calculate things, and not anything physical.)

...

 

Thanks for reporting!

Nima is a prominent string-community guy, recently moved from Harvard faculty to Princeton IAS.

Over the years I have seen a number of arguments by string thinkers as to why all the LQG approaches must necessarily be "bound to fail", and it is interesting to hear what may well be the current favorite argument.

 

If you get more words from Nima about why LQG must fail, please post them if and when convenient, Ben. Or simply further elaboration.

 

I'm thinking this may be the best or most salient arguments currently available because I have a high regard for Nima as a top string/phenomenology leader.

Let's see if he has more to say

[BenTheMan]

He's usually surrounded by an entourage of graduate students, but I'll try to ask him sometime about this argument.

 

And to be fair, I don't know that Nima would call himself a string theorist.

 

Also, at TASI in Bouder, I got Joe Polchinski to drink a toast to Loop Quantum Gravity. His argument agains LQG is that it is less ``natural'' than string theory. For example, in strings, you only assume that the fundamental particle is not a point but a string, and go from there. By making normal assumptions (anomaly cancellation, unitarity, etc.) one is led to a rich low energy phenomenology, a prediction for the number of space-time dimensions (which is absent in GR and loops), etc. In loops, however, one has to invent many more tihngs to make the theory work.

 

Nima's argument makes much more sense to me, especially if we expect gravity to look like a gauge theory at very high energies.

[Severian]

It is a rather bogus argument in my opinion.

 

Firstly, I don't think the Landau pole in QED has ever been proven (though I could be wrong).

 

Secondly, gravity looks nothing like QED so I see no reason why there would be a Landau pole in gravity.

 

Even if there were, it's presence must be due to a poor description of the theory itself, not the approach taken (i.e. LQG). A Landau pole is intrinsically non-physical and is only tolerated in QED because we expect a UV completion.

 

Don't believe the hype about NA-H, especially not from his grad students.

[BenTheMan]

Firstly, I don't think the Landau pole in QED has ever been proven (though I could be wrong).

 

Well, QED breaks down at the weak scale, which is what we expect---the Landau pole is just a sign that something is wrong with the theory somewhere, maybe 10^38 GeV or something ridiculous like that. But it is a generic (and real) feature of the theory.

 

Secondly, gravity looks nothing like QED so I see no reason why there would be a Landau pole in gravity.

 

The argument is that we have one example of trying to fix the UV limit of a strongly coupled gauge theory by latticizing it---QED. And discretizing the path integral in that context fails miserably. In some regime we expect gravity to look like a gauge theory, so it makes sense to compare it to other gauge theories, and see what we can learn.

 

You may wish to point out that latticizing QCD has produced very beautiful results. And you would be 100% correct. The problem is, of course, that when we do this, we are looking for the IR completion of a well-defined UV theory.

 

Even if there were, it's presence must be due to a poor description of the theory itself, not the approach taken (i.e. LQG). A Landau pole is intrinsically non-physical and is only tolerated in QED because we expect a UV completion.

 

The point is not so much the appearance of the landau pole, but the general failure of trying to build a UV completion of a theory by latticizing it---perhaps I was a bit unclear in the original post.

 

The big difference is the starting point. In Loops, one starts with an effective field theory (GR), and tries to complete the UV. In String Theory, one starts with a well-defined UV theory, and tries to find an IR realization. This is most likely why the landscape is an inevitible feature of string theory untill we understand fully how to compactify it---we don't know HOW to run the theory down exactly, in other words. If we did it wouldn't be a problem. But this doesn't change the fact that string theory is very well defined in the UV, and has at least one (or 10^500) consistent realizations.

 

Don't believe the hype about NA-H, especially not from his grad students.

 

Ahh yes. So you know him personally? I will say that if you can't get excited listening to Nima talk about physics (even if you don't agree with him), then you can't get excited about physics.

[Severian]

Well, QED breaks down at the weak scale, which is what we expect---the Landau pole is just a sign that something is wrong with the theory somewhere, maybe 10^38 GeV or something ridiculous like that. But it is a generic (and real) feature of the theory.

 

As I said, I have never seen it proven. Remember you can't use the renormalization group equations because they break down when the coupling becomes non-perturbative. Ironically you have to use a lattice, but I thought that had only been done for [math]\phi^4[/math] theory (Luescher?).

 

The argument is that we have one example of trying to fix the UV limit of a strongly coupled gauge theory by latticizing it---QED. And discretizing the path integral in that context fails miserably. In some regime we expect gravity to look like a gauge theory, so it makes sense to compare it to other gauge theories, and see what we can learn.

 

As you yourself point out, QCD has no Landau pole but it is a gauge theory, so it is certainly not generic. Also note that QCD never reaches its infra-red pole due to hadronization. I suspect that QED would do something similar at very very high energies - that is non-perturbative interactions with the vacuum would turn the beta function around. (I don't see how this would work though since you don't have enough freedom in the theory to create bound states.)

 

The point is not so much the appearance of the landau pole, but the general failure of trying to build a UV completion of a theory by latticizing it---perhaps I was a bit unclear in the original post.

 

I understand your point, but I would not expect my final theory of everything to be divergent in the ultraviolet. I think that would be a sign that the theory is wrong. So I don't see any inconsistency in having an upper cut-off on the energy set by a lattice. Even if the Landau pole were present in the theory, the cut-off itself prevents it. Are you saying that a viable theory has to permit arbitrarily high energies?

 

The big difference is the starting point. In Loops, one starts with an effective field theory (GR), and tries to complete the UV. In String Theory, one starts with a well-defined UV theory, and tries to find an IR realization. This is most likely why the landscape is an inevitible feature of string theory untill we understand fully how to compactify it---we don't know HOW to run the theory down exactly, in other words. If we did it wouldn't be a problem. But this doesn't change the fact that string theory is very well defined in the UV, and has at least one (or 10^500) consistent realizations.

 

This is just an aesthetic argument. To my mind, string theory's big problem at the moment is that it is non-predictive, so it really doesn't get out of the starting gates as a desirable theory. Unlike some people, I am willing to give string theory a chance to actually make some quantitative (or even qualitative) prediction, but until it does, why should I even consider it? I think it was a big tactical mistake for certain string theorists to invoke the landscape and admit that string theory give you anything you want.

 

Ahh yes. So you know him personally? I will say that if you can't get excited listening to Nima talk about physics (even if you don't agree with him), then you can't get excited about physics.

 

I wouldn't say I know him personally. We have met and I have heard several of his talks. He recently gave a talk about his 'OSET' idea at CERN and insulted just about every experimentalist in the room - they weren't very happy afterwards. He comes over as very arrogant and doesn't pay very much attention to the literature. I think he is very good, and has some nice ideas, but he is no Witten (or Weinberg).

[BenTheMan]

I think we might be talking past each other. The point of the argument (probably obfuscated by me in the original post) is, very specifically, that discretizing a path integral to complete the theory in the UV hasn't worked so well in the other example that we have, specifically QED. QCD doesn't really apply because we have a well-defined theory in the UV, and we are running it down to strong coupling.

 

So I don't see any inconsistency in having an upper cut-off on the energy set by a lattice.

 

Sure---we never SEE these problems until we try to work it out. This was the hope behind the lattice formulation of QED, I guess. As long as you're ok with sacrificing Lorentz Invariance (which most Loop people don't mind), then fine---make your cuts.

 

Even if the Landau pole were present in the theory, the cut-off itself prevents it. Are you saying that a viable theory has to permit arbitrarily high energies?

 

This is probably a matter of taste, right? It depends on if you admit arbitrarily high energies into the theory. The cutoff isn't anything physical, it's just a place holder.

 

This is just an aesthetic argument. To my mind, string theory's big problem at the moment is that it is non-predictive, so it really doesn't get out of the starting gates as a desirable theory.

 

You won't find any arguments here!

 

We have met and I have heard several of his talks. He recently gave a talk about his 'OSET' idea at CERN and insulted just about every experimentalist in the room - they weren't very happy afterwards. He comes over as very arrogant and doesn't pay very much attention to the literature.

 

Again, no complaints. But he is the type of fellow who either ends up being spectacularly correct (and changing the field) or famously wrong. I mean---he's not even forty yet and he's got a permanant position at the IAS.

[Martin]

... The point of the argument (probably obfuscated by me in the original post) is, very specifically, that discretizing a path integral to complete the theory in the UV hasn't worked so well in the other example that we have, specifically QED...

 

LQG is not about discretizing a path integral. So the connection between what Nima said and actual LQG is elusive at best.

 

the LQG community is publishing papers in several distinct approaches, it is family of related approaches rather than a single one. The Spinfoam approach can be described as a kind of path integral---you don't use a LATTICE though. It is also called a "sum-over-histories" approach. There is no fixed underlying spacetime geometry that you work on, and there is no DISTANCE CUTOFF.

Spinfoam may not be the kind of path-integral-like approach that Nima is used to, but it does has some resemblance.

 

In the original post I couldnt find a clear connection with either usual LQG or Spinfoam. In neither case does one "discretize the space-time, put the theory on a lattice,". The theories are built on a continuum (differentiable manifold) with no fixed geometry. There are results like discreteness of the volume operator that are proved as a theorem. But one does not put in discreteness "by hand".

Ok. First take QED at weak coupling. The theory is very well defined---we can compute scattering amplitudes and runnings of beta functions, etc. What one quickly notices is that QED has a Landau pole, at a place where the (inverse) coupling runs to zero. When the inverse coupling runs to one, the theory ceases to have a well-defined perturbative limit. So let's imagine a universe where we actually WANTED a UV completion of QED.

 

The best way we know how to treat a non-perturbative gauge theory is to discretize the space-time, put the theory on a lattice, solve for something, and pray that the answer we get is independant of the lattice spacing. We have had great success in this vein,...The problem is that... trying to understand the UV completion... far from unique.

 

doesnt seem to make connection with work by LQG community

Either way, when we put QED on a lattice, it becomes something that is no longer QED. Indeed, when we look at the IR behavior of the new theory, we have lost all of the predictions of QED, as well as the beautiful IR limit---in short, the IR limit of the theory we found by discretizing QED is not QED.

 

That is fine but I have to repeat that LQG and Spinfoam approaches AFAIK have nothing to do with putting General Relativity on a lattice. In what is probably the most usual form of LQG, you start work with a continuum, your configurations space consists of continuum geometries---represented by HOLONOMIES and the conjugate FLUXES. Everything is continuous so far. You get a uniqueness theorem. You eventually prove theorems about the area and volume operators.* You find that you can construct a BASIS for the kinematical Hilbert space using objects that have some similarities to lattices---they are labeled graphs. But that is not essential---there are other ways of describing the Hilbert space.

 

Nima's argument does not seem to connect to anything definite and recognizable. It would help if he would simply go to the recorded talks of the LOOPS '07 conference and say WHOSE TALKS does his discussion apply to?

 

There is currently no one "bible" of LQG, it is a fast-moving field and people are exploring a considerable variety of different paths to understanding space, time, and matter. So he would have to say what current approach or approaches he is talking about.

Nima then argues that this is why LQG is bound to fail. ...

 

???

 

The only way we could possibly begin to understand the problem is to discretize the path integral in a lattice-like formulation, and search for a theory that is independant of the lattice spacing.

 

that again! I don't think this applies. Where in any LQG work does anyone ever pick a "lattice spacing" or even any minimum distance cutoff?

 

But this is exactly what fails in the case of QED, and is exactly what is attempted by the LQG program.

 

I don't understand why he says this "is exactly what is attempted by the LQG program."

 

there are many programs being pursued by the LQG community but I don't know any one that corresponds accurately to what he is talking about.

 

However, no problem. No reason he should keep himself up to date on others' research.

 

*when the area and volume operators turned out to have discrete spectra (in this version of LQG) it was taken as evidence of some discreteness in space at the fundamental level. these are theorems you have to prove----you don't have those results in every approach.

 

Actually what we should do is try to suggest the range of different approaches being worked on by the Loop community!

That could be fun and interesting.

 

there is the recent (June) international conference, many of the talks are online with audio and slides

http://www.matmor.unam.mx/eventos/loops07/program.html

plenary talks

http://www.matmor.unam.mx/eventos/loops07/plen_abs.html

contributed talks

http://www.matmor.unam.mx/eventos/loops07/cont_abs.html

[ajb]

Does Loop Quantum Gravity rely on a space-time cut? i.e. we assume [math]M \simeq R \times \Sigma[/math] and then we have to pick exactly how we make this identification.

 

If so I am always a little uncomfortable with situations like this as this cut is not canonical and we have diffeomorphisms which mix coordinates on [math]R[/math] and [math]\Sigma[/math].

[Martin]

Does Loop Quantum Gravity rely on a space-time cut? i.e. we assume [math]M \simeq R \times \Sigma[/math] and then we have to pick exactly how we make this identification.

 

If so I am always a little uncomfortable with situations like this as this cut is not canonical and we have diffeomorphisms which mix coordinates on [math]R[/math] and [math]\Sigma[/math].

 

The Spinfoam approach, which is what the majority of the LQG community have been working since around 1998, and the related GFT, which came out of that---do NOT rely on a cut.

 

The original LQG which got most of the attention say 1988-1998 is similar to a popular version of CLASSICAL General Relativity (e.g. ADM formalism) which DOES rely on a cut.

 

This leads to what people call "frozen time" presentation. The quantum state is defined using an arbitrarily chosen space-like 3D manifold and must be in the kernel of the Hamiltonian operator which therefore functions as a CONSTRAINT.

 

You may be "uncomfortable" with frozen-time formalism, which gets used a lot in Classical GR and does bother people----ADM goes back to around 1960 and the Hamiltonian Constraint idea goes back, I believe, to Dirac. Mathematically it turns out to be OK but it is unintuitive to a lot of people.

A huge amount of discussion has been expended on this, probably more in the Classical GR area than in QG, but in QG as well.

 

Anyway in the mid 1990s PROBLEMS appeared in the definition of the Hamiltonian Constraint for the original LQG, and by around 1998 the majority of researchers were looking at the Spinfoam formalism---also Group Field Theory (GFT) appeared about that time. These were 4D approaches with no cut.

 

From a theoretical/logical/mathematical standpoint there is nothing wrong with Dirac's idea of a Hamiltonian Constraint or the frozen time formalism, they had merely encountered a snag the first attempt to define the constraint. So a few brave souls stubbornly persisted in working on what is known as "canonical" LQG. They did not ALL move over to Spinfoam, GFT, etc.

 

For example. Rovelli has been doing Spinfoam (i.e. 4D) approach but Thiemann has been doing "canonical" LQG.

 

It makes an interesting story, because just recently 2005 - 2007, the small bunch persisting with frozen time canonical LQG have had some success. This was reflected at the Loops '07 conference last month. Thiemann gave the main survey talk.

 

A lot more is happening---this is just a bare outline concerning the 4D versus 3D issue which you brought up. Thanks for asking though! I am glad you are interest, ajb.

[BenTheMan]

Martin---

 

I don't want to misrepresent Nima's position, and it is clear that I must have misunderstood his argument. I haven't had a chance to ask him about it, so as to clarify my understanding.

 

The comments he made were in regards to taking a weakly coupled theory, that is defined in the IR, and trying to run it up to a strongly coupled, UV regime. The example he used was QED, which has been studied on the lattice at strong coupling.

 

Either way, this is the Loops program, no? Take a well defined theory (i.e. Einstein-Hilbert action), which is weakly coupled in the IR, and try to extrapolate back to the UV completion.

 

In regards to LQG being formulated on a lattice, this is from Lee Smolin's ``Invitation to Loop Quantum Gravity'', http://arxiv.org/abs/hep-th/0408048:

 

The area and volume operators can be promoted to genuine physical observables, by gauge fixing the time gauge so that at least locally time is measured by a physical field. The discrete spectra remain for such physical observables, hence the spectra of area and volume constitute genuine physical predictions of the quantum theory of gravity.

 

Is this no longer the state of the art? It seems that this is a (Lorentz violating'' hard cutoff, a la Lattice QCD.

[Martin]

Hi Ben,

just for clarity, let me put that quote from Smolin in a quote box

The area and volume operators can be promoted to genuine physical observables, by gauge fixing the time gauge so that at least locally time is measured by a physical field. The discrete spectra remain for such physical observables, hence the spectra of area and volume constitute genuine physical predictions of the quantum theory of gravity.

 

I've gotten to expect quotemarks because three years ago when I used to omit quote marks or some indication like that people sometimes got confused where the quote stopped and where i started talking and I got told off.

 

And then you continue and ask:

Is this no longer the state of the art? It seems that this is a (Lorentz violating'' hard cutoff, a la Lattice QCD.

 

I think it is a major LQG result. I mentioned it a lot in what I wrote earlier in this thread. discreteness of spectrum of area and volume operators.

 

it does not imply that space is discretized like a lattice. it is a statement about measuring area and volume

 

it's quite interesting there have been scores, maybe hundred, of papers written about this.

 

curiously, it DOES NOT EVEN IMPLY BREAKING Lorentz invariance!

 

Some people have constructed modified forms of special relativity, in part inspired by this. Others have shown that the mere fact of discrete spectrum of the area observable does not necessitate any modification---but you can if you want. It is called DSR and there is, again, a considerable literature.

 

I can't reproduce the subject in a small space.

 

Anyway all I can say is you don't get a good picture if you reason that space must be a lattice simply because a measuring device which is directed to give the area of something (a desk top) can theoretically only give an answer from a certain infinite set of numbers.

 

that certainly does HINT STRONGLY at some kind of discreteness at a fundamental planck-scale level, doesnt it? And that applies, of course, not to the models that most people in the LQG community are working on. That area and volume result is vintage 1990s canonical LQG proper.

 

Unfortunately most of the community is working on Spinfoam, or Group Field Theory, or else on applied stuff. In Spinfoam and GFT they don't have the discrete spectrum result! I should also have mentioned Causal Dynamical Triangulations, which doesn't either.

 

I realize it must be frustrating. It is a very fastmoving field and hard for anyone in Nima's position to follow, I would expect.

 

Offhand I would suggest not reading that 2004 paper of Smolin because it is old. Also because his viewpoint and research, while extremely interesting, is not representative of the community. He is kind of a creative outrider and trailbreaker.

 

there are 2007 papers that give a conventional brief introduction----one by Ashtekar and one by Bojowald. If Smolin is a far-ranging outrider, those two (and also Rovelli's group) are right in the middle of the wagon train .

the recorded talk that Rovelli gave last month at Loops '07 would give you a more accurate feel for the state of things. In my humble view.

 

Let me get the Ashtekar and Bojowald papers, and the link to Rovelli's talk, in case anyone is interested.

 

Bojowald (beginning of paper has brief intro to LQG)

http://arxiv.org/abs/0705.4398

 

Ashtekar: "An Introduction to Loop Quantum Gravity Through Cosmology"

http://arxiv.org/abs/gr-qc/0702030

 

Ashtekar: "Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions"

http://arxiv.org/abs/0705.2222

 

Rovelli's talk, "The LQG vertex", is in the program of the year's big Loop community conference:

http://www.matmor.unam.mx/eventos/loops07/program.html

warning though: Rovelli works in the Spinfoam approach but he CALLS it LQG--it has not yet been shown that the two approaches are equivalent. I don't understand why he calls it LQG. Maybe he is adopting the verbal habits of certain string theorists , who call everything in non-string QG by the name LQG. Who knows, maybe those string theorists are RIGHT to lump everything researched by the non-string QG community into one and call it "LQG" . But then the community cannot be said to be united by any common approach, they have no one element in common---unless you count freedom from fixed background geometry

[ajb]

I have been looking into multisymplectic formalism, which is a covariant form of Hamiltonian mechanics. As such it should be idea of discussing gravitational theories. However, the formalism isn't really complete and is difficult to work with. Also, quantisation is not understood.

 

In this formalism we treat space and time on equal footing and avoid the space-time cut.

[BenTheMan]

it does not imply that space is discretized like a lattice. it is a statement about measuring area and volume

 

Anyway all I can say is you don't get a good picture if you reason that space must be a lattice simply because a measuring device which is directed to give the area of something (a desk top) can theoretically only give an answer from a certain infinite set of numbers.

 

Unfortunately most of the community is working on Spinfoam, or Group Field Theory, or else on applied stuff. In Spinfoam and GFT they don't have the discrete spectrum result! I should also have mentioned Causal Dynamical Triangulations, which doesn't either.

 

Rovelli works in the Spinfoam approach but he CALLS it LQG--it has not yet been shown that the two approaches are equivalent. I don't understand why he calls it LQG. Maybe he is adopting the verbal habits of certain string theorists

 

At least, I'm glad you can see why one would be confused by these statements. It is also odd that Loop Quantum Gravity's main proponent is disconnected from the field.

 

Let me ask a direct question, which may not have an answer. Do momenta larger than the Planck scale make sense in Loop Quantum Gravity? If yes, then how could one ever describe such a thing, when your operators are required to give discrete answers? If no, then how does this NOT violate Lorentz Invariance?

 

=============

 

Please go easy on me, I am but a simple phenomenologist!

 

I also want to make it clear that I am probably misquoting Nima. (If he or one of his students is reading this, then apologies!)

[Martin]

At least, I'm glad you can see why one would be confused by these statements. It is also odd that Loop Quantum Gravity's main proponent is disconnected from the field.

 

Hi Ben, I can see why EVERYBODY should be confused as long as we have this bad semantic situation. "LQG" is used, especially by outsiders, to mean two different things.

 

It is the general catchall name applied to the NON-STRING QG community and all their (typically background independent) approaches. But also it is used to apply to some stuff that was worked on by some people in the 1990s.

 

I am not sure who is really the presentday LQG community's "main proponent". Certainly Ashtekar and Rovelli are guiding lights, who always speak up at conferences and ask penetrating questions.

 

the LQG community tends not to get involved in controversy----folks don't spend much time criticizing String, or proving to themselves that it must fail etc. They always invite some String Theorists to their conferences, so far, and welcome them cordially etc.

 

I suppose you mean that Lee Smolin is the non-string QG "main proponent".

His book, calls for more opportunities for non-string research especially in the US. But he is not necessarily pushing his OWN line of research which is quite different from what others (Asht. Rovel. Bojowald. Reuter) are doing.

If you read it the book is complimentary to string, many nice things to say, and I think quite unselfish----he doesnt unduly push his own pet research line. He's asking for more chances for postdocs in the US in ALL the various non-string QG lines------somewhat the way it is shaping up in Europe.

 

I dont see that as "strange" though. I don't see why you call it strange for him to be a proponent of some changes in research funding policy (but not for especially selfish motives).

 

Let me ask a direct question, which may not have an answer. Do momenta larger than the Planck scale make sense in Loop Quantum Gravity? If yes, then how could one ever describe such a thing, when your operators are required to give discrete answers?

 

We are talking about standard LQG, I'm not sure what to call it:confused:

old-LQG. The kind people are mostly not pursuing now but which still an important landmark for the field. You are saying the AREA AND VOLUME operators have discrete spectrum. That is true. In the canonical LQG context this has been proven (but not for spinfoam, GFT, CDT, Reuter's QEG etc...).

 

In that particular context we know that the area and volume operators have

discrete spectrum----I don't see what that means about momenta?

 

But the answer to your question is yes momenta of macroscopic objects make sense. Momenta are not required to be Planck scale:D . People used to have questions about that but AFAIK they've been satisfactorily resolved.

=============

 

 

I also want to make it clear that I am probably misquoting Nima. (If he or one of his students is reading this, then apologies!)

 

I wouldnt worry. It is more likely that I am not accurately enough describing the current situation in the non-string QG community. Whatever you have said is not especially surprising or bothersome. I have to go and am responding in a hurry. I will try to get back later or tomorrow.

 

Interesting discussion, Ben! thanks for the opportunity to talk about these things!

[BenTheMan]

In that particular context we know that the area and volume operators have

discrete spectrum----I don't see what that means about momenta?

 

Well, for example, if length is quantized, and energy is 1/L, the energy should also be quantized. Right?

[Martin]

Well, for example, if length is quantized, and energy is 1/L, the energy should also be quantized. Right?

 

I understand what is puzzling you, I habitually make these sorts of conversions---mass to energy to frequency and wavelength and momentum etc etc

 

One normally equates all these things----essentially by mentally setting hbar and c equal to unity.

 

One does it mentally without thinking about it. but it doesn't apply in this case and the reason would require delving into what actually the area operator does.

 

I will not be able to give you a satisfactory explanation, so you will have to take this mainly on faith.

 

When it was proven (again in this canonical LQG context, not in all approaches being worked on) that AREA had a discrete spectrum, and the spectrum was calculated, this did not automatically prove that VOLUME would have a discrete spectrum and that result came only later after more work.

 

Furthermore the volume spectrum has not yet been calculated!

 

Naively, one would think that if area has a discrete spectrum that would immediately imply that LENGTH must also and also volume and all the other measurments that one can think of (that you and I just mentioned).

 

But that is simply not true. Area discrete spectrum does not imply that length or volume is discrete, or that anything else is discrete.

 

Again naively or intuitively one would expect that once the area spectrum had been CALCULATED one might be able to get the spectrum for length ("why not just take the square root?") and to calculate the spectrum for volume ("lets just cube the length eigenvalues!").

 

But that naive approach does not work. The spectrum of the volume operator HAS NOT YET BEEN CALCULATED.

 

===========================

 

Maybe the way to understand this in the sense of overview is to say that a revolution in the LQG community occurred about 1998.

 

1996 was the year Martin Reuter started the Assymptotic Safety program he calls QEG. (if you havent listened to his talk at Loops '07 you really should!)

 

and 1998 was the year Renate Loll and Jan Ambjorn started CDT

 

and about the same time Krasnov and Freidel started Group Field Theory (GFT)

 

and a bunch of people (Baez, Rovelli, ...I forget who all) started Spinfoam.

 

Since the 1998 revolution I don't think most people know what theories or approaches they mean when they say "LQG". It's really difficult to get an accurate overview! Basically all I can say is there is a LQG COMMUNITY which is defined by participation in conferences and workshops.

 

People jump back and forth between different approaches because they are all somehow related in philosophy and method like members of a family but without any one unique defining feature.

 

At Loops '07 Oriti talked about GFT and said it could unify Spinfoam and CDT as a common framework, and Rovelli presented a result on Spinfoam suggesting that it might assimilate (and change) the old canonical LQG.

I guess the thought is that there are different paths up the mountain and that some will be dead ends and some will continue up and eventually converge.

And as the different approaches converge they will CHANGE in subtle ways.

 

To me right now the most exciting approach is Reuter's. He has co-workers at a lot of places, but his homebase is Mainz. Probably the nearest other approach is CDT (Ambjorn and Loll, homebase Utrecht). In his talk at Loops 07, Reuter repeatedly referred to the earlier talk given at the conference by Jan Ambjorn. I would like to see how Reuter's QEG and CDT and GFT and Spinfoam link eventually link up.

 

Reuter is applying QEG to cosmology now----that was what the whole second half of his talk was about. So we should be able to compare preductions with Martin Bojowald's LQC (Loop formalism applied to cosmology)

 

It is exciting right now:D we are sort of ten years into what I see as the 1998 "revolution".

[BenTheMan]

Martin---

 

Thanks for the history of the LQG revolutions, but I really want to know the physics of what is happening here.

 

understand what is puzzling you, I habitually make these sorts of conversions---mass to energy to frequency and wavelength and momentum etc etc

 

So, you're telling me that dimensional analysis fails in quantum gravity?

 

Furthermore the volume spectrum has not yet been calculated!

 

So the Smolin quote is wrong, where he explicitly says that the spectra of the two operators is discrete, and that it can be seen as a prediction of the theory?

 

Sorry if these questions are circular, but I'm just looking for some simple answers about quantum gravity outside of strings. I understand some of the rudiments of string theory (think: volume one of Polchinski modulo chapter 2, which I am assured that nobody understands), but don't really understand anything about other approaches to QG. Don't be affraid to get technical---I probably won't be convinced otherwise.

[Martin]

Hi Ben, somehow I missed your post earlier. Just now saw it and will respond

 

Furthermore the volume spectrum has not yet been calculated!

So the Smolin quote is wrong, where he explicitly says that the spectra of the two operators is discrete, and that it can be seen as a prediction of the theory?

 

The volume operator has been proven to have discrete spectrum. As far as I know, its spectrum has not been calculated yet. Detailed knowledge of the points in a set is not generally necessary in order to prove the set is discrete.

 

Nothing here suggests that Smolin was wrong

If the quote you mean says it has been proven that the area and volume operators have discrete spectra then the quote is right!

 

The last I heard, the spectrum of volume has not yet been calculated.

 

So, you're telling me that dimensional analysis fails in quantum gravity?

 

No I am not telling you that. Dimensional analysis is used in all kinds of theoretical physics including LQG and other QG approaches.

 

However in Quantum Mechanics you cannot always use dimensional analysis to tell you the spectrum of an operator---even when you think you ought to be able to!---sometimes it takes more work.

 

To illustrate with a simple analogy, general arguments persuade me that no device can measure a length that is less than planck length.

 

But the reciprocal of planck length is planck momentum----equivalent to what you can give a gentle shove with one hand, hardly a big momentum!

 

One can easily measure momentums much greater than 1/L where L is the planck length.

 

The same thing carries over to quantum OBSERVABLES. Dimensionally, two observables can be in a simple algebraic relation---like reciprocal or square etc.---and yet their spectra need not be in that simple relation.

 

... Don't be affraid to get technical---I probably won't be convinced otherwise.

 

I'm not anxious to convince you of anything, that I can think of. You've chosen a line of PhD research, you need to pursue it with determination and complete it.

 

I think you most recently said you were in Phenomenology? Stringy-type phenomenology to be sure. But still phenomenology (because the emphasis on comparing theory to observable results) has a slightly different character from pure theory. You can move more easily from stringy to non-stringy phenomenology later if your interests shift post-PhD. According to the numbers I have seen the CAREER PROSPECTS are better in phenomenology (and cosmology) than they are in straight string.

 

However you said you want to learn more about non-string QG.

I already gave you advice on that one. First off, you need to find 5 - 10 minutes so you can scan thru those 30 slides I gave the link to. It wont take long because there are only a few sentences on a slide, and maybe a picture.

 

As a general rule, someone who thinks that non-string QG is represented by Lee Smolin, probably doesn't know much about QG. He's a great guy but he's not the only player to watch. Also the research that Smolin's group is doing is not at all typical---they have a way of including features of the standard particletheory model into the networkformalism of gravity, so different kinds of particles become a part of the geometry of the gravitational field. This is very new and offbeat stuff---only got started in 2006. To get an accurate picture of QG, as a first order approx you should IGNORE the very novel work that is uncharacteristic of the whole.

 

My experience of other string theorists is they tend to be somewhat naive about the competition. They often do not know the names of the important researchers (besides L.S.) or what kind of research is being done or what the results are. I don't blame them, because life is short! I only worry when they pretend they know something about non-string QG and start explaining why it will never work

 

Eventually, if you want to understand something about non-string QG then you need to find 45 minutes so you can listen to Reuter's talk (while scrolling thru the slides.) I've listed some of the other leaders of QG in another thread, but I suggest Reuter (for someone like yourself with limited time) because he talks the kind of ordinary Quantum Field Theory language that you are likely to understand. Also his approach is one of the older lines being pursued in the LQG community---the original paper goes back to 1996---and there are signs that his approach is starting to be very influential.

 

Here are Reuter's Loops '07 slides:

http://www.matmor.unam.mx/eventos/loops07/talks/PL3/Reuter.pdf

 

his Loops '07 audio:

http://www.matmor.unam.mx/eventos/loops07/talks/PL3/Reuter.mp3

[BenTheMan]

The volume operator has been proven to have discrete spectrum. As far as I know, its spectrum has not been calculated yet. Detailed knowledge of the points in a set is not generally necessary in order to prove the set is discrete.

 

It probably isn't unreasonable to assume that the volume eigenvalues are in units of the Planck Length? Just by naive dimensional analysis---there aren't any other scales in the problem, are there?

 

However in Quantum Mechanics you cannot always use dimensional analysis to tell you the spectrum of an operator---even when you think you ought to be able to!---sometimes it takes more work.

 

I disagree. You always know the scales in the problem, so at the very least you can ballpark it. Just like the QED thread in another sub-forum---the guy wanted to know how QED treated the diffraction of light. The answer is that it doesn't---the scale of QED (i.e. the only dimensionful parameter in the theory) is the electron's mass (which is about a fifth of the Bohr radius), so QED effects become important at the Compton wavelength of the electron, which is MUCH smaller than any diffraction grating you'll ever be able to build.

 

I may be missing something, and please point me to a counter-example if I am wrong. But in gravity the only dimensionful parameters we have are the Planck parameters---this means that the relevant time, distance, energy, and length scales are all in Planck units. This means that all of your operators have to give you eigenvalues in those units, UNLESS you introduce another scale or parameter into the problem. In string theory, there is the string coupling.

 

But the reciprocal of planck length is planck momentum----equivalent to what you can give a gentle shove with one hand, hardly a big momentum!

 

Come on Martin---the scale is important. Sure you could shove me and give me Planck energy, but I'm also made of 10^25 ish particles. A counter example---each proton in the LHC beam has an energy of 14 TeV or so. Individually, that's about the equivalent of a paperclip. But all of the protons put together have as much kinetic energy as a fully loaded air craft carrier moving at 40 knots.

 

One can easily measure momentums much greater than 1/L where L is the planck length.

 

I don't buy it. This is like saying that one can measure energies smaller than hbar. Isn't there some analogue of the uncertainty principle at work here? And besides, you seem to be ignoring the scale of the problem again.

 

According to the numbers I have seen the CAREER PROSPECTS are better in phenomenology (and cosmology) than they are in straight string.

 

Absolutely:) Plus, it's a tremendous rush to imagine calculating something that someone will actually MEASURE some day.

[Martin]

 

The volume operator has been proven to have discrete spectrum. As far as I know, its spectrum has not been calculated yet. Detailed knowledge of the points in a set is not generally necessary in order to prove the set is discrete.

 

It probably isn't unreasonable to assume that the volume eigenvalues are in units of the Planck Length? Just by naive dimensional analysis---there aren't any other scales in the problem, are there?

 

However in Quantum Mechanics you cannot always use dimensional analysis to tell you the spectrum of an operator---even when you think you ought to be able to!---sometimes it takes more work.

 

I disagree. You always know the scales in the problem, so at the very least you can ballpark it. Just like the QED thread in another sub-forum---the guy wanted to know how QED treated the diffraction of light. The answer is that it doesn't---the scale of QED (i.e. the only dimensionful parameter in the theory) is the electron's mass (which is about a fifth of the Bohr radius), so QED effects become important at the Compton wavelength of the electron, which is MUCH smaller than any diffraction grating you'll ever be able to build.

But the reciprocal of planck length is planck momentum----equivalent to what you can give a gentle shove with one hand, hardly a big momentum!

I may be missing something, and please point me to a counter-example if I am wrong. But in gravity the only dimensionful parameters we have are the Planck parameters---this means that the relevant time, distance, energy, and length scales are all in Planck units. This means that all of your operators have to give you eigenvalues in those units, UNLESS you introduce another scale or parameter into the problem. In string theory, there is the string coupling.

 

But the reciprocal of planck length is planck momentum----equivalent to what you can give a gentle shove with one hand, hardly a big momentum!

 

Come on Martin---the scale is important. Sure you could shove me and give me Planck energy, but I'm also made of 10^25 ish particles. A counter example---each proton in the LHC beam has an energy of 14 TeV or so. Individually, that's about the equivalent of a paperclip. But all of the protons put together have as much kinetic energy as a fully loaded air craft carrier moving at 40 knots.

 

One can easily measure momentums much greater than 1/L where L is the planck length.

 

I don't buy it. This is like saying that one can measure energies smaller than hbar. Isn't there some analogue of the uncertainty principle at work here? And besides, you seem to be ignoring the scale of the problem again.

...

 

None of this relates to what I was trying to explain to you, Ben.

 

I was not talking about estimating the rough order of magnitude of the numbers, or guessing their scale. What I said (which started the discussion) was that the area operator spectrum has been calculated in (canonical) LQG and the spectrum of the volume operator had NOT been, the last I heard.

 

That is a series of numbers is known exactly in the area case---one has analytical formulas for all the numbers in the spectrum, which can be generated as needed and evalutated as accurately as desired.

 

This is not the case with the volume operator. The work hasnt been done yet.

 

However it has been proven mathematically that the spectrum for volume is discrete---it is countable, bounded away from zero, etc.

 

Of course one can do dimensional analysis and one can make guesses about the rough size of the lowest nonzero eigenvalue for volume----Planck scale presumably. But I wasnt talking about such estimates.

 

You seemed to think it was odd that the area spectrum was calculated and the volume spectrum was not---and you questioned this. So in everything you quote here I was responding to that: using intuitive examples to try to explain to you why one doesnt expect to get the preceise eigenvalues of one quantum operator in a naive way from the eigenvalues of another merely because the two classical measurments are dimensionally related, like area and volume.

I was not talking about "scale" and "ballparking it" or whether suchandsuch would be in "units of Planck length".

 

Apparently I didnt do such a good job of explaining.

 

In any case it's nice of you to keep the dialog going.

[BenTheMan]

Ok, perhaps we are talking past each other a bit.

 

The point I wanted to make was that one expects the eigenvalues of the volume operator to be on the order of the Planck scale, just by dimensional analysis. Maybe there are some factors of pi or root two or something floating around, but at the end of the day the Planck length should dictate the size of these eigenvalues.

 

In any case it's nice of you to keep the dialog going.

 

I'm game as long as you are I'm always game to talk about physics.

 

Before we move on---I think we've agreed that the volume operator should give eigenvalues that are Planck Length cubed, wether or not we can actually calculate the exact values...yes or no?

[Martin]

...

Before we move on---I think we've agreed that the volume operator should give eigenvalues that are Planck Length cubed, wether or not we can actually calculate the exact values...yes or no?

 

No in the sense that I would expect the vast majority of the eigenvalues to be enormously larger than that----e.g. many of them would be be larger by a factor of 10⁹⁰ or 10¹⁰⁰----e.g. a cubic centimeter.

 

But your comment has the right spirit. We can make it a bit more precise and agree on it! I would expect that one out of a huge number of typically much larger eigenvalues, namely the the SMALLEST nonzero value, should be on the order of Planck Length cubed.

 

The corresponding thing happens with the area operator. It has many many larger eigenvalues but it has s SMALLEST nonzero value which is on the order of Planck Length squared.

=============

there are factors like squareroot two and pi etc etc involved but IIRC its on that order.

=============

 

Ben what concerns me is that you seem to have fallen prey to some sort of illogic, at least in my view.

 

You, and a number of other stringers, say WE HAVE NO COMPETITION. (you have said that in a post recently) and then as if to reassure yourself about that you start asking about VINTAGE 1990s CANONICAL LOOP QG!

 

And people like Nima and others (Distler, Bergman...) give "arguments" for why LQG must necessarily fail and therefore represents no competition

Their ideas of what the competition is---what the other community is doing---always seem out of date!

 

In fact you DO have a very active, growing, and intellectually resourceful competion in the form of a QG community which around 1998 branched out into interesting directions (NCG, spinfoam, GFT, Reuter's stuff, CDT-triangulations, etc.) and which is JUST NOW BEGINNING to hold annual conferences.

 

The first Loops conference was Loops 05, then the European Science Foundation funded the QG Network---there was the 2007 QG Network school, and then Loops 07. And the QG Network has a big international conference set for 2008, which will be "Loops 08" but by a different name.

 

these conferences already draw 150 participants, and they are not talking about the vintage 1990s area and volume operator!

 

It seems to me you would rather know who the REAL COMPETITION ARE and find out about what they are ACTUALLY RESEARCHING and what the results are. Finding out could be more valuable than just nourishing a false image of the competition and repeating arguments why it "can't succeed" which don't connect with the reality.

 

AFAICS what you told us that Nima told the grad students at Princeton string summerschool----what he said about why the competition cannot succeed, and the reasons he gave----simply DID NOT MAKE CONTACT WITH THE REALITY of the growing non-string QG community.

 

the only way to get contact would be for people like him to attend a conference like Loops 07, which was just held, or to study-up using the online slides and audio. Stringfolks are always welcome at Loops conferences.

 

I'm not saying they should do anything I havent tried to do myself in the corresponding sense---reciprocally---e.g. I listened and watched video of some of the highlights of Strings 07, the Madrid conference. For me the highlights were the last five minutes of David Gross talk and question session at the end of Ed Witten's talk where someone asked him what did his talk have to do with string theory. I also watched considerably more of Strings 05, the Toronto conference----particularly liked the Thursday evening Panel Discussion airing people's thoughts about "The Next String Theory Revolution". It can be really enlightening to look over at what another bunch is talking about among themselves.

[BenTheMan]

No in the sense that I would expect the vast majority of the eigenvalues to be enormously larger than that----e.g. many of them would be be larger by a factor of 1090 or 10100----e.g. a cubic centimeter.

 

Come on man give me some credit! Sure the spectrum can be in principle infinite (or semi-infinite), but the dimensionful parameter is the Planck Volume---like hbar in quantum mechanics. This means the lowest lying states in the Hilbert space are of order the Planck volume, up to possibly some numerical factors.

 

Ben what concerns me is that you seem to have fallen prey to some sort of illogic, at least in my view.

 

The faulty logic of...dimensionful analysis? In the past few posts, I haven't really made any arguments for or against any other approaches to gravity---I've only asked questions based on dimensionful parameters.

 

AFAICS what you told us that Nima told the grad students at Princeton string summerschool----what he said about why the competition cannot succeed, and the reasons he gave----simply DID NOT MAKE CONTACT WITH THE REALITY of the growing non-string QG community.

 

The point is that your volume operator gives back discrete values, as you have admited. This means that in your path integrals, you have a hard, Lorentz Violating cutoff at the Planck length (whether you like it or not) because the phase space doesn't exist above the Planck scale---they don't live in your Hilbert Space. In this sense you are trying to solve gravity by discretizing the path integral, an approach that doesn't always work. You can see this if you try to regularize QED with a hard UV cutoff---it doesn't really work. This was Nima's argument, as I understood it.

 

It seems to me you would rather know who the REAL COMPETITION ARE and find out about what they are ACTUALLY RESEARCHING and what the results are. Finding out could be more valuable than just nourishing a false image of the competition and repeating arguments why it "can't succeed" which don't connect with the reality.

 

Martin---I don't care about the competition. They are not competing for the jobs that I want, I promise you. If I never learn another thing about Loop Quantum Gravity, I will be able to sleep at night.

 

I posted this argument of Nima's to start a discussion, and I was under the illusion that there were people here who could discuss these things with me. If this is not the case, then perhaps I am in the wrong place. This place seems to have more than a few people who think string theory is wrong, whether they want to admit it or not (cf---The Trouble with Physics is STILL the book of the month, even though it looks like the discussion thread has been locked and no one actually read the book to start with), despite the fact that there doesn't really appear to be any discussion on the topic.

 

What I really want is to have (semi-)technical answers to questions, so that I can learn (or at least get a flavor for) the physics. I don't have the money or the time to go attending Loops conferences (I don't even plan to attend the Strings conference, unless they invite me or it's within driving distance). I don't really care to be told how miguided I am, or how short-sighted I am, or how I really need to read more papers or attend more conferences.

[Martin]

I A good percentage of the string graduate students I have met don't really care about the ultimate fate of the string theory edifice... It is quite clear to everybody that I have talked to, though, that there are no real competitors, at least at this point in the game of quantizing gravity.

 

Martin---I don't care about the competition. They are not competing for the jobs that I want, I promise you.

 

You first mentioned "competition". I have been responding. The kind of competition I mean is between theories, research lines, approached to quantizing gravity. I think you meant that at first, in your post a few days back. Now you are talking about competition for jobs.

 

when the conversation is so fluid it makes it hard to talk sensibly. Probably we are both at fault for not being clearly enough focused.

 

I told you earlier that almost all the research being done by the non-string QG community (theories competing with string in the "game" you mentioned) do NOT have a discrete spectrum area and volume operator result.

 

You say Nima gave an argument based on discreteness. The implication was that the approaches to QG being followed by the Loop community will not work.

 

Nima's argument fails. First of all, it sounds like he doesnt have any idea of what 90 percent or more of the community is up to.

 

Two of the best approaches CDT and Reuter's have no smallest length, or area, or volume. Likewise GFT as far as I know. Spinfoam approach has no discreteness result about the area and volume operators.

 

Secondly, even if we just look at vintage 1990 canonical LQG that has the discrete area and volume spectrum, the argument you gave here doesn't work

 

The point is that your volume operator gives back discrete values, as you have admited. This means that in your path integrals, you have a hard, Lorentz Violating cutoff at the Planck length (whether you like it or not) because the phase space doesn't exist above the Planck scale---they don't live in your Hilbert Space. In this sense you are trying to solve gravity by discretizing the path integral, an approach that doesn't always work. You can see this if you try to regularize QED with a hard UV cutoff---it doesn't really work. This was Nima's argument, as I understood it.

 

There is an extensive literature about this. In approaches like canonical LQG where there is discreteness this has been RECONCILED in several ways with Lorentz invariance. One paper I recall was by Carlo Rovelli. It is an old problem and it's been years since Rovelli solved it. I doubt you will read it but perhaps I should get the link.

 

http://arxiv.org/abs/gr-qc/0205108

Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction

Carlo Rovelli, Simone Speziale

12 pages, 3 figures

(Submitted on 25 May 2002)

 

"A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts and give the conditions under which its action is unitary."

 

I also tend to doubt that Nima or any of the other string folks you talk to have heard of this paper.