What is LQG?

[Martin]

the lines of research currently being pursued by members of the LQG community is seen by some as a challenge or competition to String community. So this interests people.

Ben and Bascule recently started threads about this, showing the interest in it.

Ben's thread reported how a notable stringy phenomenologist, Nima, gave an argument to some grad students at a Princeton summer workshop proving that LQG cannot possibly succeed. this suggests that some of them might have wanted reassurance that a perceived rival is doomed to fail, as a means of gaining greater confidence.

Several string blogs have often presented arguments of this sort (Motl, Distler, Clifford's Asymptotia). At one point in the past Wikipedia had a long list of reasons why LQG must inevitably fail.

All this makes it interesting to discuss what, after all, is LQG?

 

the actual research that the Loop community does has gone thru many changes or 'revolutions' since the original work circa 1990. Actually for much of that time you could hardly say there was a proper *community* since there were only a few people working----not enough to have an annual conference.

 

The LQG community, as such, is really quite NEW. You tell research communities by their annual conference(s) and the LQG community ONLY JUST BEGAN to have one. they had Loops 05 in 2005, and then they didnt have one in 2006, and now this year that had Loops 07. So its like a motor that is just beginning to crank up, and is still missing beats.

 

A community has LEADERS and you can tell who the leaders are partly by who is invited to be a PLENARY SPEAKER at the big international annual (which Loop might be starting to have).

 

And there should be identifiable COMMON THEMES that run thru all or most of the different lines of research pursued by the community and represented at the conference.

 

So we can if we want, throw out our preconceptions and just take an objective look at the community's first two Loops conferences and see WHO gave invited plenary talks at both and WHAT did they talk about.

 

have to go. I will try to do a bit more on this today, later.

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CONTINUED

 

Another defining event was the funding in 2006 by the European Science Foundation (ESF) of the QUANTUM GEOMETRY NETWORK.

It is supported by the governments of some 8 countries. IIRC the initial funding commitments go for five years. You can find out details at the QG website

 

the QG Network organizes and sponsors workshops, conferences, and gives individual research grants. It's first conference will be summer 2008 and its first SCHOOL was this year. Being invited to lecture at the school is somewhat like being invited to give a plenary talk.

 

For statistical purposes, let us give a SCORE to individuals depending on how many of these events they got invited.

 

Carlo Rovelli 3 (as you might expect he did plenary at both Loops 05 and 07, and he lectured at the QG school)

Martin Reuter 3

Abhay Ashtekar 2

Lee Smolin 2

Martin Bojowald 2

Thomas Thiemann 2

Laurent Freidel 2

Jan Ambjorn 2

Daniele Oriti 2

Etera Livine 2

Alejandro Perez 2

Raphael Sorkin 2

 

I have to go and check to see if I have missed anybody.

2005 plenaries

http://loops05.aei.mpg.de/index_files/Programme.html

2007 plenaries

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

first QG Network school

http://www.fuw.edu.pl/~kostecki/school.html

 

Keep in mind the imperfections of any quantitative measure. Several of those who get score 2 here WOULD have been at all three had they not been too busy to accept the invitation to lecture at the school or for some other non-essential reason. John Barrett who is the director of the European Science Foundation QG Network should be there because he, in effect, made the QG school happen. As well as giving a plenary talk at Loops '05.

But again Barrett is probably too busy to show up at all these community events. Still this way of listing people does give some idea.

 

they have a variety of different specialties----there is a diversity of QG approaches that all somehow get under the Loop tent. We can list these although the abbreviation are not likely to mean anything. I shall list only the CURRENT research interest that is relevant. Like from 2005 onwards Rovelli has been doing spinfoam, though in the 1990s he was one of the main developers of old-LQG. I shall just list spinfoam for him.

 

Carlo Rovelli 3 spinfoam

Martin Reuter 3 asymptotically safe quantum gravity and cosmology (QEG)

Abhay Ashtekar 2 applications to cosmology (LQC)

Lee Smolin 2 braiding as a way to include the standard model particles

Martin Bojowald 2 applications to cosmology (LQC)

Thomas Thiemann 2 master constraint dynamics, algebraic quantum gravity (ALG)

Laurent Freidel 2 spinfoam, including Feynman diagrams of usual quantum field theory

Jan Ambjorn 2 causal dynamical triangulations (CDT)

Daniele Oriti 2 group field theory (GFT)

Etera Livine 2 spinfoam, group field theory (GFT)

Alejandro Perez 2 extending topological field theories, string-like objects in 4D*

Raphael Sorkin 2 causal sets

 

*Sorry I cant adequately describe his latest work. He recently co-authored a paper with John Baez about strings that aren't like the "string theory" ones.

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WHAT ARE THE COMMON THEMES of these people's different lines of research? i.e. the different approaches to a quantum theory of gravity, do they share some common feature or assumption?

 

Minimalism, no-frills, no extra dimensions. They all want to quantize GEOMETRY. They assume gravity IS geometry. (Some suspect matter might turn out to be geometry too---e.g. particles might be kinks in space---which might explain how matter affects curvature.)

They mostly all start with a BARE CONTINUUM having no prior metric on it-----mathematically it is the distance function or metric which defines a geometry and a smooth manifold without any distance function on it is geometryless. EINSTEIN GEN REL is that kind of theory. It does not make a prior choice of metric. In fact the metric function is the VARIABLE which describes the gravitational field.

 

In all these approaches you are looking for a quantum theory of the geometry of spacetime interacting with matter. You hope that finding the right approach will reveal the underlying microscopic elements from which space, time, and matter arise----the common ground from which the regular macroscopic world emerges.

 

An important part of the program is that you do not accept the geometry of space as a GIVEN. You want it to be fully dynamic and variable, so you don't make any prior commitment in the theory to any particular background geometry. In whatever approach, the geometry itself must be a quantum variable. You don't assume some fixed space and have things move around in it. "The stage is one of the actors in the play."

 

The reason that the QG community has this common theme of "independence from background metric" is because EINSTEIN'S 1915 GEN REL ALREADY HAD THIS FEATURE of starting with a formless continuum. Gen Rel is "background independent".

 

One of the things that characterizes the QG community is wanting to quantize Gen Rel (the geometrical theory of gravity) in a way that CONSERVES THE ESSENTIAL IDEA of background independence and which adds as little as possible extra machinery, in other words NO EXTRAS. Or as little extras as you can manage.

[BenTheMan]

Ben's thread reported how a notable stringy phenomenologist, Nima, gave an argument to some grad students at a Princeton summer workshop proving that LQG cannot possibly succeed. this suggests that some of them might have wanted reassurance that a perceived rival is doomed to fail, as a means of gaining greater confidence.

 

I think you are reading too much into this. A good percentage of the string graduate students I have met don't really care about the ultimate fate of the string theory edifice---they think it is interesting enough to write a PhD on it. 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.

 

An important part of the program is that you do not accept the geometry of space as a GIVEN. You want it to be fully dynamic and variable, so you don't make any prior commitment in the theory to any particular background geometry. In whatever approach, the geometry itself must be a quantum variable. You don't assume some fixed space and have things move around in it. "The stage is one of the actors in the play."

 

IS the number of dimensions derived from first principles, or put in by hand?

 

Also, it's not clear to me how important background independance actually is. The example I can think of is that we generally have to introduce gauge invariance to do calculations in quantum field theory. But in order to get sensible results out, we have to pick a gauge, because our hilbert space gets messed up with things like states of negative norm. So we introduce gauge invariance, and then gauge fix the theory, which makes it no longer gauge invariant. Just like in GR---the gauge invariance in GR translates as diffeomorphism invariance. In order to get numbers out of GR, one has to pick a metric (i.e. Schwarzchild metric), which makes the theory no longer background independant. So why is background dependance so important? You have to pick a gauge to do calculations anyway, right?

[Martin]

...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.

 

IS the number of dimensions derived from first principles, or put in by hand?

In the case of most non-string approaches you pick dimension = 4 ahead of time because that corresponds to our experience and the rest of established workaday physics.

 

In one approach, CDT, dimension 4 turned out as a RESULT. Jan Ambjorn talked about that at Loops '07. In 2005, Ambjorn's co-author Renate Loll wrote that in any successful quantum theory of gravity, the dimensionality of space should be a quantum observable

and might depend on the energy or scale at which you probed. they aren't there yet, but they are on the way and making progress.

 

I am not arguing with you. I think you want to point out a deficiency in many of the non-string QG approaches (i.e. LQG community's research).

So far, they only do gravity ON A MANIFOLD CHOSEN TO BE 4D but which does not have any prior chosen metric.

 

so that shows there is room for improvement! the better you get, the more fundamental, the less you have to assume in advance and the more EMERGES.

 

Right now you could say that CDT is in the lead in this department, because, in a very limited way, it gets the approximately correct dimension to EMERGE. the dimensionality at various scales is an observable---they run computer simulations and measure the dimensionality in random universes at both micro and macro scale and they get macro dimension to be around 4, micro can be 1.9-2.1

 

Some interesting papers by Ambjorn and Loll about this in 2004 and 2005.

Also see their survey paper "The Universe from Scratch"---it has references to prior work.

 

Also, it's not clear to me how important background independance actually is. The example I can think of is that we generally have to introduce gauge invariance to do calculations in quantum field theory...

 

My experience has been that LQG people don't waste time being critical of String. they don't HARP on the fact that the non-string QG approaches use background independence as a guiding principle (as something carried over from General Relativity, to which they want the corresponding quantum theory).

 

what I've seen repeatedly is self-appointed String defenders like Jacques Distler and Aaron Bergman MINIMIZE THE IMPORTANCE of background independence. To me, this comes across as defensive.

 

It makes me think---"Gee, if background independence is so un-important, it is funny these guys are so defensive about String's ambivalence or lack in that department, and why should they be so anxious to tell me it's not important?"

 

the point is the LQG researchers have chosen background independence as one of their guiding principles. They are happy with it. They're making rapid progress right now. they don't sit around saying "We're good because we're B.I. and String is bad because it isn't B.I."

 

As a stringer you have no need to defend against the idea of background independence or against the average Joe Loop. Loopers will keep on pursuing background indep approaches because it works for them.

 

I can't speak for them but I think they have no interest in criticising String, and simply would just like a share of the theory jobs in the US comparable to what they have in Europe, UK and Canada.

 

I think in science, when you don't know which way is right, you need to fund exploration in various different approaches. That's what the other countries are doing but the US is something of an extreme case. Only one non-string QG group (Penn State) in the whole country---by group I mean more than one faculty member.

 

 

In order to get numbers out of GR, one has to pick a metric (i.e. Schwarzchild metric), which makes the theory no longer background independant.

 

No, Ben. A particular metric is a SOLUTION of the theory. The THEORY is formulated without relying on any background geometry. The theory is background independent. Individual solutions ARE particular metrics, how could they be independent of a particular metric---they would have to be independent of themselves;)

 

To get back to what you said:

...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.

 

You probably have not listened to Martin Reuter's talk. I really think you should. From what you've said I get the impression that the people you have talked to don't have much notion what's going on in the non-string QG community. They may be in denial or shutting it out. It never did anyone any good to nourish the illusion that they've "no real competitors".

 

Reuter gets the Einstein-Hilbert action (with quantum corrections) as a prediction of the theory. He doesnt put it in by hand at the start. He essentially reverses the verdict of non-renormalizability that was passed on gravity back before 1980. You should know about these developments.

[BenTheMan]

Martin---

 

Don't mistake this for an attack on non-string QG---firstly, I want to provide a counterargument in as many places as possible to people who claim that string theory is wrong, with little or no knowledge of the subject. Like it or not, Lee Smolin cast non-string QG as an underdog in his book, the media siezed on this, and now there are people all over these discussion boards parroting the arguments that they read but don't understand. Internet discussion fora are full of people who are willing to eat whatever the media feeds them, instead of trying to understand the whys of the thing. The irony, of course, is that I have done the same thing in another thread, which leads me to the second reason for trying to discuss this---I don't really understand the edifice that is non-string QG.

 

In the case of most non-string approaches you pick dimension = 4 ahead of time because that corresponds to our experience and the rest of established workaday physics.

 

Well, sure---on large scales. What if we find a large extra dimension at LHC---will that alter any of the QG conclusions? Or can you fiddle around with equations to get any number of space-time dimensions.

 

Has anyone ever tried picking a differnet dimension (like 10 or 11 or 350) to see what happens?

 

In one approach, CDT, dimension 4 turned out as a RESULT. Jan Ambjorn talked about that at Loops '07. In 2005, Ambjorn's co-author Renate Loll wrote that in any successful quantum theory of gravity, the dimensionality of space should be a quantum observable

and might depend on the energy or scale at which you probed. they aren't there yet, but they are on the way and making progress.

 

So, in one approach---this doesn't seem like a robust feature of quantum gravity. But I do agree that the number of dimensions should be a prediction of any approach to QG. (This is one of the best arguments, in my opinion, for strings---this and the natural appearance of space-time symmetries and chiral fermions. These things almost come for free.)

 

It never did anyone any good to nourish the illusion that they've "no real competitors".

 

I would have to say that it also never did anyone any good to nourish the illusion that there are real competitors when there aren't any.

 

Can Loop Quantum Gravity give the standard model? Three generations? A heavy top? No experimental signatures that should have already been seen by now? Gauge coupling unification? There are several string models which satisfy these constraints, and there have been since the early days of string model building (c. 1987), WAY before Witten's 1995 paper. Your reply will doubtless be something like ``We just haven't studied it enough, but look at these papers''.

 

Also, these successes came relatively quickly after string theory's birth in 1985. Perhaps this is a social thing though---most string theorists worked on particle physics before they took up strings, and most non-stringy QG people seem to be gravity guys.

 

From what it sounds like, though, the field is very dispersed. Perhaps this is analagous to the pre-duality situation in string theory, where there were five consistent string theories?

 

No, Ben. A particular metric is a SOLUTION of the theory. The THEORY is formulated without relying on any background geometry. The theory is background independent. Individual solutions ARE particular metrics, how could they be independent of a particular metric---they would have to be independent of themselves

 

Right---I realized my mistake after I read this... Gauge invariance in GR is diffeomorphism invariance, which is COORDINATE invariance, not background independance. The metrics are the fields in the Einstein-Hilbert action, which is where I screwed up.

[Martin]

In my experience internet skepticism regarding String goes back at least to 2003---KKLT, Susskind's pronouncements, and lively discussion on Usenet sci.physics.research. What i pick up dates well before Smolin's book which came out September 2006.

 

Here at SFN I don't know anyone who read Woit's book and I don't know of anyone who changed their mind because they read Smolin.

 

Smolin's book is complimentary of String and admiring of its successes. Criticism is more of lopsided funding policy which applies especially inside the US. And other sociological things that have more to do with groups of people and their politics. I think my experience with people has to some extent born out Smolin's sociological points so I tend to suspect they are to some extent valid.

 

So if we are talking about the string theoretical framework ITSELF, his book is descriptive, illuminating, and generally POSITIVE. I think you are mistaken to accuse people of "parroting Smolin" when they express a suspicion that string research has fallen short of expectations or whatever they say.

 

Personally I am not interested in critiquing String ITSELF. I am intensely interested in the work of people like Reuter, Bojowald, Ambjorn, Rovelli...and i have only limited time. To my judgement I saw more exciting new or unpublished results in the recorded online talks at Loops 07 than I did in the online videos of Strings 07. If I want to keep abreast of the action I have to budget my time, so I am not going to bother criticising string research.

 

But I am critical of a kind of defensive denial or inattention I see in the community. Refusal to take stock of interesting developments. Continued misconceptions. Sometimes I swear it looks like "circle the wagons! cover your ears, and say loudly nonstring approaches cannot possibly succeed! we have no competition "

 

Ben, I really think it would be GOOD for you to listen to Reuter's Loops '07 talk----it would broaden your vision enormously because it would give you a taste of current non-string QG research that is totally different from what you seem to have picked up from the string-folks you have been talking to. You would find many of your impressions directly contradicted, I am confident.

 

In case you decide to sample what Reuter has to say, here is a SFN thread with lots of links

http://www.scienceforums.net/forum/showthread.php?t=27748

Here are his 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]

Ben, I really think it would be GOOD for you to listen to Reuter's Loops '07 talk----it would broaden your vision enormously because it would give you a taste of current non-string QG research that is totally different from what you seem to have picked up from the string-folks you have been talking to. You would find many of your impressions directly contradicted, I am confident.

 

When I have a free hour that I wish to fill with new physics, then I will listen to his talk. And one day when I no longer have several projects to work on I will try to actually read some LQG papers. Untill then, I would like to ask questions to people who know more about the field than I do, when I have ten or fifteen spare minutes to read answers and construct responses. I was under the impression that that was what this thread was.

[Martin]

When I have a free hour that I wish to fill with new physics, then I will listen to his talk...

 

Good! It's a promise! I realize how busy you must be (grad school)

 

In the meantime, for your convenience, I will tell you as concisely as I can what some of the HIGHLIGHTS of Reuter's talk were.

 

the headline is that in 1996 Reuter succeeded doing something Steven Weinberg thought up and tried to do in 1979, but failed. Weinberg knew it was the right thing to do and he managed to do it in a lower dimension toy version, but he lacked the tools to succeed in d = 4.

the idea is "asymptotic safety"

 

Weinberg observed (back in 1979) that gravity was perturb. NONrenormalizable. But he said suppose the RG (renorm. group) has a UV fixed point---or aka high energy or microscopic scale fixed point. Reuter calls it "non gaussian fixed point"

then instead of being screwed by nonrenormalizability and having to specify an infinite number of parameters, you only have to specify a FINITE number and the fixed point sucks you in as you let the momentum k run to infinity and that determines all the other parameters.

so you only have a finite number----like TWO---to worry about.

Great, this is sometimes called NONperturbative renormalizability. Or 'asymptotic safety'

It is SAFE to let k go to infinity because the fixed point keeps things under control and the RG trajectory just homes in on it.

Weinberg was able to show that in lower dimension case GRAVITY WAS NONPERTURB. RENORM'BLE, or in other words gravity was asymptotically safe.

 

In 1996 Reuter extended this to d=4, and quite a bit of the past 10 years have been spent with him and others checking that it was really right and deriving consequences. He now says beyond reasonable doubt. there is an infinite dimensional space of THEORIES, that is to say a space of ACTION FUNCTIONAL. he is only able to SLICE this space and project down onto a finite dimensional subspace of action functionals.

then on the subspace they can compute the flow trajectories. There they see an attractor or fixed point

 

The labor of checking involves repeated tests to make sure that this is not merely an artifact. That there really is the same fixed point up in the infinite dimensional space of the full theory.

 

I have been watching Reuter and reading his papers for about 3 years now and have been rather cautious. Now I am taking it as a serious possibility.

 

The consequences for cosmology are impressive. His trajectory shows how newton G and cosmo Lambda RUN which changing scale and offer possible explanation of inflation needing NO INFLATON and of acceleration needing no dark energy.

Also HE DOES NOT PUT EINST-HILBERT ACTION IN BY HAND. The renorm group flow takes care of that because the fixed point turns out to be a quantumcorrected version of the Einst Hilbert action. he also has some stuff on STRUCTURE FORMATION the spectrum of fluctuations visible in the map of the CMB.

 

So Reuter is on a roll at the moment. He has checked his main thing. Gravity is renormalizable after all. And he has a natural running of the two important parameters. And he is cranking up his PREDICTIONS.

 

that is a kind of thumbnail for you. the LOOPS 07 Reuter SLIDES is only 30 pages, and many of those just have one or two sentences. So any time anybody wants to scan the slides, it is quick and easy and you get another view of the highlights. It is listening to the audio which takes time---45 minutes or whatever.

 

Hope this helps

[abskebabs]

Martin, I was under the impression that Causal sets was separate to LQG. I was intrigued by the general idea, and will read up on it at some point at this website:http://www.einstein-online.info/en/spotlights/causal_sets/index.html

 

What is its relation to LQG though? I would guess background independence, but what else?

[Martin]

Martin, I was under the impression that Causal sets was separate to LQG. I was intrigued by the general idea, and will read up on it at some point at this website:http://www.einstein-online.info/en/spotlights/causal_sets/index.html

 

What is its relation to LQG though? I would guess background independence, but what else?

 

There is an awful semantic mess which I think is due mainly to OUTSIDERS who want to have a word that lumps together the research community that rivals string----these would be the 150 some people who took part in the recent Loops '07, more or less. Or who regularly participate in that kind of conference (not just a one-time visit)

 

Outsiders refer to it all mushed together as "LQG", but if you take a very strict definition only a small fraction work on canonical LQG as it was developed in the 1990s

 

the nonstring QG community (that is CALLED LQG) works on

Spinfoam

CDT (causal dynamical triangulations)

Causal Sets

GFT (group field theory)

Master Constraint and Algebraic Quantum Gravity (AQG)

Asymptotically Safe QG

a simplified LQG applied to cosmology (LQC)

 

Nobody consistently cuts it any special way. I hear you! You want to separate out Causal Sets! Well fine. It is different from the rest. But if you separate out causal sets then should you also separate out CDT?

 

In the end, out of verbal laziness people want a catchall term that includes ALL the viable approaches that people are actively work on and which in some sense "rival" stringy thinking.

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

 

To respond to your question---I rephrase it what is the relation of Causal Sets to all the other main approaches in non-string QG?

I do not know of any common element it shares with any of them besides, as you say, background independence.

Renate Loll, a leader in the CDT approach, has shown considerable interest. She had a workshop at Utrecht with a Causal Set group from the UK. She hired Joe Henson, a Causal Set guy, as a post doc. She SUPPORTS Causal Set work even tho her research is CDT. And I have seen some papers that attempt to find mappings between Causal Sets and some other approaches----to work out correspondences. So it is the kind of thing that interests people. But I know of nothing solid and memorable by way of a linkage.