During the last couple days, some interesting commentary on quantum gravity has appeared at a couple places on the web. One is at John Baez’s latest edition of his proto-blog This Week’s Finds in Mathematical Physics. John is mainly writing about operads, but he begins by saying a bit about why he’s working on pure math rather than quantum gravity these days:
Work on quantum gravity has seemed stagnant and stuck for the last couple of years, which is why I’ve been turning more towards pure math.
He mentions the “landscape” and the problems it is causing for string theory, suggesting a reason Susskind’s “anthropic” nonsense is getting attention:
perhaps it’s because nobody really knows how to get string theory to predict experimental results! Even after you chose a vacuum, you’d need to see how supersymmetry gets broken, and this remain quite obscure.
But instead of spending time bashing string theory, John admirably also has a critical take on his own side of the LQG/string theory controversy, noting that
it has major problems of its own: nobody knows how it can successfully mimic general relativity at large length scales, as it must to be realistic! Old-fashioned perturbative quantum gravity failed on this score because it wasn’t renormalizable. Loop quantum gravity may get around this somehow… but it’s about time to see exactly how.
Jacques Distler also has an interesting posting about quantum gravity, based on his introductory lecture to the string theory class he is teaching this semester. He explains what some of the generic problems with quantum gravity are, from an effective field theory/renormalization group point of view, and how string theory gets around them. There are also some interesting comments about observables in quantum gravity and the signficance in this context of non-trivial gauge transformations at infinity. Unfortunately, unlike John, Jacques doesn’t believe in being very explicit about the problems his side is having (to be fair, maybe that’s the topic of another lecture). He does mention background independence and refers to discussion elsewhere, where students could learn about the lack of a non-perturbative formulation of the theory. But his claim that string theory “provides a unique, or nearly unique UV completion” seems to me seriously misleading, and deserving of elaboration lest the uninitiated get the wrong idea.
Jacques does deal in a somewhat peculiar way with a commenter named Jason who is happy with the idea of a quantum gravity theory that can’t predict anything at all at the Planck scale. Instead of making the obvious point that believing in a theory that can’t predict anything is not what scientists do, Jacques writes
Careful, Jason. A certain self-anointed String Theory gadfly might hear you.
Perhaps Jacques meant to write “self-appointed”, since I’d never thought of myself as a “gadfly” until Sean Carroll recently referred to me as such. If I were the sort to self-anoint, I suppose I’d prefer something more serious sounding than “String Theory gadfly”, maybe “String Theorist’s worst nightmare”…..
This quote is also from John Baez’s TWF post:
“Math is (at least for me) a less nerve-racking pursuit, since the truths we find can be confirmed simply by discussing them: we don’t need to wait for experiment. Math is just as grand as physics, or more so. But it’s more wispy and ethereal, since it’s about pure pattern in general – not the particular magic patterns that became the world we see. So, the stakes are lower, but the odds are higher. ”
This seems like such a cop out! I mean, yes the stakes are high and the odds low when working with the fundamentals, but if the most qualified people don’t work on this — and it does desperately need to be worked on — who will? And what is tenure for if not working on risky endeavors? I do agree the math itself is beautiful, but it’s so much better and more important when it’s the universe’s math one is trying to figure out.
I guess this just emphasizes the fundamental dilemma with pure math from a physicists point of view, and the dance theoretical physicists and mathematicians do around one another. Quite often mathematicians wandering away from physically motivated math and into their own creations will make something up that is later found to apply to the physical world, but even more often it doesn’t. For mathematicians this is not a gamble at all, but for a physicist this is the biggest gamble there is.
Gadfly — heh, yah, you’re a gadfly the same way the kid who said the emperor had no clothes was a gadfly.
Hey Peter, I don’t know if I should ask you this via email, or in comments, or where, but do you know much about the geometry of BRST transformations? I figured you would and I wanted someone to talk with about it. Email would be my first choice.
-Garrett
First time I head (read) the word “gadfly”. So you bite. Well.
gadfly: n. a fly that bites horses and cattle
– Oxford paperback dictionary
Swedish: broms. Norvegian and west Swedish dialects: klaegg.
Dear Peter,
Thanks for this. It is good to lay out the strengths and weaknesses of all the approaches. It is true that the big challenge facing all background independent approaches is showing that the classical spacetime geometry is recovered in the low energy limit. But my own view is that John is too pessimistic. There have been for years results which show that LQG has semiclassical states, and that predictions, such as for the possible deformation of Lorentz invariance, can be gained by studying their excitations. (See summary and references in section 4.5 and 5.1 of hep-th/0408048.) So it is wrong to give the impression there are no results supporting the conjecture that the low energy limit of LQG is GR. And we should not forget the rigorous results that show that LQG and spin foam models are finite theories, so the question of the low energy limit is well posed, something not achieved in earlier theories.
Of course if the theory is right-and we never assume so-we must show more. We must show that the ground state is semiclassical, by solving the dynamics. This is a hard problem, analogous to showing that the ground state of water is a solid. But as this is the focus of attention there are beginning to be significant, non-trivial results on how classical spacetime can emerge from a background independent quantum theory. The best so far are not in LQG, they are the Ambjorn- Jurkiewiczcy-Loll results on CDT, hep-th/0404156. More is coming, I know of 3 papers in preparation by different authors that contain interesting new approaches or results on this problem. So stay tuned and (to John) don’t loose heart.
Having said this, I should also say that my own view is that it is not likely that LQG, CDT or anything else now on the table will simply be the right thing. I believe these are all models, necessary steps from which we learn how to do non-trivial calculations in background independent, diffeomorphism invariant quantum field theories. As we gain control over them we are beginning to use the new language and tools gained to address not only quantum gravity but the other big problems such as unification and quantum cosmology. The right theory will solve all of these. And I believe it will do so by featuring a genuine emergence of classical spacetime geometry from something more fundamental.
As for string theory being the unique UV completion, the claimed uniqueness requires imposing two physically unjustified assumptions, 1) that it makes sense to an arbitrarily high energy to separate the spacetime geometry into a fixed background and gravitons of arbitrarily high energy and 2) those graviton states transform under the ordinary Poincare transformations, no matter how high the energy. The first appears false in any consistent non-perturbative unification of gravity and quantum theory including CDT and LQG. The second is much less compelling since we learned that Poincare invariance may be deformed, as in deformed or doubly special relativity theories. These allow the relativity of inertial frames to be consistent with energy and/or momentum cutoffs. At least in 2+1 gravity coupled to matter, we know this is how the theory achieves consistency. And there are indications (far from proofs) that the same will be true in 3+1 when we get the low energy limit sorted out.
Of course, the best news is that AUGER and GLAST will in only a few years tell us the fate of Lorentz invariance. The need to firm up our predictcions before the experiments report is what keeps us working hard on these problems.
-Lee
Garrett,
John Baez is a very good mathematical physicist who knows a lot of physics, so I’ve been kind of sorry to see that recently he hasn’t been directly working on physics. It’s a loss for the field. But for most mathematicians, I think it’s a good thing if they learn some physics, but then instead of directly working on it, use what they have learned to come up with some new mathematics. What physics is really suffering from these days is a lack of needed new tools, and when mathematicians pursue good new mathematics, they often end up generating the kind of tools physicists need, even if that’s not what they were trying to do.
About BRST: I’ve been thinking a lot about this in recent years, but it’s a complicated subject and here’s not really the place to say much about it. From the Hamiltonian point of view, BRST is basically Lie algebra cohomology, but in a somewhat exotic “semi-infinite” context. From the Lagrangian point of view, it’s related to the whole Mathai-Quillen formalism for constructing Thom forms, explicit representatives of the Poincare-dual of a slice of the group action. In this context I suspect there’s more to the relation between the Hamiltonian and Lagrangian point of view than many people think. If you’re interested in talking about this stuff, we should do it by e-mail for now, although I should also write more about this here or in another form. I’m hoping once the semester gets started, I’ll finally have time for this sort of thing.
Lee,
Thanks for you comment, it’s very interesting and helpful. The contrast between the evangelism and refusal to acknowledge problems that characterizes many string theorists, and the much more straightforward and scientific attitude of the LQG community is really remarkable.
Distler wrote:
http://golem.ph.utexas.edu/~distler/blog/archives/000612.html#AdviceF1
Comments?
Arun.
I’ve always felt that ultimately a successful theory of quantum gravity has to also explain where the standard model comes from, partly for the reason Jacques explains, partly for the reason that I don’t see how a quantum gravity theory can ever be tested unless it also has something to say about particle physics (I’m less optimistic than Lee about finding tests of quantum gravity using experiments like AUGER and GLAST).
I don’t think Lee or other LQG people really disagree with this. If you look at his comment here, he is clear that he sees LQG and related approaches to quantum gravity not as a final theory, but as worth studying to get a better handle on background-independent theories, something that might then point the way to the right theory, one which would tell us about unification. Similarly, the more sensible among string theorists acknowledge that current ideas about getting unification out of string theory don’t work, but see further investigation of string theory and its relation to QFT as the most promising thing to think about that might lead to new ideas that do work.
Jacques is right to point to a basic problem that LQG must face up to, but he ignores even more serious basic problems that string theory unification faces. The fact that the vacuum energy is the order parameter for supersymmetry breaking is an even less subtle problem that one could say dooms any attempt to quantize gravity using any supersymmetric theory, including the superstring.
If you believe Jacques that his argument “dooms any attempt to study quantum gravity in a field-theoretic context”, so you should give up on field theory, you should also give up on string theory because of the vacuum energy argument (and a host of others….). But once you’ve given up on field theory and string theory, you may not have any ideas left to work on, which creates kind of a problem.
Lee,
Lubos Motl wrote a long comment to the same two opinion pieces by John Baez and Jacques Distler on his own blog. Would you dare to comment on Lubos’ remarks against LQG, especially the argument(s) that it cannot get the BH entropy right ?
Thank you,
Wolfgang
Hi Wolfgang,
Thanks for asking. It is always good to have critics and a few of the points Lubos mentions are correct. But not most. I ‘ll avoid the temptation to get into a point by point rebuttal and would just ask those interested to read the section on frequently asked questions in my review hep-th/0408048, which covers most of the points. On recent developments, he appears to mischaracterize Rovelli’s new paper, gr-qc/0508124, which is to my understanding significant progress. There is a lot in that paper and it also depends on a series of technical developments that directly address some of the issues Lubos raises, for example about observables, that Rovelli and his collaborators have carried out over the last few years. Rovelli et al impose a boundary to define a convenient set of observables, but this is not, as Lubos seems to think, the same as giving up background independence.
The situation with regard to black hole entropy, Immirzi, and quasi normal modes is still evolving and I don’t think Lubos’s characterization is correct. My own current understanding is contained in a new version we just posted of hep-th/0409056.
I agree that background independent quantum theories of gravity, including LQG, must address the problem of unification. We have some new ideas and results about this that I’m pretty excited about which will be announced at the Loops 05 conference.
-Lee
So, e.g., that 2+1 general relativity has been successfully quantized is a red herring (done without constraining the matter content of the 2+1 theory); success in a similar program in 3+1 general relativity without constraining the matter content of the 3+1 theory would simply yield another toy model with conceptual and technical insights that might apply to a physical theory? That is, a “quantum general relativity” may exist, but by the Georgi/Distler argument, cannot be a theory of physics?
Censored again. Ever tried holography, Woit. It is not science fiction, and believe me it does require string theory. Your book panning string theory has got the biggest denial of my entire life.
Gordon,
I deleted some of your comments because they didn’t make a lot of sense or add anything to the discussion here. Sorry, but doing this seems to be necessary to keep you and others from filling up this forum with off-topic or non-sensical stuff. If you don’t like the fact that this space is moderated, and want to be able to say whatever you want, get your own blog, it’s free and easy to set-up.
Before criticizing the book, you might want to first read it.
Unless you have comments that make sense and are on the topic of the posting, please don’t submit them, I’ll continue to delete them.
I don’t know much about deformed lorentz symmetries, diffeomorphi-la-shi-siscms, or ringing black holes (although I do have vague memories about some BRST ramblings).
Anyway. . . as a condensed matter theorist I do know about discrete topological objects, spin networks, verticies and edges, etc. I also know that it is impossible to get long-range-anything unless there are extra terms in the lagrangian/free energy. Meaning you have to add interactions or some background pressure or temperature fields. . .something. (I don’t need any theorems to tell me that, I know it’s true).
Now, I speak condensed mattereeze fluently but I’ve only taken quantum graviteeze 101. Nevertheless, I will attempt to translate.
You can have spin networks/foams and discrete topological objects all day long, but until you add interactions (whatever that means) or some other background stuff you will never have long range order.
Peter,
Quick factual correction: the vacuum energy is an order parameter for SUSY breaking only in globally SUSY theories (where this does not matter since it is not measurable). In supergravity this is no longer the case, as there are some positive and some negative contributions when SUSY is broken, and vacuum energy can be anything.
Peter,
If you click on my name you go into a disussion of the fifth dimension as being the spacetime fabric responsible for gravity:
http://eskesthai.blogspot.com/2005/08/fifth-dimension-is-spacetime-fabric.html
This looks like a more sensible approach than the usual ‘consistent theory of quantum gravity’ that ST is supposed to provide, since this approach unlike usual ST actually seems to predict things.
Nigel
Moshe,
The argument I gave was certainly over-simplified, you’re right that it’s only for global supersymmetry that supersymmetry breaking implies positive energy and you get a direct connection between the supersymmetry breaking scale and the vacuum energy.
But if you try and get around this by breaking supersymmetry using supergravity, it’s true that you no longer have the above argument, and the vacuum energy is not necessarily positive, but its scale is now typically the Planck energy, no? So, to get a small enough vacuum energy you have to fine-tune the theory for no good reason to one part in 10 to the 120th or whatever, right? Correct me if I’m wrong, I’ve spent a fair amount of time trying to understand models of supersymmetry breaking, but still find the subject very complicated with all sorts of possibilities. But from what I have understood of the subject, as far as I know no one has an idea for a supersymmetry breaking mechanism that gives a vacuum energy of anywhere near the right scale. As far as I can tell the reason this is so hard comes from the fact that, depending on how you break supersymmetry, the scale of the vacuum energy involves the supersymmetry breaking scale and/or the Planck scale.
Is there some known way to get an appropriately small energy scale when you spontaneously break supersymmetry in supergravity (i.e. without fine-tuning or anthropism)?
Peter,
The statement you had before, about having a positive CC in theories where SUSY is spontaneously broken, would have amounted to falsifying SUSY back in the days when the CC was thought to be exactly zero. Also troubling is the relation between SUSY breaking scale and the vaccuum energy. In any event, one has no choice but to think about things in SUGRA, the vacuum energy is not measurable otherwise (and also, of course, we do have gravity in our universe).
\
Sure, no good way of solving the CC problem dynamically is known, in SUGRA or otherwise, as I said the vacuum energy could be anything. If I knew how to answer this I would not post it as a comment on a blog…
\
In the context of SUGRA there is really no direct relation between the SUSY breaking scale and the vaccum energy. Also, none of the scales is Planckian- the SUGRA modifications to the vacuum energy are suppressed, not enhanced, by the Planck mass (so that one gets the right limit in the globally SUSY case).
\
In that context there is the old idea of no-scale models where you get zero CC as a consequence of some symmetry (till you break the no-scale structure, which you have to do…). These are typically the models one gets as the low energy limit of flux compactifications.
best,
Moshe
Hi Moshe,
I wasn’t trying to imply that the direct relation between vacuum energy and supersymmetry breaking in the global supersymmetry case falsified the idea of supersymmetry, that would be just about a mathematical theorem, and too easy. Of course you have to couple to gravity somehow, which makes the question much more complicated. But this still seems to me analogous to Jacques’s renormalization group argument: it’s not a rigorous no-go theorem, but shows that generically you’ve got a big problem of principle, one you have to find a way around somehow.
Thanks for your clarifications, but I’m still confused about some things. For any given supersymmetry breaking mechanism the vacuum energy should be computable in terms of the various energy scales in the problem, including ones we know about (Planck scale, weak scale…), as well as hypothetical ones for things like messenger particles and supersymmetry breaking in various sectors. Do you know of a good reference that explains how this works out in various possibly realistic scenarios? The papers I’ve looked at where people try and get implications for phenomenology out of various supersymmetry breaking scenarios seem to mostly ignore the vacuum energy problem.
Finally, I’d assumed that KKLT sort of scenarios led to vacuum energies generically at the Planck scale, just because of the often-heard argument that the existence of more than 10 to the 120th of these things implied that some were likely to have small enough vacuum energy. What does set the vacuum energy scale in these scenarios?
The CC is of course a “big problem of principle”, and there is always fine tuning involved. In the context of SUSY it is not immediately obvious the required fine tuning is allowed, but it is. Given that, I am not sure if SUSY makes the problem any better or worse.
\
In KKLT, or earlier SUGRA models, the CC comes as a difference of two positive definite quantities, each of which is of the order of the SUSY breaking scale (which is typically low in these scenarios). Most of the effort in these directions is to be really careful that EFT methods are justified, so among other things there are no Planckian energy densities involved.
\
For reviews you can look at Nilles’ famous one, and there is a physics reports on no-scale supergravity (both have over 500 citations, so they are easy to find).
Hi Moshe,
Thanks a lot for the references, that’s very helpful and I’ll take a look at them.
From what you say about KKLT and earlier SUGRA models, they give a vacuum energy of order the SUSY breaking scale unless you fine-tune, no? That’s what I’d very naively expect, if you’ve managed to avoid introducing Planck-scale effects. Granted it’s only in the SUSY/SUGRA context that the whole question of the vacuum energy is well-posed, but this has always seemed to me evidence that there’s something fundamentally wrong with the idea of SUGRA based unification, or, less negatively, it’s missing something very important.
Garrett writes:
>This quote is also from John Baez’s TWF post:
> “Math is (at least for me) a less nerve-racking pursuit, since
> the truths we find can be confirmed simply by discussing them:
> we don’t need to wait for experiment. Math is just as grand as
> physics, or more so. But it’s more wispy and ethereal, since it’s
> about pure pattern in general – not the particular magic
> patterns that became the world we see. So, the stakes
> are lower, but the odds are higher. �
>
>This seems like such a cop out! I mean, yes the stakes are high
>and the odds low when working with the fundamentals, but if the
>most qualified people don’t work on this — and it does
>desperately need to be worked on — who will?
It’s not clear that quantum gravity (or particle physics) “desperately needs to be worked on”. There are a lot of problems, like finding a vaccine for AIDS, that desperately need to be worked on. Quantum gravity and particle physics are different.
First of all, nobody is dying for lack of a solution to these problems. Secondly, these problems will only get *easier* as time passes. Right now our technology lags far behind our knowledge of physics. We are nowhere near making the kinds of machines our current knowledge of physics would let us build. If we let technology catch up for a few decades – or centuries – we’ll be in a better position to do experiments and make astrophysical observations that could give us some extra clues. Also, our understanding of mathematics will keep getting better, and it’s quite possible there’s some math we don’t know that’s holding us back.
Mind you, I’m *not* saying everyone should wait before working on quantum gravity. I dived in and worked on it for about 10 years, and other people should too – and other people will regardless of whether I think they should! But, there’s no need for anyone to work on this stuff who doesn’t want to.
So, I’ve decided that before I get too old I’d like work on some stuff that I’m *sure* will be good. In my work on quantum gravity I came up with some quite nice math, but most of this math will only be *really* exciting if the physical theories I was pondering turn out to be right, or at least a step in the right direction. Luckily, I also have the option of working on math that I’m *sure* is exciting, regardless of how things go in physics.
>And what is tenure for if not working on risky endeavors?
Tenure is for working on big projects that you wouldn’t dare start without having job security. This does not imply you have to pick projects that are unlikely to succeed.
> I do agree the math itself is beautiful, but it’s so much better
> and more important when it’s the universe’s math one is
> trying to figure out.
Certainly this is what physicists think, but I’m in a math department, and mathematicians are allowed to hold quite different opinions on this subject.
Mathematicians tend to feel that the most important math is math that would be important *regardless* of what the laws of physics turn out to be: fundamental stuff that applies all over the place. Certain patterns are so powerful that calling them merely “beautiful” drastically understates their importance. We haven’t found all of them yet – there are a lot staring us in the face that we’re just beginning to recognize – and tracking them down is incredibly exciting.
So, I don’t feel it’s a copout for someone to work on math instead of physics, as long as they’re good at it, they like it, and they try to tackle the biggest, most important problems they can.
In short: it may be less important to work on physics when there’s a high chance one is barking up the wrong tree and ones work will wind up in the dustbin of history, than to do math that’s clearly good.
This issue, of course, is part of what Peter’s blog is all about.
But, I understand the disappointed feelings you are expressing, because physics is a wonderful quest. It’s very hard to give it up, even in times like ours when it’s hard to tell if real progress is being made.
John, could you perhaps take a longer look at Tony Smith’s math? The patterns do not get more beautiful. There’s even still some physics.
First of all, nobody is dying for lack of a solution to these problems. Secondly, these problems will only get *easier* as time passes.
Now you mention it, it could be worth to point out that, actually, everyone is dying because time passes.
John Baez,
What things could possibly convince you to go back to quantum gravity research?
At this point the only major thing which could possibly convince me to ever go back to doing any quantum gravity research, is if somebody ever finds a way of getting around the anthropic/landscape stuff in string theory without making things any worse. From a quantum field theory perspective, it would be impressive if somebody ever found an easy way to get around the Sagnotti nonrenormalizable 2-loop result for “pure” quantum gravity, without resorting to any paradigms like strings and/or loops.
There’s no such thing as the anthropic/landscape principle. Since when G is interpreted as an anthropic argument in Newton’s Law of gravitation ?? Cause sure you can find an anthropic reasoning for about everything. It’s just like numerology, if you look for it you’ll find it everywhere.
If you fine tune your theory using so called parameters and you’re still able to make predictions that’s nothing of a short coming. Sure you won’t get the ultimate-theory-of-I-don’t-know-what, but you’ll do some physics.
JC: impressive if somebody ever found an easy way to get around the Sagnotti nonrenormalizable 2-loop result for “pure� quantum gravity, without resorting to any paradigms like strings and/or loops.
If you haven’t already seen it, you might be interested in some work of Martin Reuter and others. This is a recent paper with references going back.
http://www.arxiv.org/hep-th/0508202
This is an earlier paper
http://www.arxiv.org/hep-th/0112089
Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
Abstract: “We summarize recent evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the lines of Weinberg’s asymptotic safety scenario…”
John Baez: in short: it may be less important to work on physics when there’s a high chance one is barking up the wrong tree and ones work will wind up in the dustbin of history, than to do math that’s clearly good.
Historians might consider the image of a dustbin unfortunate because it makes them out to be Dumpster Divers. And others as well, including physicists, who learn from the successes and failures of the past. Maybe history is not exactly a dustbin.
Apparently it was Leon Trotsky who coined the cliché. I found this account in a NY Times review:
…mutinies in the army, land seizures in the countryside and intrigue and conspiracy in the cities. The Bolsheviks were the chief beneficiaries of the disorder, and in November armed Bolshevik detachments in St. Petersburg and Moscow dealt the tottering provisional Government its death blow. When the Mensheviks protested, a onetime Menshevik turned Bolshevik, Leon Trotsky, scornfully consigned his former comrades to ”the dustbin of history.”
http://www.nytimes.com/books/98/01/18/reviews/980118.18issermt.html
Aside from the bad press that history gets in John’s post, I see a lot of truth and little to object to. It’s great when people are free to work on what they are enthusiastic about and perceive as going forward. There are good reasons why a person who sees quantum gravity research as stalled and stagnant for the past couple of years should work on something else. I think that how one sees it must be to some extent a personal vision reflecting one’s individual point of view. In my case, I see the field as having been especially active since the May 2004 Marseille conference which John reported in
http://math.ucr.edu/home/baez/week206.html
and therefore as not at all stagnant.
Alejandro Rivero: Now you mention it, it could be worth to point out that, actually, everyone is dying because time passes.
It’s my understanding that neither quantum mechanics nor relativity possess a notion of “now”. I recall reading that Einstein made reference to this in a letter he wrote within a few months of his death: “For those of us who believe in physics, this separation between past, present, and future is only an illusion, although a persistent one.”
Carl
JC asked: What things could possibly convince you to go back to quantum gravity research?
Well, first of all I’d be unable to completely quit quantum gravity research even if I wanted to, because I have two grad students working on spin foam models: Derek Wise and Jeffrey Morton. But this is a good thing, because I don’t want to completely lose track of this field.
Among other things, we’re working on Freidel, Louapre, Barrett et al’s ideas on how to describe particles in 3d quantum gravity as “spin networks with loose ends” – a wonderful realization of Wheeler’s old dream of “matter without matter”. Spin networks with loose ends are also mathematically related to D-branes, especially in topological string theory. We want to clarify these ideas using n-categories, following the strategy outlined in last year’s quantum gravity seminar at UCR (see my website). Crudely, there’s a 2-category with:
particles as objects
spin networks going between particles as morphisms
spin foams going between spin networks as 2-morphisms
and this fact, when worked out in detail, gives a rather beautiful new picture of how matter, gravity and spacetime could fit together – at least in 3 spacetime dimensions! Building a realistic theory along these lines would be a lot harder, since many of the details use mathemagical features special to 3d spacetime.
But, to answer your question, what could get me working harder on quantum gravity is some evidence that we can find a mathematically elegant background-free quantum theory that can reduce to general relativity in a suitable limit. I see no reason why such a thing can’t be found if we drop the restriction on “mathematical elegance” – but I like things that use beautiful math.
This is precisely why I mentioned Carlo Rovelli’s new paper. Getting the two-point function for gravitons on Minkowski spacetime out of loop quantum gravity would be a marvelous bridge between the background-free approach and perturbative quantum gravity. Carlo does it in a rough-and-ready way: can we fill in the details? I’ll be in Marseille next February talking to him about this.
I just don’t want to burn myself out staying up all night struggling with these issues when I could be having fun doing cool math. If it works, it works. If it doesn’t, it doesn’t.
From a quantum field theory perspective, it would be impressive if somebody ever found an easy way to get around the Sagnotti nonrenormalizable 2-loop result for “pure� quantum gravity, without resorting to any paradigms like strings and/or loops.
Someone has pointed out the papers of Lauscher and Reuter, which are quite fascinating and fit together suggestively with the work of Ambjorn, Jurkiewicz and Loll. I urge you to check them out.
John Baez: Someone has pointed out the papers of Lauscher and Reuter, which are quite fascinating and fit together suggestively with the work of Ambjorn, Jurkiewicz and Loll. I urge you to check them out. That someone was I. Here are the links again:
http://www.arxiv.org/hep-th/0508202
http://www.arxiv.org/hep-th/0112089
Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
Abstract: “We summarize recent evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the lines of Weinberg’s asymptotic safety scenario…�
Ambjorn Jurkiewicz and Loll point out the connection of CDT results with Reuter’s QEG in their new survey paper
http://www.arxiv.org/hep-th/0509010
on the first paragraph of page 24, right before the conclusions.
the connection is that both QEG and CDT get a macroscopic 4D space with an approximately 2D fractal structure at very small scale. It is a striking convergence since the two approaches appear very different.
Another reason I find these results interesting is because it also works the other way around. If you start with 2D gravity you find that the fractal dimension of your lattice is actually 4. This is an old result of dynamical triangulation/lattice gravity.
Of course it is also true that in 4D gravity the action is concentrated on the 2D triangles.
What is perhaps interesting from this for the spin-foam guys is the idea that collapsing 4-simplices do not necessarily mean everything is wrong.
I am sorry to post twice in a row.
But I would just like to add that in Regge Quantum Gravity and other lattice gravity approaches (in the Euclidean sector) one finds two phases. In one the 4-simplices tend to collapse and in the other they do not (this is usually called the “well-defined” phase). Changing the coupling parameters gets you from one phase into the other.
If the phase-transition would be 2nd order, the problem of quantum gravity would have been solved 15 years ago.
Recently it has become clear that the phase structure of lattice gravity theories is quite complicated, but the CDT results are definitely encouraging.
IMO you should not worry about posting twice-in-a row Wolfgang. These are interesting things and if you have more to say I hope you will not always wait for others to reply!
Two interesting posts in a row by one person is certainly better than two posts in a row by two people that say nothing except it is OK to have two interesting posts in a row by one person.
>Work on quantum gravity has seemed stagnant and >stuck for the last couple of years, which is why I’ve >been turning more towards pure math.
Some pedantry.
Physics, unlike math, is an experimental science.
The probability of someone discovering the nature of quantum gravity by “pure thought” is on the order of someone guessing the “right” vacuum of the string landscape or all of the molecules in the room where I’m typing this comment ending up in a cubic centimetre in the corner.
Theoretical particle physics was at it’s most productive when there was a flood of new experimental data in need of explanation.
When there’s a similar flood of quantum gravity experiments, then we may have similar progress.
I’d put it the other way – we won’t know we’ve had progress until there is a flood of quantum gravity experiments.
“When there’s a similar flood of quantum gravity experiments, then we may have similar progress. ”
Well when Einstein discovered GR he was not driven by experiments. It is only when the theory was there that experiments could be proposed. Who would have think of measuring the difference in time flow in the gravity field before ?
I think that quantum gravity phenomenon are likely to be even more remote from our intuition. Maybe they are plenty of them we already know of but don’t reckognise as such. Einstein said something like “it’s the theory which tells what we can observe”.
Furthermore, trying to make quantum theory and GR compatible in some way is something someone ought to do, if only for “the honour of the human mind”.
> Well when Einstein discovered GR he was not driven by
> experiments.
An important input to GR was the equivalence principle, derived from empirical evidence.
In contrast, one important input to M-theory/string theory is supersymmetry and unfortunately there is no empirical evidence for it (yet). This may change with the LHC.
I assume that one or more important idea, based on empirical evidence, is needed to find a quantum theory of gravitation.
Maybe we have such evidence already and just do not understand how to turn it into a basic principle, but maybe we have to be more patient until somebody finds the missing clue.
Come on, now: Entertain us
This has gone on for too long.
Move on
Fabien: Furthermore, trying to make quantum theory and GR compatible in some way is something someone ought to do, if only for “the honour of the human mind�.
Hello Fabien! I have often enjoyed reading your excellent blog. An extra pleasure to have the opportunity both to read French and get some comments on conferences taking place in Paris from the local perspective.
I agree that upholding the honor of the human mind is a good aim. Have the highest admiration for those rare researchers whose work does this.
Peter has a link to Fabien’s blog at the righthand margin, so I wont paste it in here
Will try and come up with further entertaining material, preferably unrelated to quantum gravity, real soon. The semester has just started here and my first class (multi-variable calculus) met yesterday. That and other beginning of semester business has been keeping me pretty busy. Soon we’ll return to your regularly scheduled programming….
Yacine Says:
I’m NOT advocating string theroy, but I disagree, and this is why:
The common denominator in every case is that life only occurs almost exactly between whatever relevant spectrum of “coincidental” potential.
For example, and without assuming stuff about inflation and whatnot:
The Big Bang produced numerous principles and laws that have yet to be broken in spite of a lot of projections and theoretical speculation about the eventual and final fate of the usable energy of our expanding universe.
The inevitable heat death of the universe is one of the more obvious projections of an expanding “entropic” universe, but this conclusion doesn’t completely justify the fact that the extremely small positive value of the cosmological constant means the big bang actually resulted in a near perfect balance between runaway expansion and gravitational recollapse, which actually puts the universe about as far away from the tendency toward heat death as you can possibly get, and yet still be heading in that direction. The principle of least action says that it is no coincidence that this near-perfectly symmetrical configuration is also the most energy-efficient means for dissipating energy, because this means that tendency toward “heat-death” is most economically restricted to the most-even distribution of energy possible.
The universe actually expresses a grand scale natural preference toward the most economical form of energy dissipation, so if the second law of thermodynamics is telling us that the entropy of our expanding universe increases with every action, then the anthropic principle is telling us that this will occur by the most energy efficient means possible, since the flatness of the universe is one of the many coincidentally ecobalanced requirements of the principle.
If the second law of thermodynamics points the arrow of time in an expanding universe, then the anthropic principle determines that time is maximized.
The anthropic principle is relevant!
Hello John Baez,
Since Loll’s causal dynamic triangulation appears to have a well-behaved semi-classical limit, with non-trial predictions on the planck scale, shouldn’t that excite you to doing research in QG?
dan
dan: Hello John Baez,
Since Loll’s causal dynamic triangulation appears to have a well-behaved semi-classical limit, with non-trial predictions on the planck scale, shouldn’t that excite you to doing research in QG?
that is such a fascinating question it’s no fair not to open it up and let others besides JB answer
my guesses are that (1) mathematicians need to refurbish and revitalize their imagination by regular treks into pure math
if it is time for that it wouldnt matter what was going on with modeling spacetime dynamics
(2)I don’t think anyone has yet seen how to apply elegant high algebra and categories to Loll’s approach.
Loll’s picture of spacetime does not even have a uniform-at-all-scales DIMENSIONALITY. Indicators of what dimension you are in correspond to observables. When you are in that place and you want to know what dimension it is in your surroundings, you take a reading from some selfadjoint operator.
so there is no off-the-shelf differentiable manifold to build structure on.
probably there is a new category of object in the briarpatch
I’m just speculating irresponsibly. I think it might take a while before any categorist or algebraist “discovers” Loll CDT
a creative mathematician should never have to justify the motions of his imagination and curiosity
in http://arxiv.org/hep-th/0508202 it looks like you can get away with using a differentiable manifold if you allow it to have an infinite sequence of metrics, all describing the same system but at different scales or energies
quote Reuter et al:But since the quantum spacetime is characterized by the infinity of equations (1.1) with k = 0 to infinity, it can acquire very nonclassical and in particular fractal features.
I suppose there is a category of such manifolds equipped with infinite sequences of metrics.
well whether there is or not, Reuter gets similar results to Loll, like largescale 4D going down to near 2D at small scale. and maybe what Reuter is talking about is more amenable to elegant treatment.
Some comments, from the perspective of a (more-or-less) mathematician:
“Physics, unlike math, is an experimental science.”
No. Math is experimental, too (and always was). Especially since we have computers (labs of the mathematicians…).
“so there is no off-the-shelf differentiable manifold to build structure on.”
It would be *very* naive to expect that spacetime is anything remotely resembling to a manifold (of course it resembles, in large scales; but i’m not talking about that), or even that it is off-the-shelf. For starters, it “is” noncommutative (math speak for quantum :). And i like to think that spacetime is an emergent phenomenon, whatever it means.
If Loll’s spacetime does not have an uniform dimensionality, i look that as a promising sign…
the program for the Loops 05 conference, October 10-14,
has been posted
http://loops05.aei.mpg.de/
click on “programme” for a list of the talks
h said:
“No. Math is experimental, too (and always was). Especially since we have computers (labs of the mathematicians…).”
Well, computers are made of matters that follow quantum mechanics, so there is randomness and uncertainty, and there is a possibility the computer makes a mistake, like say in one out of every 10^17 instructions. It’s an extremely small possibility, but nethertheless computers are not 100% error-free, due to quantum mechanics.
We humen are made of quantum mechanical matters, too. And so we could make mistakes, too. And we make far more mistakes than a computer does. How do you avoid that? You build redundances. If several computers or several person come to the same output, it is very unlikely all simutaneously make the same mistake. But the possibility is still not zero.
Because of quantum mechanics, nothing is completely certain. Therefore, that renders mathematics an experimental science.
For example, Perelman proved the Poincare Hypothesis. But we do not know for certainty whether his proof is correct or not. So we invite a couple of experts to exam his proof. But the process is difficult and takes two years for a complete proof read of the paper. And there is always a chance that you made at least one mistake during two years, and draw the wrong conclusion. Several experts draw the wrong conclusion at the same time is more unlikely, but it is still something of none-zero possibility. So, proofs like Perelman are quantum mechanical: you can approach the classical limit of 100% certainty, but you can not reach 100% certainty.
And without 100% certainty, mathematics is rendered an empirical experimental science.
I must also point out that the odd of a large group of people make mistakes simutaneously is actually much higher than you would expect. Just look at the 2004 US election, or look at how people at various levels reacted in this labor day hurricane of 2005.
Quantoken
Perhaps related to Quantum Gravity are two relatively recent articles:
[1] ‘Wave acceleration of electrons in the Van Allen radiation belts by Richard B. Horne et al [http://www.nature.com/nature/journal/v437/n7056/abs/nature03939.html]
[2] ‘Observational Evidence for Extra Dimensions from Dark Matter’ by Bo Qin, Ue-Li Pen, Joseph Silk [http://xxxDOTarxivDOTorg/abs/astro-ph/0508572 ]
These articles led to the following question that Quantum Gravity and Superstring Theory strive to answer.
How would one recognize dark matter or dark energy if or when detected?
Clearly the torus [a folded doughnut] described in [1] by Richard Horne [et al] is a three dimensional unseen entity of non-optical electromagnetic energy generated by the Earth’s magnetic core. These radiation belts trap particles that apparently do not react with optical electromagnetic energy. Some sources state that the primary populations are protons for the inner belt and electrons for the outer belt. [http://farside.ph.utexas.edu/teaching/plasma/lectures/node22.html]
Joseph Silk [et al] refer to dark matter ‘betrayed by the gravitational tug’ [2] which does not seem to rule the possible association with electromagnetic fields, sequestered protons or electrons.
Could these two papers be related?
Are non-optical electromagnetic fields within the realm of dark energy?
Are ‘naked’ protons and electrons in the realm of dark matter?
TGD based interpretation of dark matter relies on dynamical hbar having a spectrum of values and various hierarchies predicted by TGD, in particullar the hierarchy of space-time sheets characterized by p-adic length scales.
The first guess was that dark matter represents a new quantum coherent phase of matter with large value of hbar. Even laser beams could represent Bose-Einstein condensate of dark photons which through decoherence transform to ordinary photons. Large hbar would not mean in perturbative context any change to classical predictions.
During the last year it has however become clear that entire hierarchy of (relatively/partially) dark matters accompanied by a hierarchy of electroweak and color physics is predicted. This hierarchy provides interpretation for the predicted classical long ranged weak and color fields in all length scales as correlates for corresponding scaled down fractal copies of standard model physics. Since the particles in question are very light and interact only via gravitation with ordinary matter, contradictions with experimental facts are avoided.
One could say that TGD Universe is like Mandelbrot fractal which has suffered inversion. Zooming is replaced by its inverse and reveals endlessly new worlds with scaled down particle mass spectra and scaled up Compton lengths.
Light dark matter is predicted to be a grey eminence even in nuclear and condensed matter physics. In particular, in the physics of living matter scaled down color interactions and electro-weak interactions with weak length scale of order atomic length scale or longer would explain among other things large parity breaking effects in living matter. Needless to say, this picture makes sense only in many-sheeted space-time.
Various aspects of this developing vision are discussed here (astrophysics), here (elementary particle level), here (nuclear physics), here (condensed matter), and here (general vision).
See also my blog page TGD diary at http://matpitka.blogspot.com.
Matti Pitkanen