## Saturday, January 29, 2005

### Troubled loop gravity

Update: I revised my research about the first undeleted comment below this article. Now I think that it was written by Paul Ginsparg, not Sheldon Glashow. The clichés "Dark Ages", "theologians" have the same explanation as before (the article by Ginsparg and Glashow) but the sentence "the competition is fierce because the stakes are so low" is a typical Ginsparg's phrase.

Lee Smolin has just sent an e-mail about the paper by Nicolai et al. to Jacques Distler and me. Recall that Nicolai, Peeters, and Zamaklar recently submitted the most meaningful article about loop quantum gravity (LQG) published since 1997, to say the least. They showed the ideas and techniques of LQG in detail, and they focused on the open problems that, so far, prevent LQG from becoming a serious candidate for a theory of anything - especially the infinitely ambiguous Hamiltonian constraint. Nicolai, Peeters, and Zamaklar have abruptly become the world's leading LQG experts. I've discussed their paper at

Well, it's not easy to write down a technical paper that would solve the problems mentioned by Nicolai et al., or at least downplay the importance of their arguments - especially because their arguments simply are correct and serious. It's easier to write a verbal e-mail, and here is one:

• Dear Jacques and Lubos,

Since you are posting dismissive comments on LQG based on Herman and friennd's review you might be interested in what we experts think. My message to them is below, comments welcome. As before, if you would like to post this, you have my permission.

Thanks,
Lee

L.M.: Note the bizarre formulation "we experts". Is this the kind of bold language that Mr. Lazaridis is impressed by? Lee's mail continues with a series of jokes (I did not edit lots of Lee's typos to keep his text authentic):

• ps You can criticize a theory, but please do not call us "true believers". Most of us have always been quite careful and precise in making claims for LQG. We have always made it clear there are open issues, always mentioning them in reviews and review talks. This is differnt from string theory where its hard to find a review or review talk giving a correct account of the precise state of open issues or a precise statement of the extent to which key conjectures are supported by present evidence. (I challenge you to find a published general review of string theory that gives a precise statement of what is known at the time of publication regarding the evidence for conjectures such as perturbative finiteness, or S-duality of does a careful job of parsing which versions of the AdS-CFT correspondence are supported by present evidence.)

L.M.: The review of AdS/CFT hep-th/9905111 has 260+ pages (and 1100+ citations). I am not sure whether 260 pages are enough for Lee. For other reviews of AdS/CFT, see hep-th/0009139, hep-th/9912164, hep-th/0209067, hep-th/0309246, hep-th/0310119 and others. For evidence on various versions of the AdS/CFT correspondence, see the 3333+ papers at Spires (citations of Maldacena). I hope that everyone understands that I can't list the whole literature about all topics of string theory - not even all the major papers that prove various points Lee mentioned.

• As you can check, there was no issue raised in the review that was not discussed and well understood in the field ten years ago. At the same time, they ignore most work done over the last 10 years which is motivated by the problemms they discuss. Imagine someone claims to write a pedagogical and general review of string theory and limits it to a technical discussion of the problem showing worldsheet perturbation theory is finite and consistent. You would call it unfair, even if you agreed it was accurate on that issue. That is roughly the situation their review presents us with.

L.M.: I don't exactly understand what's unfair about the fact that the stringy perturbative expansion is finite and consistent. A review of perturbative string theory that limits to a technical discussion of stringy perturbative expansions looks completely fair to me - is not it a tautology? A more up-to-date review should also discuss nonperturbative physics. Well, I am sure that the people who prefer weird philosophical speculations that contradict our knowledge about physics won't be satisfied with a technical review, but this fact certainly does not make such a review less meaningful.

Perhaps, Lee did not mean a real review but rather a non-technical article that would claim that something may be wrong with string theory, without doing any meaningful calculations. OK, I would not call this a "review" - perhaps a silliness.

Lee's statement that Nicolai et al. neglect the LQG literature in the last 10 years is simply not true as everyone can easily check; let's avoid stronger words. Finally, let me use Lee's permission and post his letter to Nicolai et al. A version of this mail without my comments is available on Peter Woit's blog.

Smolin writes to Nicolai et al.

Dear Friends,

Thanks very much for all the time and work you put into your review. While I disagree with a number of your assertions, both in point of detail and of attitude, what is certainly very much appreciated is your evident willingness to "get your hands dirty," learn the technicalities and attack key problems. It is very good that you do this, as indeed too few of us loop people have taken the time to try to learn the details and attack problems in string theory.

L.M.: Well, Lee is definitely right that no one in LQG has learned string theory at the technical level. An open question is whether this is possible, at least in principle.

Some points you raise have been underappreciated. The issue of what happens to the chiral anomaly, and whether there is fermion doubling in LQG is one I have suggested to many graduate students and postdocs over the years, but so far no one takes it up. It would be good to know if LQG forces us to believe in a vector model of weak interactions.

L.M.: This formulation is really cute. On one hand, Lee does not want others to call him a true LQG believer. On the other hand, he's ready to let LQG "force him to believe a vector model of weak interactions" - as opposed to the V-A model (left-handed chiral couplings) incorporated in the Standard Model. A vector, non-chiral model of the weak interactions has been falsified for 50 years or so, and the thinking of a person who could be "forced to believe it" - by a set of tools that have absolutely no justification whatsoever - is not a scientific one.

At the same time, the major difficulties you raise were underestood to be there more than ten years ago. This is especially true with respect to issues concerning the hamiltonian constraint such as the algebra and ultralocality.

What is missing from your "review" is an appreciation of how the work doneover the last ten years addresses these difficulties. Indeed the fact that much work in the field has been on spin foam models is exactly because the problems you worry about do not arise in spin foam models. I will explain this below. Other work, such as Thiemann's master constraint approach, also is motivated by a possible resolution of these problems.

L.M.: Note that Lee's answer is getting tougher right now, as the quotation marks around the word "review" help to show. Lee wants Nicolai et al. to appreciate something that does not really exist. Incidentally, Nicolai et al. noticed that some LQG people have partially abandoned the canonical LQG and jumped at the spin foam models - whose equivalence to the old picture is very unclear. The spin foam models don't solve the problems with the infinite ambiguities either, as Nicolai et al. explain in one of their sections.

As you will appreciate, like any active community of 100+ people there is a range of opinions about the key unsolved problems. I have the sense that you are aware of only one out of several influencial points of view.

The view your concerns reflect is what one might call the "orthodox hamiltonian" point of view towards LQG. According to this, the aim of work in lqg is not so much to find the quantum theory of gravity as to work through the excercise of quantizing a particular classical theory, which is Einstein's. From this point of view, the program would fail if it turned out that there was not a consistent canonical quantization of the Einstein's equations.

While I will refer to my own views so as not to implicate anyone else, you should beware that this is not necessarily the dominant view in the field. It is a respectable view, and I have the greatest respect for my friends who hold it. But, were it to fail, many of us would still believe that loop quantum gravity is the most promising approach to quantum gravity.

L.M.: Even if the Ashtekar program fails, we will think that LQG is the most promising approach - but you should not call us "true believers". ;-) Weird.

This is not avoidence of hard problems, there are good physical reasons for this assertion, which I'd like to explain.

What I and others have taken as most important about Ashtekar's great advance is the discovery that GR can be writen as a diffeomorphism invariant gauge theory, where the configuration space is that of a connection on a manifold Sigma, mod gauge transformations and Diff(Sigma). This turns out to be true not only of Einstein's theory in 4d but of all the classical gravity theory we know, in all dimentions, including supergravity, up to d=11, and coupled to a variety of matter fields.

L.M.: Note that the subsequent research could not find a single piece of evidence for Lee's speculations that gravity can be written in this way. Also note that "Ashtekar's advance" is equivalent to the ideas that were assumed to be failed in the first place. If there is no Hamiltonian realization of Ashtekar's picture, there won't be any other realization either.

This is a kinematical observation and it leads to a hypothesis at the kinematical level, which is that the quantum theory of gravity, whatever it is, is to be written in terms of states which come from the quantization of this configuration space.

L.M.: I find these sentences entertainingly self-contradictory. How can someone say "Whatever quantum gravity is, it must be this particular naive 19th century model"? The probability that the correct theory of quantum gravity is exactly what Lee says is something like 10^{-1700}. The belief in this kind of model is nothing more than a random guess.

This as you know, leads directly to the diffeo classes of spin net states. Furthermore, given the recent uniqueness theorems, that hilbert space is unique for spacetime dimension 3 or greater.

L.M.: Well, all infinite-dimensional separable Hilbert spaces are isomorphic. But that's far from creating a physical theory which must also have a unique or almost unique Hamiltonian or another observable that describes its dynamics.

Thus, o long as the object is to construct a theory based on diffeomorphism invariant states, it cannot be avoided.

L.M.: This is such an obviously incorrect statement that I'm not sure whether Lee really believes it, or he just believes that others will believe him. If one looks at all the different descriptions of various vacua in string theory, all of them prove that Lee's point is wrong - and there are many different types of loopholes that make Lee's conclusion extremely easy to avoid.

The main physical hypothesis of LQG is not that the quantum Einstein equations describe nature. It is that the hilbert space of diffeo classes of spin nets, extended as needed for matter, p-form fields, supersymmetry etc, is the correct arena for quantum gravitational physics. Given that the theorems show that this hilbert space exists rigorously, this is a well defined hypothesis about physics. It may hold whether or not the Einstein equations quantized give the correct dynamics.

L.M.: Right, that's one of the ways how to formulate the "big" hypothesis of LQG. A subtlety is that every time such a hypothesis becomes a little bit more concrete, one can falsify it in a few minutes.

A lot already follows from this hypothesis. It gives us states, discreteness of some geometric diffeo invariant observers, a physical interpretation in terms of discrete quantum geometry etc.

L.M.: Well, yes, a lot of contradictions with physics of our Universe - such as the Lorentz symmetry breaking of order one - already follows from that "innocent" assumption.

But there is also a lot of freedom. We are free to pick the dimension, topology, and algebra whose reps and intertwiners label the spin networks. This then gives us a large class of diffeo invariant quantum gauge theories, of which the choices that come from GR in d=4 are only one example. These are possible kinematics for consistent background independent quantum field theories.

L.M.: Lee obviously seems to think that the more freedom a theory gives him, the better.

Now let us come to dynamics. I believe the most important observation for an understanding of quantum dyannics in this class of theories is that all gravitational theories we know, in all dimensions, super or not, are constrained topological field theories.

L.M.: One can hardly ever get a theory with local degrees of freedom from a theory without local degrees of freedom. Even if something like that were possible for a mysterious reason, extraordinary claims require extraordinary evidence.

(See my latest review, hep-th/0408048, for details and references for all assertions here.)

L.M.: You can also see most of the assertions on my blog; the existence of written assertions itself does not make the statements serious.

This means they are related to BF theories by non-derivative constraints, quadratic in the B fields.

A lot follows from this very general observation. It allows a direct construction of spin foam models, by imposing the quadratic constraints in the measure of the path integral for BF theory. This was the path pioneered by Barrett and Crane. The construction of the Barrett Crane and other spin foam models does not depend on the existence of a well defined hamiltonian constraint.

L.M.: Well, so if this is true, then it proves that the Hamiltonian LQG is not equivalent to the spin foams.

The properties that have been proven for it, such as certain convergence results, also do not depend on any dynamical results from the hamiltonian theory.

The relation to topological field theory is also sufficient to determinethe basic form of fields and states on boundaries. In 4d these give the role of Chern-Simons theory in horizon and other boundary states. Thus, it gives the basic quantum geometry of horizons.

L.M.: That's an uncontrollable approach to ideas. A black hole is a finite energy object in spacetime, and a quantum theory of gravity must describe it as a generic state. Inventing a new kind of explanation and dynamics for the horizons is unjustified. Note that the main idea of LQG is to construct space from "atoms" and "links". Black hole is another example of "space", and already for the black holes, the original "atoms" and "links" are not enough. So one invents a new type of physics for the horizons, and argues that there is the Immirzi parameter that solves the discrepancies. All the predictions of the Immirzi parameter are falsified by explicit calculations, but it does not matter.

Once we have the basic form of spin foam models, which follow from the general relation to BF theories, we can consider the problem of dyanmics in the following light. Given the choices made above, the spin foam amplitudes are chosen from the invariants of the algebra which labels the spin networks. There is then a large class of theories, differing by the choice of the spin foam amplitudes. Each is a well defined spin foam model, which gives amplitudes to propgate the spin network states based onthe chosen dimension and algebra.

L.M.: Well, this is exactly why Nicolai et al. say that the spin foam models in their current form are not a well-defined theory. If the amplitude of any basic process is undetermined and there is an infinite amount of such unknown but relevant things, then we know nothing. Moreover, it seems obvious that the infinite ambiguity is not just a temporary state of affairs but a very basic defining feature of LQG.

The lack of uniqueness is unaviodable, because there is a general class of theories, just like there is a general class of lattice gauge theories.

L.M.: That's a completely wrong comparison - pure gauge theories have no dimensionless parameters at all if they're asymptotically free. The main problem is not a couple of discrete choices - such as the spacetime dimension. The main problem is the ambiguity of the details of the Hamiltonian - or the amplitudes of the microscopic spin foam processes. I am afraid that Lee is not interested in these "details".

These theories exist, and the general program of LQG as some of us understand it, is to study them.

L.M.: Lee obviously uses the words "theory" and "exist" with a different meaning than the rest of us. If a system of ideas can't predict quantitative results after a finite number of measurements, then it does not exist as a physical theory. A non-physicist can construct a class of theories in which anything can happen in the Universe, depending on God's decisions. Does it mean that he has found a real physical theory?

From a modern, renormalization group point of view, the first phsyical question to be answered is which of these theories lead to evolution that is sensible, i.e. which spin foam ampltidues are convergent in some approrpiate sense. The second physical question is to classify the universality classes of the spin foam models and, having done this, learn which classes of theories have a good low energy behaivor that reproduces classical GR and QFT.

L.M.: The religious person can say the same things. From a modern, genetic point of view, the first physical question is which God's decision lead to finite answers. The second question is to classify the universality classes of God's decisions and, having done this, learn which classes of God's decisions reproduce the fossils that the evolutionary heretics have claimed to diminish the importance of creation. ... Well, one can always say these words and define some questions, but it does not mean that they're good questions. This is a point that Lee does not want to understand - that a whole idea or approach is identified as less valuable if it leads to no explanations of known facts and relations between them and no predictions. For Lee, the discrete structure is a dogma, and independently of the number of decades in which the research shows that it is a weak idea, it must be studied.

It is of course of interest to ask whether some of these theories follow from quantizing classical theories like GR and supergravity, by various methods. But no one should mind if the most successful spin foam model, in terms of both matheamtical elegance and physical results, was not the quantization of a classical theory, but only reproduced the classical theory in the low energy limit. How could one object from a physics point of view, were this true?

L.M.: The reason why this question is meaningless in reality is that there are no successful spin foam models, and most likely, there never will be any.

This is the point of view from which many of us view the problems with the hamiltonian constraint you describe.

The next thing to be emphasized is that there is no evidence that a successful spin foam model must have a corresponding quantum hamiltonain constraint. There are even arguments that it should not. These have not pursuaded everyone in the community, and this is proper, for the healthiest situation is to have differing views about open problems. But it has persuaded many of us, which is why many people in the field turned to the study of spin foam models after the difficulties you describe were understood, more than ten years ago.

L.M.: I wonder why they think that they have a "theory". What they have and can agree about is the religious - and most likely, falsified - assumption that the spacetime looks like some kind of LEGO. The situation of every other, more detailed question is fuzzy. No question can be ever answered if physics is approached in this way - and it is probably not even their goal to answer a question. Moreover, it is not the LQG people, but Democritus (and Maxwell who designed aether and FitzGerald who constructed an actual model) who should be credited for these (wrong) ideas.

For example, Fotini Markopoulou argued that, as the generators of infinitesimal spatial diffeos do not exist in the kinematnical hilbert space, while generators of finte spatial diffeos do exist, the same should be true for time evolution. This implies that there should only be amplitudes for finite evolutions, from which she proposed one could construct causal spin foam models.

L.M.: The fact that the geometrical operations cannot be written in terms of generators is another manifestation of the non-separability of the Hilbert space and ultralocality of any rules that one can construct within the framework. At any rate, it is a sign of an inconsistency. In every working and consistent theory, the generators G of some operation can simply be written as the limit for epsilon going to zero of (T(epsilon)-1)/epsilon where T(epsilon) is the finite transformation by epsilon. If one can't do these things, something is definitely not working with the math.

This was partly motivated by the issue ultralocality. (Btw, you dont emphasize the paper that first raised this worry, which was my gr-qc/9609034). The worry arises because moves such as 2 to 2 moves necessary for propagation do not occur in the forms of the hamiltonian constraint constructed by Thiemann, Rovelli and myself, or Borissov. This is because they involve two nodes connected by a finite edge.

However, the missing moves are there in spin foam models. This concretely confirms Fotini's argument. In fact, as Reisenberger and Rovelli argued, invariance under boosts generated by spacetime diffeo requires that they be there. For one can turn a 1-3 move into a 2->2 (0r 1->4 into 2-> 3) move by slicing the spin foam differently into a sequance of spin networks evolving in time.

L.M.: Well, yes, this is the first part of a proof that one can't ever obtain a Lorentz-invariant (or approximately Lorentz-invariant) theory in this framework. Obviously, our friends are never patient or brave enough to finish the proof.

So we have two arguments that suggest 1) that the problem of ultralocaity comes from requiring infinitesimal timelike diffeos to exist in a theory where infinitesimal spacelike diffeos do not exist and 2) the problem is not present in a path integral approach where there are only amplitudes for finite timelike diffeos.

L.M.: The Lorentz violation has nothing to do with using the Hamiltonian or the path-integral formalism. The existence of a symmetry is a completely physical question, and of course that the spin foams violate the Lorentz symmetry as much as the spin networks with a Hamiltonian.

One can further argue that if there were a regularization of the hamiltonian constraint that produced the amplitudes necesary for propagation and agreed with the spin foam ampltidues, it would have to be derived from a point splitting in time as well as space. This suggests that there is a physical inadquancy of defining dynamics through the hamiltonian constraint, in a formalism where one can regulate only inspace and not in time.

Let me also add that there is good reason to think that the other issues such as the algebra of constraints arise because of the issue of ultralocality. Thiemann's constraints have the right algebra for an ultralocal theory.

It was for these and other reasons that some of us decided ten years ago to put the problems of the hamiltonian constraint to one side and concentrate on spin foam models. That is, we take the canonical methods as having been good enough to give us a kinematical frameowrk for a large class of diffeo invariant gauge theories, but unnecessary and perhaps insufficient for studying dynamics.

L.M.: The scientists should not use these vague words. It's not just that the spin network Hilbert space is insufficient: it's that a description based on it is guaranteed to be wrong. But the LQG practitioners usually do not like to make clear statements. The more vague the picture is, the more one can jump in between different inconsistent statements and avoid the fact that these models - and the basic dogma that underlies them - have been falsified.

At the very least, making a point splitting regularization in both space and time seems a much more difficult problem and hence is less attractive than spin foam methods where one can much more easily get to the physics. Given that the relation to BF theory gives us an independent way to define the dynamics, and path integral methods are more directly connected to many physical questions we want to investigate, there seemed no reason to hold back progress on the chance that the problems of the hamiltonian constraint can be cleanly resolved.

Nothing I've said here means that I am not highly supportive of Thomas's and others efforts to resolve the problems of the hamiltonian dynamics-I am. But it must be said that a "review" of LQG that focues on this issue misses the significance of much of the work done the last ten years.

L.M.: It's easy to miss something if this something is almost equal to zero.

Let me make an analogy. No one has proved perturbative finiteneess of superstring theory past genus two. I could, and have even been tempted to, write a review of the problem, highlighting the heroic work of a few people like d'Hoker and Phong to resolve it.

L.M.: The difference is that there exist hundreds of reasons to think that an inconsistency that would suddenly appear at 3 loops in the superstring expansion is a highly unlikely thing. The integrals over the moduli spaces are free of UV divergences in the bosonic string, and we can prove that the IR divergences disappear in the superstring. Then there are lots of formalisms - Green-Schwarz light-cone gauge string and its non-perturbative completion, namely matrix string theory; Berkovits' pure spinor formalism - that make it pretty insane to believe that something could go wrong. The proof of consistency is almost complete.

Update: Well, Hiroši Ooguri has kindly pointed out that I should remove the doubts about Berkovits' proof in hep-th/0410079. Hiroši believes that Nathan's proof is complete and simple enough to be understood. The only reason why I did not make a clear statement is my limited ability: I have not been able to understand why Nathan's pure spinor prescription is unitary, or equivalently why its results are equivalent to the RNS prescription. It's the composite character of the "b" ghost that is conceptually difficult for me - but most likely, it's just because I am slower. Hiroši also refers to another proof of perturbative finiteness by Mandelstam that combined the virtues of the RNS and GS formalisms, and argues that Nathan's proof is more straightforward.

On the other hand, Nicolai et al. and others have an almost complete proof that the things can't work in LQG. Of course, if someone thinks that an arbitrarily small uncertainty about anything implies that all bad ideas are equally good as all good ideas, it's hard to explain him that his belief is not rational. In string theory, all the quantitative consistency checks etc. always work. In LQG, they never work, and it makes a difference.

Well, someone can be tempted to write a review claiming that the higher-order superstring amplitudes probably don't work - but only a person who does not care whether others think of him as a good or less-than-good physicist could submit such a review simply because there exist no arguments whatsoever that the expansion should suddenly break down.

I think it would be useful if someone did that, as their work is underappreciated.

L.M.: Well, the "experts" don't share Lee's opinion. It's an interesting piece of math, but it's certainly not one of the most interesting current tasks for string theory. Everyone knows what the answer is, the main answer has been obtained using other means, and most of us are not terribly interested in completely rigorous proofs. We're more interested in big physics questions, not some particular minor tasks associated with a specific formalism, a formalism that does not have to be the most appropriate one to attack a problem.

But it would be very unfair of me to call this a review of, or introduction to, the state of string theory.

L.M.: I don't think it would be unfair; it would be just silly. If someone writes a paper in which he claims that he believes that at 3 loops, stringy perturbative expansion suddenly breaks down because of some mysterious, unspecific, undescribed new effect, he has the full right to express this opinion. But the rest of us have the right to decide whether we think that the author of such a paper is intelligent, and Ginsparg has the right to reject every submission.

Were I to do so, I would rightly be criticized as focusing on a very hard problem that most people in the field have for many years felt was not crucial for the development of the theory. This is not a perfect analogy to what you have done in your "review", but it is pretty close.

L.M.: It is not close because Nicolai et al. show very explicit things that are going wrong if one actually tries to calculate; what Lee is saying is just a promotion of a highly unlikely, unjustified, non-quantitative, and wild hypothesis whose only goal is to support a bizarre piece of ideology.

There are other mis-statments in your review. For example, there are certainly results at the semiclassical level. Otherwise there could not be a lively literature and debate about predictions stemming from LQG for real experiments.

L.M.: Well, it's easy to falsify Lee's "logical" conclusion just by looking at reality. There exist speculative papers that talk about the experimental predictions of "the theory" even though there is no well-defined theory. The reason why this is possible is simply that a piece of paper or hard disk can tolerate anything. ;-)

See my recent hep-th/0501091 for an introduction and references. Of course semiclassical states do not necessarily fit into a rigorous framework-after all, WKB states are typically not normalizable. But I would suggest that it may be too much to require that results in QFT that make experimental predictions be first discovered through rigorous methods. At the standards of particle physics levels of rigor, there are semiclassical results, and these do lead to nontrivial predictions for near term experiments. It is possible that a more rigorouos treatment will in time lead to a rigorous understanding of how classical dynamics emerges-and that is a very important problem. But given that AUGER and GLAST may report within two years, may I suggest that it is reasonable to do what we can do now to draw predictions from the theory.

In closing let me emphasize again that your efforts are very well appreciated. I hope this is the beginning of a dialogue, and that you will be interested to explore other aspects of LQG not covered by or addressed in your review.

Sincerely yours,
Lee Smolin

1. This comment has been removed by a blog administrator.

2. This comment has been removed by a blog administrator.

3. Q: Why are superstring / loop quantum gravity debates so fierce and bitter?

A: Because the stakes are so low.

Without Nature as the final experimental arbiter,
these debates are purely metaphysical - no different than the theological debates of the Dark Ages.

No amount of hysterics and histrionics on the part of the competing proponents will change this reality - physics an experimental science.

4. Dear Shelly,

note that your comment has not been deleted - unlike the comments of your friends above - because the owner of this blog recognizes not only your great contributions to physics, but also your entertainment skills, your originality between the critics of string theory, and your Nobel prize. ;-)

All the best
Lubos

5. LS - In closing let me emphasize again that your efforts are very well appreciated.Now this has got to be the dumbest thing Smolin wrote, or is it? Why would anyone appreciate a rabid dog? Maybe because everytime Lubos writes a commentary like this, more physicists start wondering if all string theorists are fanatical theologians rather than scientists.

6. Hi Lubos

Why don't you give your view of current and important open problems in string theory? Isn't there any place where string theory might go wrong, even if the probibility seems so low to you. Otherwise you seem to be subjective. Also it might help beginners like me to appreciate what is the difference between the seriousness level of problems in two areas.

Thank you again

7. This comment has been removed by a blog administrator.

8. Dear Serkan, thanks for pointing out your blog, it looks interesting! I will try not to forget and include a link to yours soon.

Meanwhile, there have been a couple of comments that I erased. Their goal was either to convert the discussions to personal ones, or to promote their authors' web sites - sort of by redirecting the traffic - which is a type of commenting that I discourage, of course. ;-)

9. Hi Lubos, I was the one asking in the comments thread of this post about whether the laws of physics would work differently in different reference frames (different slicings of the spin foam) according to LQG...in my last comment there, I quoted an email from Lee Smolin where he addressed this same question:

The rules that attribute to each spin foam history an amplitude are independent of how they are sliced.  They are of the form of a product of amplitudes, one for each elementary event or unit of four volume. Thus, the product is independent of, and in fact does not refer to, a slicing of the quantum spacetime history into space and time.Furthermore, detailed rules have been found, I'd be curious where that piece of disnformation comes from. [This was in reference to a comment I made that I was under the impression no detailed rules for the dynamics of spin networks were known] There are several explicit propoosals which have been studied in a lot of detail. The best studied is called the Barrett-Crane model. Its rules are explicitly lorentz invariant.  It has also benn proved analytically and checked numerically that the resulting amplitudes are ultraviolet finite.Are you claiming these statements of Lee Smolin's are wrong, or did you just mean something different when you said LQG breaks Lorentz invariance? Have you studied the Barrett-Crane model mentioned above, for example?

10. Hi Lubos,
how do you know that the anonymous comment you did not delete was from Sheldon Glashow? If you are right and it is really him, I agree: No matter what he says it should be kept. I disagree with Prof. Glashow's view of string theory as much as anyone, but he does deserve the respect of being listened to. If he is wrong, as I think, he will pay the price for that by being remembered as a brilliant genius who turned into a stubborn old man. Anyway, it's remarkable that you can attract people like him to your blog.
Best wishes,
Dan

PS: I accidentally left this remark under the alien story first. Sorry.

11. Dear Dan,

of course that I am honored if Sheldon Glashow reads my blog - even if he writes something about me that is less than flattering! :-) Finally, he would not be the only Nobel prize winner who reads this blog.

Why do I think it is Sheldon Glashow? It's a rather detailed analysis of the language:

First of all, the "theologians" in "Dark Ages" is precisely what they used against string theory 10 years ago (with Ginsparg):

http://www.frontlineonnet.com/fl1801/18011020.htmSecond, the sentence "physics is an experimental science" is an exact quote that Shelly Glashow also used on various occassions, for example in "The Elegant Universe" on PBS.

Third, you may say that someone is just immitating Glashow, but there are good reasons to think that exactly now, the probability of a Glashow visit is large, given my comments about their recent exchange with Cumrun Vafa. I believe that the immitators would not calculate this increased probability into their plans because the immitators are usually not too smart.

Finally, Glashow was born on December 5th, much like Heisenberg and me ;-) (Mozart died on that day), so this may increase my understanding where he's coming from. You know, in some sense I completely agree with Glashow's straightforward viewpoint about physics - he just makes wrong conclusions about the physics beyond the Standard Model. But he can afford it because as a co-author of the Standard Model, he's safe. He's permanently safe. ;-)

Dan, incidentally, I believe that Prof. Glashow has always been stubborn and was going directly to the big goal, and this is a great part of his success.

Did I get it right, Prof. Glashow?

All the best
Luboš

12. Dear JesseM,

the quote of Smolin is almost exactly what I was saying - the amplitude associated with a given history - spin foam - does not depend on any slicing you might imagine. This is why no one can argue that if I slice it differently, I should be using a different spin foam, or anything like that.

Then my argument follows. You take a typical spin foam that you believe to contribute to the path integral in spacetime that looks like the Minkowski space. You slice the history along the hyperplanes of a highly boosted observer, and you will find out that she can't see the right Lorentz contraction simply because there is still a lot of intersections of the hyperplane with the spinfoam, which keeps the areas large and does not contract them by the usual Lorentz factor.

This implies that the violation of the Lorentz invariance is always of order 100% - a complete violation that is falsified experimentally. I continue to argue that it is not hard to decide whether a theory as simple as this one can lead to an approximate Lorentz symmetry, and the answer is no.

When Lee says that the Barrett-Crane models are Lorentz invariant, I think that he mixes the Lorentz symmetry and Lorentz signature. One can try to define the model in the spacetime that is supposed to be the real spacetime - without analytical continuation to the Euclidean spacetime.

http://arxiv.org/abs/gr-qc/9904025

This is what we mean by a Lorentzian formulation. But the Lorentz symmetry is an entirely different issue. If you look at the end of the Barrett-Crane paper, they recognize that the non-compactness of the Lorentz group gives them an infinity, and they try to "regularize" this problem by a quantum deformation of the Lorentz group. This divergence - coming from the fact that the unitary representations of the Lorentz group are infinite-dimensional - is kind of equivalent to my argument. This histories are only Lorentz-invariant if they're singular.

These problems have led Crane and many others to propose piles of new loop quantum gravities - for example one in which the areas are continuous and the length is discrete:

http://arxiv.org/abs/gr-qc/0301017

The fact that several unwanted types of divergences don't disappear in the Barrett-Crane model and the resulting path integral - large j limit of the Riemannian 10j symbols - can't reproduce semiclassical gravity was shown by Baez, Christensen, and Egan:

http://arxiv.org/abs/gr-qc/0208010

A similar problem of the model was found by Freidel and Louapre:

http://arxiv.org/abs/hep-th/0209134

It's just clear on general grounds that these things can never work and lead to a meaningful theory, but those people will never give up - it's a religion. They will always say that they can still try to modify something else, and so on.

Best
Luboš

13. Lubos, if you believe it can be proved rigorously that no version of LQG could possibly respect Lorentz-invariance, have you considered writing this up in a short paper? That way, either the LQG theorists would have to admit they couldn't find any step in your proof that was wrong and therefore you are correct on this point, or else they would be able to pinpoint a particular step where the proof goes wrong and you would have to admit that you couldn't be sure a Lorentz-invariant LQG theory is impossible. Either way, this debate about the compatibility of LQG and Lorentz-invariance would be settled.

14. Lee's repsonse has a very different effect on grad students, who do not belong to the LEE club. His comments on Nicolai's very thoughtful paper is that the issues raised in this paper are "non issues". According to Lee, 10 years ago, a "few" people addressed the issues and "moved away" from the Hamiltonian formalism. Of course as lesser mortals we and "nicolai" did not know anything about it!!

Hey Hamiltonian constraint is not an issue people, since it can be so easily swept under the carpet and now we make progress with spin foams. So the basis upshot is what? Nicolai's paper is 10 years too late?

I agree with the Prof. Glashow, if that is who it is!! that this debate is fierce and rabid!!

But, I think it should be. If 10 years ago, this issues was resolved, what import does bojowald's work Have (amongst the very few LQG works that I liked only because it actually tied to solve a problem)? and by the way why did someone not write an article saying "forget Hamiltonian: onwards with spin foam" so that we could be better informed. That's why this debate needs to rabid!!! communication has been very very poor. At least Nicolai's paper elicits a response, but for the entire community, this response should be on arxiv.org, and not confined to this blog, so that young researchers can form an opinion from this debate.

15. Dear Jesse,

whether one can prove it *rigorously* for any version of LQG? Hardly. Certainly not me. One would first have to define rigorously what "any version of LQG" means. Of course, if the concepts of LQG are generalized in such a way that it includes string theory, for example, you may also get a Lorentz-invariant LQG. ;-)

The assumptions of these proofs are a bit vague, and therefore the proof is also vague. But yes, I seem to think that a summation over discrete histories filling the spacetime can be proved as rigorously as your definition of the theory to be either singular, or topological without local degrees of freedom, or Lorentz-violating.

In all regular path integrals we've ever seen, the typical configuration contributing to the path integral is non-differentiable anyway, and the localization to the smooth configurations is just a method to calculate. I also think that one can show that a theory in which only "nice" configurations are summed over in its Feynman's formulation may be proved to lead to a non-unitary theory in general.

Best
Luboš

16. It's not often I'm mistaken for a Nobel Laureate (or Paul Ginsparg who I don't know).
Thanks for the chuckle.

However, you research leading to a wrong conclusion (two misses now) does illustrate what can happen when theory is not subject to experimental verification.

To continue with the analogy, the space of all possible people who could have written these comments is very large (as is the space of possible theories), but the probability of you naming the right person (finding the right theory) is vanishingly small without experimental guidance.

I'm a complete dilletante in the string field theory,
but I do have a simple question.

Q: In standard QFT the perturbative calculations are done in the context of a flat background metric. In string theory, which is said to unify QFT and GR, does this unification now enable one to do the analogous perturbative string calculations in a background-free context, ie, do the spacetime variable naturally become part of the dynamical system as in GR?

17. From a laymen perspective and having spent time following the dvelopement of these two different approaches I was quite interested to see that the SRian approach of LQG and the GRian approach of Strings would not have found relatiosnhips based on the Srian approach?

String Amplitudes(continous feynman path) and LQG (discrete images of monte carlo methods relegated to the varying changes) relationship of quantum gravity perspectives seem so close to me, but of course my knowledge seems far from the frames of references of both yourself Lubos Motl and Lee Smolin.

It will be interesting to see this dialogos of eide developed, form this harmonic convergence?

18. In a theory with spontaneous symmetry breaking, the generators of the internal symmetry cannot be defined within a superselection sector. This is because the "full" Hilbert space is nonseparable. Therefore, spontaneous symmetry breaking is inconsistent and there is definitely something wrong with the math.

Let's attack the spontaneous symmetry breaking crackpots, shall we?

19. Dear Anonymous,
what you write is much more correct than you think.

You example is not just an example - it is an exact description of the situation here. The fact that one can't define the generators of translations (momenta) and the Lorentz transformations is indeed exactly because the states related by translations belong to different superselection sectors. This really means that all continuous geometric operations with the spacetime are spontaneously broken.

In LQG, there is a huge continuous number of superselection sectors, which is related to its non-separability.

This clearly violates observations and very consistency with reality. Locally, the translations are definitely unbroken in anything that at least remotely resembles our Universe.

Best
Lubos

20. In general relativity, the relevant symmetries are not translations and Lorentz transformations but diffeomorphisms and of course diffeomorphisms are spontaneously broken by ANY nonzero metric tensor a.k.a. vierbein or densitized dreibein as the case may be.

21. I accept the status of crackpot being the laymen that I am and it is hard for such junior members to penetrate the language barrier, but I am sincerely trying.:)

Thank you for the correction on symmetry breaking.

To make the leap of photons held to the brane it was from the "other end" that being in the bulk graviton concentration would have also helped to identify the boundry of this brane?

22. At sufficiently short distances (in the particle physics language: high energies), the Poincare subgroup of the diffeomorphism group is always locally restored. This is called the equivalence principle. Physics in freely falling frames locally follows the rules of special relativity without gravity. A theory that does not have this feature, at least approximately with a very small epsilon, is falsified.

23. This comment has been removed by a blog administrator.

24. Thank you Lumo for orienteering and your Martian patience.

String Theory, Universal Mind, and the Paranormal

The point in regard to mathematical thinking, which motivates our model, is the following. Consider first of all what the brain does in visual perception. Here the primary information from the visual receptors goes through various levels of processing until it ends up as a high-level representation of the content of the visual field. It is not unreasonable to identify mathematics as a similar process, except that higher levels of abstraction are involved in this case. With the visual case, the mechanics are straightforward: the visual field typically contains for example edges, for which abstraction a dedicated neural system has evolved, related to our ability to perceive edges. It is hard to see why we should have such ready access to higher mathematical abstractions having little connection with experience (Penrose 1994). One resolution of the problem would be for mathematical concepts to be in some way ‘in the physics’, rather than being emergent properties of brains. In case it is felt that such a drastic solution is not necessary to explain our ready access to mathematical ideas, and that neural networks can provide an adequate explanation, a stronger argument for the existence of some kind of Platonic realm can be made on the basis of the aesthetic aspect of music (Josephson and Carpenter 1996)Yes I recognized high energy, and the return to the planck epoch.

Since Reinmannian geometry is the mathematical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry." Brian Greene

Issues with Glast, were headed in this direction from what I understood when looking at the gamma ray burst?

Being restricted, with regards to energy determinations, cosmological views become interesting applications looking towards the planck era. I do see Glast determinations falling short of planck epoch being fully discriptive by those same glast determinations. Would Smolin agree with this?

Although, Smolin's approach is leading through scientific procedures, when moving towards planck views, a new geometry must emerge?

Ideally, it was one more view of the harmonical spectrum being understood as far I as I could see.:)

25. I love a good thrashing of LQG as much as anyone, but jeez Lubos, get over yourself.

26. While L.M. with more or less logic refutes most of Smolins letter, he can apparently not find a general string rewiew - surely AdS-CFT isn't all of the subject. This is unfortunate since it would be interesting if it exists.

The discussion illustrates why it is so difficult for an interested outsider to find the right track. The 'stringulation' of sci.phys.strings and the venom makes it hard to feel the fangs,... uh, facts, behind. It throw me in a loop for 3 months before I got stringed out.

Often you get the feeling of watching the following episode of the String Trek series:

"Captain's log, string date 20+ (?):

Captain Quirk (Motl):
- That Loopy Qlingon Group is still out there! And now it seems the Higgs field is leaking in the space-time manifold!

Chief Engineer (Wissen):
- Aye! I can fix that with the gauge couplings. But it will take the life of 3 undergraduates and a massive release of papers.

Science Officer (Schrieber):
- But remember Jim, Qlingons are people too!

Unfortunately the real McCoy (experimental evidence) is still absent from the plot."

27. Dear torbjorn,

you don't need to call it a "review". We have textbooks of String theory, and Joe Polchinski's book is now the most famous one.

About 200 different reviews of string theory and various aspects of it are summarized in

http://arxiv.org/abs/hep-th/0311044Best
Lubos

28. Dear lumo,
thanks for your guidance across the string landscape; I guess I will be busy for a while! ;-) "Review" was Smolins words.

And darn it, that was supposed to be 'Captains blog' and 'the lifes of'! Why is it that my keyboard always seems to be a few keys short? :-)

29. This comment has been removed by a blog administrator.

30. This comment has been removed by a blog administrator.

31. "I also think that one can show that a theory in which only "nice" configurations are summed over in its Feynman's formulation may be proved to lead to a non-unitary theory in general."

Certainly most of the time, I would agree with that. But not in general! There are textbook cases of 1+1 gravity where doing such a prescription yields perfectly sensible and unitary results. Bizarre, but true.

In general im very skeptical of the path integral, especially in the case where d > 4. You need quartic terms or higher in the lagrangian to be bounded from below (a stable theory) and its quite straightforward to see that you end up with strong coupling at the cutoff point, hence any UV limit cannot be treated by perturbation series. Such an enterprise is speculative by nature, lest you can find some nonperturbative examples and match answers.

32. This message occurs at my blog and I think it is relevant to also post a copy here since now Lubos no longer visit my blog as he promised:

http://quantoken.blogspot.com/2005/02/blackhole-entropy-lqg-and-super-string.html

Both the super string camp and the LQG camp claimed their derivations of the Bekenstein-Hawking black hole entropy as their biggest success of their theories. In my judgement, claiming the derivation of Bekenstein Hawking entropy, such a trivial feat, as their biggest success, is completely "childish" and only shows the lack of "innate" ability on the part of each camp to comprehend what is the REAL physics behind the blackhole entropy!

I am going to show one very trivial derivation of the black hole entropy and how it is proportional to the event horizen surface area divided by Planck area. One that is different from Hawking's but much simpler.

But first, one has to realize two things:
1.Hawking entropy is not an empirical experimental evidence, but merely the result of a gedanken "experiment", e.g., mind exercise.
2. The entropy is a DIMENTIONLESS physical quantity.

Since Hawking entropy is just a mind exercise instead of empirical experimental result. Any claim of deriving the same result as Hawking merely shows that your theory does not have any logical inconsistency or conflict against the line of logic that Hawking's gedanken mind exercise. That's all. You still have not made any connection with the physics reality, unless, of course, that the Hawking formula is confirmed by a REAL experiment, not a gedanken one.

So, if a theory is able to derive Hawking entropy, it's good but really not a big deal. But if it can not, then there is a huge trouble in that it is logically inconsistent with Hawking's reasoning and what Hawing based his reasonings on.

Actually, any consistent theory at all will always leads to the Hawking formula, give or take a trivial numerical factor which is of the order of one, a numerical factor that both LQG and super string had struggled a bit to get right.

Now back to the dimentionless-ness of entropy. Given some basic physics quantities and known physics constants for a black hole, how would you construct an entropy formula that gives a dimentionless quantity? To construct such a formula, all the units should cancel out. That gives you pretty good clue to almost certainly arrive at the only correct answer.

We are given:
1.G, the gravity constant that is involved in any thing related to gravity
2.hbar, anything that envolved entropy needs to count quantum micro states.
3.C, light speed is certainly involved in anything related to spacetime.
4.M, the mass of black hole. We certainly need that.

There is nothing more we need. How would you construct a dimentionless number out of these 4 quantities? An immediate possibility is similar to the electromagnetic coupling constant, the fine structure constant, we can construct a gravity coupling constant here using:

S = G*M^2/(hbar*C) (1)

And that is the Hawking entropy formula, give or take a numerical factor!!! Actual it is only bigger than the Hawking entropy by a factor of 4*PI. Actually that is the only simple way to get a dimentionless number out of the 4 quantities!!!

How come? We know the radius of a black hole is proportional to its mass:
R = 2*G*M/C^2 (2)
So:
M = R*C^2/(2*G) (3)
So the (1) becomes:
S = (1/4)*R^2/(G*hbar/C^3) = (1/4) * R^2/lp^2 = (1/(4*PI)) * (1/4) * A/lp^2 (4)

So it differ from Hawking formula by 1/(4*PI).

Now, let me try to use a totally different but much simpler gedanken experiment to derive an entropy formular similar to Hawkings. It's trivial. Any one can think out a hundred different gedanken experiments, all arrive at the same result, differing by only a numerical factor.

Let's start with a black hole of almost zero mass, and gradually increase its size by throwing in photons in appropriate wavelength.

We do not want to throw in photons whose wavelength is much smaller than the size of the blackhole, since they will lose a great portion of their energy by gravity red-shift, and we do not know how much the mass of blackhole is increase. We do not want to throw in photons of wavelenth much larger than the blackhole size either, since then the photo will diffract around the blackhole completely, without absorbtion.

Let's choose photo wavelength
Lambda = diameter of blackhole = 2*R (5)

Such photons will be absorbed with its energy largely unchanged, increasing the blackhole mass by the equivalent mass of the photon energy. The increase of mass is:
delta M = delta E * C^2 = 2*PI*hbar * C^3/lambda = 2*PI*hbar*C^3/(2*R) (6)

We know that each photon carries an entropy of exactly one, regardless of the photon's energy, so the increase of black hole entropy for each photon is one:
delta S = 1 (7)

Therefore:
dM = PI*hbar*C^3/R * dS (8)
dS = 1/(PI*hbar*C^3) * R * dM (9)

Now, since
R = 2*G*M/C^2, which is M = C^2/(2G) * R (10)
dM = C^2/(2G) * dR (11)

Put it into equ. (9):
dS = 1/(PI*hbar*C^3) * R * C^2/(2G) * dR (12)

Integrate equ. (12) from zero:

S = (1/(4*PI)) * R^2/ (hbar*C^3/G) (13)
S = (1/4*PI^2)^2 * (1/4)* A / lp^2 (14)

Again we ontained virtually the same Hawking entropy, except for a small numerical factor. I could easily get the factor correct if I am willing to try a little bit numerology like the LQG and super string camp did in their crackpot theories.

So you see it is really not a big deal at all to have derived the black hole entropy proportional to horizen area divided by Planck area.

Quantoken

33. This comment has been removed by a blog administrator.

34. This comment has been removed by a blog administrator.

35. Lubos practices censorship.

Admit it, you've got a crush on loop quantum gravity and Smolin is your hero!

36. You see that you can be both brief as well as tolerably polite. Your latest posting contains all the meaningful information from your previous multi-kilobytes rants. Everyone can determine for herself whether I am a secret fan of loop quantum gravity. ;-)

37. Just to say hello from a friendly soul. I thought that you will find my comments on quantum gravity entertaining - even if it would be surprised if you would agree with them - see my blog Open System.

38. Just to say hello from a friendly soul. I thought that you will find my comments on quantum gravity entertaining - even if it would be surprised if you would agree with them - see my blog Open System.