Not Even Wrong

Today’s Guardian has an article by a writer who recently visited the Institute in Princeton to talk to Witten and others there about string theory. The author of the piece makes the obvious analogy between Witten and Einstein, and asks the string theorists about Einstein’s 20-year misguided and failed attempt to unify gravity and electromagnetism during his years at the IAS. String theory and Einstein’s failed program get further identified by the author’s claim that if Einstein were alive today he would be working on string theory, and by a quote from Seiberg that “Being in the place where Einstein was is clearly an inspiring idea.”

Seiberg also has something very true to say:

“Most string theorists are very arrogant,” says Seiberg with a smile. “If there is something [beyond string theory], we will call it string theory.”

Witten’s attitude towards string theory seems to remain unchanged, he’s quoted as saying:

“Critics of string theory say that it might be too big a step. Most physicists in other fields are simply agnostic and properly so,” says Witten. “It isn’t an established theory. My personal opinion is that there are circumstantial reasons to suspect that it’s on the right track. ”

His recent work on twistor string theory is mentioned, including the fact that there was a workshop at Oxford last week on the subject. About this, the writer reports

“Witten is not convinced yet. ‘I think twistor string theory is something that only partly works,’ he says.”

I wonder exactly what he meant by that. What’s the part of twistor string theory that he thinks doesn’t work?

Most new preprints in mathematics and physics these days are posted on the arXiv, but every so often I run into interesting new things worth reading that haven’t appeared there for one reason or another. Here are some recent examples:

Some lecture notes on Lie algebras by Shlomo Sternberg. Lots of topics covered I haven’t seen anywhere else, especially the material on the relation to Clifford algebras and the Kostant version of the Dirac operator.

Lecture notes by Constantin Teleman about his recent work on topological field theories and the Gromov-Witten theory of BG, the classifying space of a group. These are notes from talks given at Gregynog, Goettingen, and Miami. I confess that, like a lot of Teleman’s work, I have trouble figuring out exactly what he is up to, but it looks quite interesting. I wish he and Dan Freed and Mike Hopkins would get around to finishing their paper on “K-theory, Loop Groups, and Dirac Families” that Teleman has been advertising as “coming soon” for quite a while…

David Vogan has an interesting draft of a review of A. A. Kirillov’s book on the orbit method in representation theory. This is the most fully developed version of what is sometimes known as “geometric quantization”. Vogan also has some notes from his lectures this past year on “Unitary representations and complex analysis” which include material on the Borel-Weil theorem and its generalizations.

Nikita Nekrasov has some Lectures on Nonperturbative Aspects of Supersymmetric Gauge Theories and a written version of his 2004 Hermann Weyl Prize lecture.

Eckhard Meinrenken has a a nice expository article on the de Rham model for equivariant cohomology.

For some interesting comments by Nima Arkani-Hamed about his model-building activities, followed by some of my own, take a look here.

Update: Jacques Distler has some comments on the Arkani-Hamed et. al. paper.

The world of particle physics web logging expanded by about an order of magnitude today, as a new web-site called Quantum Diaries came on-line. The idea seems to be to celebrate the 100th anniversary of Einstein’s remarkable 1905 papers by getting 25 physicists from around the world to set up web logs so people can follow what they do during 2005.

Most of the participants are experimentalists, with just three theorists as far as I can tell. The theorists are John Ellis of CERN (see here for a story about him), Stephon Alexander of SLAC, and Jochen Weller of Fermilab.

Interestingly, all three of the theorists are spending at least part of their time working on cosmological or astrophysical topics, which gives you some idea of where the field is headed. Also, none of them are working on string theory at the moment, which also gives you some idea of where the field is headed.

As a completely unrelated aside, today I came upon the web-site of Brian Powell, a graduate student of Will Kinney’s at Buffalo studying cosmology. He’s more pro than anti string theory, but irreverently funny. His comment that “many people criticize string theory because it’s sort of becoming fashionable to do so” warmed my heart. On the other hand, the fact that he links to something I wrote about Witten’s talk at Santa Barbara with the terms “Witten gets socked in the groin” kind of upsets me.

As of yesterday, I’ve started deleting comments from this weblog if they seem to me to be completely off-topic or make no sense. By the end of last year, the comment section here had begun to turn into something I couldn’t stand to read and didn’t want to be associated with. This was not a tolerable situation.

Please only post comments if you have something interesting to say related to the topic of the posting. If you want to share your thoughts with the world about the biological basis of homosexuality, quantum computing, etc., etc., please do it somewhere else than in the comment section of a posting about the issue of the predictivity of current formulations of string theory.

This has already wasted far more of my time than I would like. I don’t want to moderate or in any way be involved in a public discussion of this, so the comment section for this particular posting is closed. If you absolutely feel you must discuss this issue with me, send me e-mail, although unless there is a very good reason, I’m unlikely to take the time to write back in response. People with on-topic comments are encouraged to continue to contribute them to earlier postings and to any future ones.

In recent years, as it has become clear that string theory can never be used to predict anything about the real world, string theorists have reacted to this state of affairs in various often bizarre ways. Tonight there’s a new review article by Steve Giddings about string theory which doesn’t even pretend that the theory will ever make a real prediction about anything. Giddings seems to think that the particle phenomenology archive hep-ph is the place to post this kind of thing, not the hep-th archive devoted to less experimentally based work. This is pretty funny, but the really hilarious thing is the way Giddings motivates string theory. In a section entitled “The problem of predictivity” he argues that our inability to make quantum gravity predictions at high energy is a problem of supreme importance, then goes on to use this to motivate the introduction of string theory, which in the end gives a theoretical framework unable to predict anything about anything at any energy.

The review does actually claim at various points that string theory “predicts” gauge theory, fermions, supersymmetry, Dp-branes, and the cosmological constant. It just neglects to mention that it doesn’t predict any characteristics of any of these things (value of the cosmological constant, any observable characteristic of a Dp-brane, how supersymmetry is broken, what kind of fermions, what gauge groups). String theory actually has nothing at all to say about even the things Giddings claims it “predicts”.

Giddings seems to be a hard core anthropist, he ends with the exciting recent insight from string theory that:

“It may in fact be that anthropic considerations fix the small relative size of the Higgs mass as compared to the Planck mass. If so this ultimately answers the question we started with, ‘why is gravity so weak?’ This is clearly a very interesting line of research, and debate continues on these and other important points.”

Actually this is only the next to last paragraph. He finally ends with the news that exp{10^120} years from now our region of the Universe will spontaneously decompactify, which he thinks is pretty kewl.

With the current anthropic nonsense exemplified by this review article, string theory has finally reached rock-bottom. It has given up any claims to being a legitimate science and has taken on the characteristics of a cult. It is long past time for those leaders of the field with any remaining scientific integrity to take a public stand that what is going on is not all right.

Perhaps this is too much ranting. My excuse would be that I’m not in the best of moods because I’ve spent my entire break between semesters being sick (don’t worry, I’m getting better). I just can’t believe the way essentially the entire particle theory establishment, including many people I have the highest respect for, continue to allow this situation to go on without public comment.

Update: Lubos Motl has news of a new, more elaborate set of anthropic nonsense coming soon from Savas Dimopoulos, Shamit Kachru, and his senior colleage Nima Arkani-Hamed (their innovation is to divide the landscape up into “countries”. I kid you not). Lubos evidently has seen this paper early, the rest of us will have to wait until tomorrow night. Even though he pretty clearly sees how unscientific this is, he has to try to find something nice to say about it since his career depends on these people. Sad to watch, actually. Postdocs and untenured people can’t take on the fight against this garbage unless they want to commit career suicide. It’s up to the tenured people. Where are they?

Further update: It seems the “countries” terminology is due to Lubos, the authors refer instead to breaking the landscape up into “friendly neighborhoods”. Which sounds even sillier than “countries”.

Yet further update: The Arkani-Hamed, Dimopoulos, Kachru paper is now available. It consists of about fifty pages of few equations and highly convoluted anthropic sorts of arguments, not about any particular theory but somehow about whole classes of theories. Kind of a meta-argument. They don’t seem to get anything at all like an actual prediction of anything out of this, the closest they get is in their conclusion about what to expect at LHC energies:

“Instead of finding a large spectrum of new particles and interactions typically needed for naturalness, we predict sparse models with few new particles and couplings, with dimensionful parameters finely tuned but close to dangerous environmental edges.”

Pretty poetic, but I think the experimentalists working on the LHC detectors are going to have trouble using that as guidance as to what to be looking for.

A preprint by Andrei Marshakov and Antti Niemi appeared on hep-th this evening making a remarkable claim. According to this preprint, a few weeks before passing away recently at the age of 93, Shiing-Shen Chern completed a preprint entitled “On the Non-existence of a Complex Structure on the Six Sphere”.

Whether or not a given manifold defined using real coordinates can be given the structure of a complex manifold is often a difficult problem. For the case of a d-dimensional sphere, clearly you can’t do this in odd dimensions, but for even dimensions, you certainly can for the case d=2. For the cases d=4 and d=8 or more, there is a topological obstruction to even finding an “almost complex structure”. In other words, you can’t find a continous choice for each point on the sphere of what it means to multiply elements of the tangent space by the square root of minus one. The case d=6 is special: you can use the octonions to construct an almost complex structure, but this complex structure is not “integrable”, it doesn’t come from any local choice of complex coordinates. One of the most famous open problems in geometry has long been the following: is there another almost complex structure on the six-sphere that is actually integrable?

It has long been conjectured that there is no such integrable almost complex structure, but no one has ever been able to prove this. Chern’s preprint contains a purported proof, but Marshakov and Niemi devote only a paragraph to the non-trivial part of his argument. From their preprint you can’t tell whether Chern has a valid argument.

I’ve heard via e-mail from a knowledgeable authority on the subject who points out that there are serious flaws in the manuscript that was privately circulated. His opinion is that Chern’s argument actually does prove something interesting, but not the full result Chern claims, so the conjecture about the non-existence of a complex structure on the six-sphere remains open.

Greg Moore has written an article for the latest Notices of the AMS entitled “WHAT IS… a Brane?”. He begins by noting that “The term ‘brane’ has come to mean many things to many people” and one of the difficulties of the subject is that one has to figure out from context what sort of brane someone is talking about.

For the case of branes of dimension greater than one, in general no one knows how to consistently quantize such objects. See Warren Siegel’s research summary for comments about this. He notes that now that M-theory shows that non-perturbatively strings are membranes in 11d, one doesn’t have a finite quantum theory of gravity, since membranes are infinite even in perturbation theory. All one has is an effective low-energy supergravity theory, which is what one had before one got involved with string theory. While at Siegel’s web-site, check out his latest parody paper called “The Everything of Theory”, which includes the following lines:

“The real problem with string theory is that there is no alternative. However, the reason there is no alternative is that no one ever bothers to look for one; in fact, there is a strong resistance to even considering looking for one. Consequently, practically all theoretical high energy physics (and even most of phenomenology) is now string theory. Thus, string theory is not so much the Theory of Everything (since it explains nothing), but rather the “Everything of Theory”, since it now encompasses all of theory. This era in string research is strongly reminiscent of the Dutch tulip trade just before the Tulip Crash of 1637. ”

I, for one, am missing the joke here…

For some new hyping of a different kind of brane, see the latest Nature, which has a piece on Nima Arkani-Hamed. Equal time is given to LQG, with a similar piece on Martin Bojowald.

Update: Lubos Motl has a long posting about branes and M-theory, which explains many things. As usual though, he insists that the full dynamics of the branes in M-theory is completely determined and unique even though he doesn’t know what it is in any phenomenolgically realistic background. To get a finite quantum theory of gravity that has anything to do with the real world out of M-theory, you need to show that you can get well-defined, finite results for the dynamics of these branes in the case of four large dimensions, the rest small. As far as I can see any claim to have this now is purely wishful thinking.

Several people wrote in this morning to tell me about Phil Anderson’s comments about string theory that appeared in the New York Times today. These originally come from John Brockman’s “Edge” web-site where he has gathered responses from more than a hundred scientists and others to the question “What do you believe is true even though you cannot prove it?”.

Beside’s Anderson’s answer, also interesting is Paul Steinhardt’s. Steinhardt refers to the currently fashionable use of the anthropic principle as “an act of desperation” and “millennial madness”, notes that the Weinberg anthropic “prediction” of the cosmological constant gives the wrong value, and even acknowledges that string theory may just be wrong. For sheer weirdness, as usual these days, Lenny Susskind is hard to beat. Brockman doesn’t seem to have located any string theorists who believe string theory but can’t prove it. Since it can’t be proved, I guess even they don’t believe it anymore.

Phil Anderson has always been somewhat of an intellectual hero for me. He’s really the person who discovered the Higgs mechanism, among many other things. Despite a reputation for being a curmudgeon, at one point he was quite kind to me. At some sort of social event at Princeton to mark students passing their generals, he came up to me and told me that he had graded my solid state physics exam. He complimented me on one problem in particular, one I had got wrong. I had realized something was wrong with my solution of that problem, noting on my exam that the result I was getting couldn’t be right and explaining why. He told me that this had impressed him, that one should always know what the result of a calculation should look like before attempting it.