Not Even Wrong

This morning’s New York Times has a long and prominently placed article about the 20th anniversary of the “First Superstring Revolution”. The Times has a long history of producing overhyped uncritical articles about string theory, for a classic example, see “Physicists Finally Find a Way to Test Superstring Theory”. This one does allow some critical voices to be heard, including Lawrence Krauss, who is quoted as describing string theory as a “colossal failure” (which is different than a miserable failure)

Krauss is also quoted as saying “We bemoan the fact that Einstein spent the last 30 years of his life on a fruitless quest, but we think it’s fine if a thousand theorists spend 30 years of their prime on the same quest.”

Witten is quoted extensively, but he doesn’t sound very optimistic these days, saying “It’s plausible that we will someday understand string theory”, and making the rather weird statement that string theory is “so vast, so rich you could say almost anything about it” (for instance that it is a colossal failure?). He also seems to have given up on the idea that there is some fundamental new symmetry underlying string theory, instead putting his hopes on the existence of some new principle for constructing space and time.

The article also says that few theorists will give up on string theory when supersymmetry is not found at the LHC, with Witten interpreting this not as evidence that string theory is wrong, just that unfortunately it will be harder to get experimental evidence for it than he had hoped. String theorists in general seem to have trouble getting their minds around the idea that it is even possible the theory is wrong. Jeff Harvey does admit that sometimes he wakes up thinking “What am I doing spending my whole career on something that can’t be tested experimentally?”, but the question of “What am I doing spending my whole career on a colossal failure?” doesn’t seem to keep him awake nights.

The article ends by quoting an exchange between Steve Shenker and my colleague Brian Greene. Shenker quotes Churchill, describing the state of research into string theory as “perhaps it is the end of the beginning”. Brian seems to be one of the few string theorists around willing to actually consider the idea that the theory might be wrong, arguing that if string theory is wrong, it would be good to know this soon so physics can move on.

A recent issue of Science magazine has an article about the “Strings and the Real World” workshop at Aspen this past summer, entitled String Theory Gets Real — Sort Of. A more accurate title for the article might be “String Theory Would Like to Get Real — But Can’t Because it Doesn’t Work”.

The article claims that up until recently string theorists were not even trying to connect string theory with experiment, but “Now a small but growing number of them are trying to forge connections between string theory and detailed data”. This is really nonsense. There have always been plenty of people doing “string phenomenology”, but it has always been a doomed subject, for reasons I’ve gone on about at length here and elsewhere. The article does mention the problem of the Landscape with the increasingly standard loony comment that “physicists may have to rethink what it means for a theory to explain experimental data”. This is absurd. There’s no question about what it means for a theory to explain experimental data and the simple fact of the matter is that this theory can’t do it.

There’s also a claim that “the cosmological constant now appears to be real, and string theorists hope to calculate its value”. This misunderstands the whole Landscape argument, which tries to justify why no one can ever hope to calculate this value.

The article also includes a sidebar which tries to explain why young people go into string theory. It quotes a Penn postdoc, Brent Nelson, as saying that he read about string theory as a teenager and couldn’t believe so many people accepted something so outlandish. But he went into string theory anyway, and now says “I haven’t learned enough… I still don’t know why I should believe”. Sorry Brent, but no matter how long and hard you stare at this particular emperor trying to appreciate the beauty of his clothing, he’s still going to be naked as a jaybird.

Finally, when asked how many revolutions will be needed to make string theory work, John Schwarz says “I don’t know, but I think we’ll need many more”. At about a decade per revolution, it looks like Schwarz now doesn’t expect to live to see this happen. Neither do I.

The second talk I heard yesterday at the Institute was by Chris Woodward from Rutgers. What he was talking about was a conjectural formula whose origins go back to a truly amazing paper by Witten from 1992 entitled Two Dimensional Gauge Theories Revisited.

There are quite a few very interesting things about this paper, but one of its ideas has become influential in mathematics under the name “Witten localization”. This involves a new principle for calculating integrals of equivariant cohomology classes. Before Witten’s work, it was well-known among mathematicians that such calculations could in many cases be reduced to a “localized” calculation about the fixed point set of the group action. This is related to the Atiyah-Bott version of the Lefschetz fixed point theorem they discovered in the mid-sixties, to general arguments about equivariant K-theory and fixed points due to Atiyah and Segal, as well as to the Duistermaat-Heckman theorem and generalizations due to Berline and Vergne. For some expositions of this material, see the paper by Atiyah and Bott published in Topology in 1984, and the book Heat Kernels and Dirac Operators by Nicole Berline, Ezra Getzler and Michele Vergne.

Witten’s idea involved a new localization principle, where integrals of equivariant cohomology classes can be localized about zeroes of the moment map rather than fixed points of the group action. This is sometimes referred to as “non-abelian localization” since it applies directly to non-abelian group actions, whereas the earlier fixed point formulas typically looked at the fixed points of actions by abelian groups.

One of the main applications of Witten localization by mathematicians has been to use it to prove in various contexts that “quantization commutes with reduction”. For physicists this is the idea that, given a classical mechanical system with a gauge symmetry, one hopes to get the same result either by first imposing constraints and then quantizing, or by quantizing and then imposing constraints. Even in the context of finite-dimensional classical mechanical systems, that this should be true is a very non-trivial mathematical statement. For a survey of some of this, see an article in the Bulletin of the AMS by Reyer Sjamaar.

Witten’s original paper applied his ideas to the calculation of the Yang-Mills partition function in two dimensions. This uses the fact that the space of connections for a non-abelian gauge theory in two dimensions is an infinite dimensional symplectic manifold, with moment map the curvature of the connection, something first observed by Atiyah and Bott in the late seventies.

Woodward’s talk involved an integration formula similar to Witten’s original one, for details about it see his recent paper. This kind of formula was also studied by Paul-Emile Paradan, see this paper and a recent detailed summary (in French) by Paradan of his work.

Woodward’s work is also motivated by trying to understand the 2-d Yang-Mills partition function as an integral in equivariant cohomology. He and Constantin Teleman have done work on a K-theoretic version of this, see their joint paper as well as Teleman’s contribution to the proceedings of the conference in honor of Graeme Segal’s 60th birthday, and his talk at the KITP in Santa Barbara last year.

I was down in Princeton at the Institute yesterday and heard two interesting talks. The first was the beginning of a series of four lectures by Paul Baum about the Baum-Connes conjecture, the second was by Chris Woodward about “equivariant localization”. I’ll write a bit about Baum-Connes here, perhaps something about the topic of Woodward’s talk in a second posting.

The Baum-Connes conjecture was first formulated in 1982 by Paul Baum and Alain Connes in an unpublished paper.Roughly it says that the K-theory of the reduced C* algebra of a group G is identical with the equivariant K-homology of a certain sort of classifying space for the group. Equivariant K-homology classes can be represented by certain generalizations of the Dirac operator, and the map to the K-theory of the C* algebra is given by taking the index of the operator.

There’s a huge literature about this by now and a few years ago Nigel Higson put together a detailed bibliography. Some recent expository articles about the conjecture include an ICM talk by Higson, a survey talk by Wolfgang Lueck, and a book by Alain Valette.

The conjecture remains unproved for discrete groups in general, and Baum said that he suspects it is not true in full generality, invoking what he called “Gromov’s principle”. According to Baum, this principle states that “No statement about all finitely presented groups is both non-trivial and true.” While the conjecture has been proved for some classes of discrete groups, there are many for which it is expected to be true but remains unproved (e.g. SL(3,Z)). For a while it was thought that the conjecture applied also to groupoids, but counterexamples for groupoids have been found.

I’ve always been fascinated by part of the philosophy behind the Baum-Connes conjecture, which is to use equivariant K-homology, classifying spaces and Dirac operators to get information about representation theory of groups in cases where little is known about this representation theory. This is in some very vague sense related to what seems to me to be going on in QFT, where Dirac operators and path integrals over the classifying space of the gauge group (the space of connections) are somehow related to the representation theory of the gauge group. The Baum-Connes conjecture itself just involves locally compact groups and thus doesn’t say anything about gauge groups, so it is not directly relevant to the case that may be of interest in QFT.

An excellent review article about the state of the proof of the Poincare conjecture by my colleague John Morgan has recently appeared. For more background on this, see an earlier posting. Morgan is a topologist, and his article contains an excellent survey of what this all has to say about the topology of three-manifolds. This past semester he has been teaching a course in which he has gone through Perelman’s proof very carefully. So far it all holds together.

The U.S. Congress has finally gotten around to producing a budget for fiscal year 2005. Some information about the budget numbers for scientific research is available here and here.

The NSF budget for research and related activities is being cut by .7% from its FY 2004 level, the first such cut in many years. The other main part of the NSF budget, that devoted to education, is being cut even more. A few years ago Congress passed a bill that was supposed to double the NSF budget over several years, but that bill is now very much no longer operative. It’s not clear yet how physics and math specifically fare under this new budget, presumably we’ll find out in the next few days.

The bulk of particle physics funding comes from the DOE Office of Science, and there the budget situation is brighter, with an increase of 2.8% for FY 2005. Again, the details of exactly what is being funded and what isn’t should soon be available.

Update: More about the new NSF and DOE budgets can be found here and here.

For a depressing look at where theoretical physics is headed, see this new article from Time magazine. I agree with the analysis of it posted here.

In the comment section of the last post, Lubos Motl points to the story of Billy Cottrell, a young string theorist at Caltech accused of being involved in the vandalism of SUVs. Evidently he has now testified against others at his trial, so the “Free Billy Support Network” (which was asking people to send string theory papers to him in prison) has been disbanded and he is being referred to as a “police informant”.

Despite being a string theorist, Cottrell seems to not be the brightest bulb around, having supposedly used a Caltech computer he was logged into to send an anonymous e-mail to the media claiming responsibility for the SUV vandalism.

The local Pasadena newspaper’s report on his testimony at his trial says that he corrected Judge Gary Klausner “when the judge asked if string theory, Cottrell’s focus at Caltech, is “an area of physics.’

“It’s the area of physics,’ Cottrell said.”

His lawyers “attributed his odd behavior in testifying to Asperger’s syndrome”, a mild form of autism.

Funny, Cottrell isn’t the only one who goes on like this about string theory. Maybe there’s a lot of autism going around.

The latest trend among prominent theorists seems to be the writing of popular books hyping the unsuccessful speculative ideas they have been working on. Two new examples of this have been pointed out by Lubos Motl over at sci.physics.strings.

Both of these books are due to appear at the beginning of next May. One, by Leonard Susskind of Stanford, is entitled An Introduction To Black Holes, Information And The String Theory Revolution: The Holographic Universe. The second, by Lisa Randall of Harvard is called Warped Passages : Unraveling the Mysteries of the Universe’s Hidden Dimensions.

Randall’s book presumably is not so much about string theory as about the idea that we live on a brane inside a higher dimensional space. As far as I can tell, there’s even less evidence for this idea than there is for string theory itself. I don’t know exactly what her attitude about string theory is, but at a public debate at the Museum of Natural History here in New York a few years ago, I remember that she scornfully dismissed the argument that string theory predicts gravity, saying something like “Yeah, it predicts ten-dimensional gravity.”