Not Even Wrong

John Ellis’s weblog has a new entry on Future Particle Accelerators which discusses prospects for a linear collider. The plan for an “International Linear Collider”, or ILC is now in its design phase, with work proceeding on a detailed design for a .5-1 Tev collider. No one has yet figured out where this would be sited or how it would be financed. The agencies responsible for this funding seem to have agreed to put off a decision about going ahead with the project until 2010.

By that time there should be a couple years of data available from the LHC, and if the Higgs particle or superpartners are found, it would be clear whether the ILC design would have enough energy to study them usefully. Also around that time is should be clear whether CERN’s more ambitious design for a linear collider, called “CLIC” and perhaps capable of reaching 3-4 Tev, is really a feasible one. If the decision is made to build the ILC design, the hope would be to have construction finished in 2015 (although this sounds overly optimistic to me), allowing several years of joint running of the LHC and ILC. If no Higgs or superpartners are found, or their mass is too high, the decision would be made to concentrate on CLIC, with construction done at the earliest in 2021.

Back in the present, the Tevatron at Fermilab is now seriously back in business after a long shut-down, recently reaching record values of luminosity. To follow what is going on there, you can keep up with the weblogs of Tommaso Dorigo and Sandra Leone of the CDF collaboration, as well as Gordon Watts and Ursula Bassler of D0.

An expository article by the the algebraic geometer Yuri Manin always has something interesting in it, and his latest, entitled The notion of dimension in geometry and algebra is no exception.

In this article Manin discusses various ideas related to the notion of dimension, ranging over fractal geometry, non-commutative geometry and theoretical physics. He begins with a quote from Glenn Gould, which is quite amusing, but of obscure relation to the notion of dimension. Then he goes on to some history, from Euclid to Leibniz, finally veering off into a fascinating discussion of the relation of algebra and geometry, and ending with the sociological comment that visual mass media is leading to a dominance of right-brain mental faculties, and thus “projects us directly into dangerously archaic states of collective consciousness.”

The body of the article includes comments on Hausdorff dimension, dimensional regularization of path integrals, the theory of operator algebras, non-commutative geometry, a weird digression on databases, and supergeometry. He also discusses “Spec Z” (the “space” naturally associated to Z, the ring of integers) making various comments about it and giving arguments for its dimension being 1, 3 and infinity. Next there are some comments on modular forms, and finally a section on fractional dimensions in homological algebra.

Its not clear how seriously one should take all of this, but Manin’s article is definitely thought-provoking.

Ken Lane has written a letter to the editor of the Boston University student newspaper to complain about its article about string theory and the BU physics department discussed in a previous posting. Lane is annoyed about not having been given a chance to respond to Vafa’s ad hominen attacks characterizing him and the BU physics department as “foolish” and “childish”. He also complains that the author didn’t seek other opinions about Vafa’s claim that string theory is what the “youngest, most brilliant physicists” are all doing.

I don’t remember whether they had shop classes at Harvard, but if they do now, maybe they should be talking to Vafa. According to the blurb for a recent talk by Jim Gates at Brookhaven, string/M-theory is “a 21st century lathe – a machine capable of remarkable precision and versatility, but requiring a skilled and experienced operator for its success.” Funny, back in the last millennium I remember when string theorists were claiming that string theory was a 21st century “supercomputer” or “spaceship” that had fallen into the 20th century.

A couple weeks ago, three string theorists, (Nicolai, Peeters and Zamaklar) posted on the arXiv a critical assessment of loop quantum gravity. Today I received from Lee Smolin something he wrote responding to them, and I’m posting it here with his permission. Lubos Motl also has put up Smolin’s text on his weblog this morning, but I thought it would be a good idea to provide a version that doesn’t include Lubos’s interspersed rantings. Smolin has some very interesting things to say, and his comments are well-worth reading by anyone who wants to understand what is going on in this field.

Somewhat off-topic, I’d also like to mention a paper by Freidel and Starodubtsev from earlier this week called Quantum gravity in terms of topological observables. The idea of trying to use topological quantum field theory to understand quantum gravity is one that I’ve always found appealing, and this paper is an interesting attempt to make this idea work. I don’t think I find it completely convincing, for one thing they seem to be breaking the topological invariance by hand. For another, TQFTs are very subtle QFTs, and the kind that might be relevant to gravity is still very far from well-understood.
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Eric D’Hoker and D.H. Phong this past week finally posted two crucial papers with results from their work on two-loop superstring amplitudes. The first one shows gauge slice independence of the two-loop N-point function, the second shows that, for N less than 3 and for low-order terms at N less than 4, there are no two-loop corrections to the low energy effective action.

D’Hoker and Phong have been studying superstring amplitudes for nearly twenty years, and are justly proud of their recent results, which are a tour de force of careful calculation. Over the years there have been many claims made about two-loop amplitudes, but until their work, no one had managed to really sort out the gauge dependence issues and write down gauge-independent amplitudes. For some comments about some of the issues involved at genus 2 and higher, see postings by Jacques Distler here, here, and here.

I don’t think D’Hoker and Phong will be coming out with complete results for genus 3 anytime soon, so the state of the art is that there is now a finite and well-defined version of the two-loop superstring amplitudes, with the problem of higher loops still open. While claims abound about the finiteness of higher-loop amplitudes, before believing them one should first take a look at the tricky problems that D’Hoker and Phong had to overcome to get well-defined two-loop amplitudes.

Update: Jacques Distler has a new posting about multi-loop amplitudes and potential problems with the Berkovits version of the superstring (he explains in more detail the possible problems with the BRST and picture-changing operators I mentioned). For some mysterious reason Jacques neglects to refer to my posting or comments about this. I encourage those commenters who seemed convinced I didn’t know what I was talking about to now take up their arguments with him.

If you’ve been following the story of the “Landscape” over the past year or so you’d remember that its proponents felt that if it could predict anything it should be able to predict whether or not there will be supersymmetry at low energies. They had great hopes for making this prediction before 2008 when the LHC presumably will tell us whether there is supersymmetry at LHC energies.

Well, tonight one of the biggest proponents of this point of view, Michael Dine, has a new paper out with two co-authors, entitled Branches of the Landscape. In it they conclude:

“From all this, it appears that it is difficult, in principle, to decide whether or not the landscape predicts supersymmetry.”

So, many string theorists now seem to believe that:

1. String theory predicts a landscape of possible vacua.

2. Given the existence of such a landscape, one can’t predict whether or not there will be low-energy supersymmetry (or anything else either).

One wonders it these string theorists ever studied elementary logic and can draw the obvious conclusion from 1. and 2.

The transparencies from the conference on twistor string theory held two weeks ago at Oxford are now available on-line.

Quite a few of the talks deal with the technical details of computing amplitudes. For the motivation from phenomenological particle theory, see the talk by Zvi Bern. As for the motivation and present state of the whole idea of relating QCD to a string theory in twistor space, the only person who really seems to have much to say about this is Witten himself. His transparencies are in three parts: part 1a and part 1b from his first talk and then a second talk in which he explains what the problems with the whole idea are and some ideas he’s been thinking about using to try and get around them.

There’s a quite interesting article on the controversy over string theory that appeared yesterday in the Boston University student newspaper. It gives some insight into the political battle now going on in many physics departments.

The Boston University physics department has always been in the shadow of its more prominent neighbors just across the river in Cambridge. A few years ago they attracted Glashow away from Harvard, and I’ve been told a big selling point for him was that he would no longer have to be part of a department dominated by string theorists. He’s one of very few particle theorists who has consistently and publicly complained about what is going on in string theory. In the article, he forcefully makes the analogy between Einstein’s failed unification efforts and string theory:

“It is tragic,” Glashow said, “but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. So when one person spends 30 years, it’s a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious.”

Ken Lane, one of Glashow’s colleagues at BU, says that “String theory is not physics” and that he doesn’t know of any BU faculty who think that string theory belongs in the physics department. He does seem to think that it belongs in a math department, something I have some problems with. While certain parts of string theory are mathematically interesting and do belong in math departments, most of what string theorists do is not mathematics. For instance, the many string theorists making anthropic arguments about the “Landscape” are not doing mathematics and it’s pretty insulting to mathematicians to say that they belong in math departments.

Lane believes string theory is on its way out, and that the LHC will finish it off:

“I think I can safely predict that string theory is going to wither and die when exciting results start coming out of the LHC.”

Cumrun Vafa of Harvard seems to be spitting mad at the idea that BU won’t hire string theorists, referring to them as “foolish” and “childish”, which is not normally language academics use when talking to the press about their Nobel-prize winning colleagues at neighboring institutions. Vafa was a student of Witten’s a year or two behind me at Princeton, but I haven’t talked to him since my postdoc days. He’s definitely a smart guy, but also definitely a fanatic.

Vafa graduated from Princeton in 1985, just as the string theory fad hit. He went to Harvard as a postdoc, where most of the senior people were pretty skeptical about string theory, although willing to hire smart young postdocs doing it. I heard he was very upset in 1986 when Glashow published his article with Ginsparg in Physics Today attacking string theory, and even threatened to leave. But over the next decade or so he managed to marginalize Glashow, get more string theorists hired, and consolidate power around them. Finally Glashow left, and by now the string theorists heavily dominate the theory group. Of the active theory faculty, Vafa, Strominger, Minwalla and Motl are full-time string theorists and Randall and Arkani-Hamed do more phenomenological work, work whose justification is often given in terms of string theory. This just leaves Georgi remaining, and at the moment he has his hands full dealing with the fact that the president of Harvard is a sexist buffoon.

For Vafa to accomplish this undoubtedly took some single-minded dedication to furthering the interests of string theory and thwarting its opponents, but now that string theory so overwhelmingly dominates the field, it’s pretty disturbing to see him continuing to behave like a complete fanatic. I’ve been told that after Brian Greene’s Nova TV show about string theory came out, Vafa was heard to say that he didn’t care if it was any good; as far as he was concerned anything that promoted string theory was great. He’s quoted in the article as saying

“Theoretical developments have indicated string theory is a very important part of physics,” Vafa said. “It has already proven foolish. It’s past the point.”

I’m guessing there’s a typo here, one assumes he doesn’t mean that string theory is foolish, but that opposition to it is. He completely ignores the argument that string theory has not predicted anything and thus is not science, calling people who make this argument “childish”. His arrogant attitude towards those who don’t believe what he does is pretty breath-taking, matched only by that of his younger colleague Lubos. He finally dismisses the whole BU physics department with the logically incoherent:

“I think they are doing a disfavor to BU. I don’t want to pass judgment, but not having a string theory group puts [BU physics] out of first rate in my opinion.”

I think he does want to pass judgement and already has. If you’re a theorist who might someday have to deal with him as someone evaluating your grant proposal, deciding whether to hire your student, etc., do you think you might think twice before making a “childish” or “foolish” public comment about what is going on in string theory these days?

There’s a new TV show called “NUMB3RS” starting tonight, whose main character is a mathematican named “Charlie”, who solves crimes using mathematics. His motto is “Everything is Numbers”.

A secondary character is “Larry”, a Caltech physicist working on 11d supergravity. In one scene he shows up trying to get mathematical help from Charlie, whose graduate student sneers at him “Why don’t you do your own mathematics, like Ed Witten or Feynman?”.

Robbert Dijkgraaf is about the most lucid expositor around on the topic of what now goes under the name “topological strings”. This week he’s been giving the Coxeter Lectures at the Fields Institute in Toronto, and the slides and audio of his introductory talk are now available on-line. I hope there will be similar materials for his other, more detailed talks.

Last week the Fields Institute hosted a workshop on topological strings and the talks are on-line, although in many cases just the audio of the talk is available, which is pretty hard to follow.