Not Even Wrong

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.”

From Sean Carroll’s weblog I see that he’s in Austin now for a session at a meeting of the Philosophy of Science Association. Philosophers of science seem to actually write up their talks in advance, and many of the talks for this meeting are already available online. Poking around on their website with papers from earlier conferences, I ran into one on Scientific Realism and String Theory by Richard Dawid.

Dawid appears to have swallowed the hype about string theory hook, line and sinker. He believes that string theory exhibits a new paradigm of how to do physics, one where the idea of being able to calculate anything about the real world and compare it to observations is passe. All that matters now is “theoretical uniqueness”, that one’s theory is the only possible one. He doesn’t seem to notice that there’s something kind of funny about people claiming that they have a wondrous unique theory, but don’t know quite what it is and can’t calculate anything about the real world with it. The S-matrix theorists of the 60s also promoted the idea that they had a wondrous unique theory, but didn’t know quite what it was. Probably one can dig up philosophy of science articles from that period about how a whole new paradigm of how to do science was required.

Dawid also seems to believe that the dualities of M-theory imply the “dissolution of ontology”, that “the ontological object has simply vanished”. In reality, what has vanished is not the ontological object, but the theory.

Over at Robert Helling’s web-site you can read an example of the latest philosophical excuses about why string theory now can’t predict anything, together with implausible wishful thinking about how this might change since “It’s just at this stage we are not yet powerful enough to make these kinds of predictions”.

For the life of me I can’t figure out why smart physicists and philosophers can’t see the obvious fact that is staring them in the face. You don’t need a new paradigm of how to do science, the old one works just fine. If you have a conjectural theoretical scientific idea, there are two ways in which it can turn out to be wrong. Either it predicts something that disagrees with experiment, or it is so vacuous that it predicts nothing. The evidence is now overwhelming that, if string theory is consistent at all, it is wrong for the second reason.

Update: Dawid actually has a whole fancy web-site about Realism and String Theory. He also has a newer paper on Undetermination and Theory Succession from a String Theoretical Perspective.

The PhilSci archive does have another paper about string theory, one by Reiner Hedrich entitled Superstring Theory and Empirical Testability. Hedrich is much less credulous than Dawid, noting about superstring theory “above all, it has fundamental problems with empirical testability – problems that make questionalbe its status as a physical theory at all.”

The KITP at Santa Barbara is holding a conference on QCD and String Theory this week, and the talks have started to appear online.

Of the ones I’ve taken a quick look at so far, there doesn’t seem to be any obvious recent progress on the 30-year old main question that everyone would like the answer to: can one find a reliable analytical technique for dealing with QCD in the infrared regiion where the effective coupling is strong? The best hope for this in recent years has been the AdS/CFT correspondence, but after seven years the state of the art there still seems to be a long ways from solving the problem one wants to solve (although it does give solutions to other problems). I’m looking forward to seeing what some of the later talks will have to say, including Larry Yaffe’s one tomorrow on “Large N gauge theories: old and new”.

Martin Veltman gave a colloquium talk at Fermilab two weeks ago and, as usual, had some very provocative comments to make. At the end of his talk he made the claim that the only thing astrophysics has contributed to particle physics is information about the number of neutrinos (from Helium abundance observations). He claims “Apart from this, Astrophysics is so far useless to us.”

He then gave some purported data about how particle physicists really felt about the impact of astrophysics and cosmology on their field. His slides say:

“Question put to many particle physicists: Do you feel that astrophysics and particle physics are joined at the hip?

Response:

Refusing to respond on the grounds that it is an obscene proposition (99.9%)
Do not know what you are talking about (9.671%)
Undecided (rest)

Questions put to particle experimenters:

Your experiment is justified by claiming that it will tell us about the first seconds of the big bang. Do you agree?

Response:

No (98.312%)
Do not know what you are talking about (1.671%)
Undecided (rest)

Do you feel that we need a new machine (linear collider) because it can be used to discover dark matter (dark energy)?

Response:

No (98.312%)
Do not know what you are talking about (1.671%)
Is this related to the death star of Darth Vader? (3%)
Undecided (rest)”

I think Veltman has a very good point. The particle physics community seems to have decided to try and sell the public on supporting particle physics, specifically a new linear collider, by claiming that such a machine will “solve the mystery of dark energy”, find “extra dimensions of space”, and tell us “how the universe came to be” (see for instance the HEPAP Quantum Universe report). This all sounds very sexy, but there’s no good reason to believe that a linear collider will do any of this. Maybe this is the right way to sell the linear collider, but personally I’m rather uncomfortable with this level of hype and wouldn’t want to be the one testifying under oath before Congress about this.

Veltman also comments that “It appears to me that the only viable solution is that this machine will be located in the US”, but given the massive deficit the Bush administration has created and current political realities, I find it hard to believe we’ll see the kind of budget increases for particle physics that would be required to make this happen anytime soon.

The Jacobian Conjecture is one of the most well-known open problems in algebraic geometry. It now seems that a proof has been found by Carolyn Dean of the University of Michigan, for the case of polynomials in two complex variables (for more variables, many people believe it is not even true). For more information about this, see Graham Leuschke’s weblog.

Dean hasn’t published any papers in almost 15 years and is nominally a lecturer in mathematics education at Michigan. There have been many false proofs of this conjecture over the years, and if this one holds up it will be quite a story. The paper doesn’t seem to be publicly available yet, but Dean will be lecturing on the proof at Michigan next month. One of the experts in the field, Mel Hochster, has gone over it carefully and is convinced it is correct. The rumor I hear is that it has been submitted for publication to the Journal of the American Mathematical Society.

Update: There’s an announcement of Dean’s talks posted on sci.math.research.

Update: Someone wrote in with a comment to another post pointing out that Dean has found a hole in her proof. For some more information about this, go here.

At his talk last year at the conference in honor of Gelfand’s 90th birthday, Atiyah posed the question of whether there is a quantum field theoretic explanation of why the coefficients of the Jones polynomial are integers. Witten’s Chern-Simons-Witten theory is a 3d QFT that computes the Jones polynomial (a topological invariant of knots or links inside a 3d manifold), but gives no obvious reason the coefficients should be integral.

One thing about the Chern-Simons-Witten story that has always bothered me is that, unlike his other TQFTs, this one is not of a homological nature. In the other TQFTs, the Hilbert space is finite dimensional because there are fermionic variables which cause cancellations such that only the homology of some complex contributes to the observables. To make any real sense of the idea of a path integral whose Lagrangian is the Chern-Simons functional, one has to do something like add a Yang-Mills term, then take a limit. By doing this one can move all but a finite part of the usual gauge theory Hilbert space off to infinite energy. It would be very interesting if there were a version of the theory which instead worked homologically like other TQFTs.

A hot topic in low dimensional topology recently has been the notion of “Khovanov homology”, which associates to a knot a complex whose homology is the Jones polynomial. For an introduction to Khovanov homology, see papers by Dror Bar-Natan (a mathematician who was a student of Witten’s) or Jacob Rasmussen. Bar-Natan has a lot of other material about Khovanov homology on his web-site.

One way of answering Atiyah’s question would be to find a 4d TQFT whose Hilbert space is the Khovanov homology of the boundary. Maybe there is some sort of gauge-theory based QFT which generalizes the Chern-Simons-Witten theory and computes Khovanov homology. But after consulting the local expert on these things (Peter Ozsvath), it seems that no one knows whether it is even possible to reformulate Khovanov homology in any sort of gauge-theoretical terms. The only known definitions of it are kind of like the pre-Witten skein relation definitions of Jones polynomials. They are based on working with a projection of the knot onto two-dimensions.

A couple weeks ago Sergei Gukov gave a talk in the math department at UCSD with the title “Topological Invariants and Khovanov Homology”, and perhaps his work has some relation to the above speculations.

Gukov is also the co-author of a paper that just appeared on the arXiv entitled “Topological M-theory as Unification of Form Theories of Gravity”. Like M-theory itself, it appears that no one knows what “topological M-theory” is, but it is supposed to be some sort of seven-dimensional theory that is related to topological strings on 6d Calabi-Yaus in much the same way M-theory is a conjectural 11d theory related to 10d superstrings. Lubos Motl has even more questions about this than I do.