Not Even Wrong

Someone wrote to me today to tell me that Harvard’s Nima Arkani-Hamed recently gave a lecture in Washington with the title “String Theory — Can We Test It?”. Somehow, I suspect that his lecture didn’t really give an honest answer to the question, since it would be hard to fill up an hour-long talk by just saying “No”.

Looking into this more carefully, it turns out that the talk was part of a “Dialogue on Science, Ethics and Religion” sponsored by the AAAS. At first I thought it was unusual to see a “Science and Religion” program paid for by anyone but the Templeton Foundation (for more about them, see here and here), but it turns out that they are the first organization listed in the list of those providing financial support for the program. I wouldn’t have guessed that the AAAS was in bed with Templeton and running programs on “Science and Religion”, but this kind of thing doesn’t surprise me anymore.

Arkani-Hamed’s talk was entitled: Naturalness versus the Superstring Landscape, or, Why Does The Universe Appear Finely Tuned? (not sure why it was advertised with the “String Theory — Can We Test It?” title). The organizer and “respondent” was James B. Miller, an ordained Presbyterian minister with a Ph. D. in Theology from Marquette University. From the abstract it appears that the talk involved Arkani-Hamed’s usual claims that split supersymmetry makes “sharp experimental predictions” for what the LHC will see (he seems to have a rather different notion of what an experimental prediction is than most scientists, much less what a “sharp” one is). He also seems to have implied that the superstring landscape scenario predicts split supersymmetry, something that actually isn’t the case, or at least is only true in the sense that the landscape predicts nothing at all, and thus is consistent with anything.

This past weekend I was in Cambridge and attended many of the talks at the JDG conference held at Harvard. The conference was nominally in honor of Shiing-Shen Chern, who died late last year, so many speakers made some connection between their work and Chern’s, especially his work on Chern classes.

Among the purely mathematical talks I attended was a very clear one by Victor Guillemin on Morse theory and convexity theorems on symplectic manifolds. The material he covered is quite beautiful, but rather old by now. His reason for covering it seemed to be that he has a new book on the topic (with Reyer Sjamaar) called “Convexity Properties of Hamiltonian Group Actions”, soon to appear from the AMS in the CRM monograph series, but also available on Sjamaar’s website.

Mike Hopkins gave an impressive talk on “Derived Schemes in Stable Homotopy Theory” which was based on very recent work by his student Jacob Lurie. This work involves defining a notion of a scheme which makes sense in the context not of the commutative rings of algebraic geometry, but instead the commutative rings of spectra in stable homotopy theory. It allows a new construction of the tmf (topological modular forms) theory of Miller and Hopkins.

Iz Singer reminisced about taking a class in geometry from Chern at Chicago in 1949, a class which he thought may have been the first one Chern taught in the US. Singer’s talk was about “Projective Dirac operators” which have an index which is a fraction. One of the main motivations for Singer’s original work with Atiyah on the Atiyah-Singer index theorem was to understand the integrality of the A-hat genus on a spin manifold as coming from the fact that it was an index. On a non-spin manifold the A-hat genus takes on fractional values, and one can use this to prove the non-existence of a spin structure. In work with Mathai and Melrose, pseudo-differential operator techniques are developed that allow one to define a sort of index in these situations where there is no spin (or even spin-c) structure.

There were several talks by physicists, or related to physics. One was by Kefeng Liu, half of which was about some new metrics on moduli space, the other half about some formulae coming out of work on topological strings. For this material, see his talk at last year’s Yamabe Conference. Vafa gave a talk on “Topological M-theory”, which he motivated by starting with the holomorphic anomaly in the topological string B-model. For quite a while it has been known that you can think of these topological string results as giving a vector in the Hilbert space one gets from quantizing H^3(M), where M is a Calabi-Yau. Topological M-theory is supposed to be something related to topological string theory in much the way the full M-theory is related to the full-string theory, so involves one-dimension higher. Thus it deals with 7-dimensional manifolds and tries to explain some of the phenomena related to topological strings on 6-d Calabi-Yaus in these terms. For more about this, there’s a talk by Andrew Neitze on-line that covers some of the same material.

Nikita Nekrasov’s talk was about “Z-theory”, which is his own name for the same ideas about topological M-theory that Vafa was talking about. He drew a version of the standard picture of the M-theory moduli space, now for Z-theory and with all sorts of mathematical objects attached to the various cusps. Nekrasov gave a similar talk in Nagoya late last year, as well as one at Strings 2004.

While a lot of interesting mathematics has come out of topological strings, the idea that that there is some grandiose unification involving thinking about 7d G2-manifolds seems to me even less promising than the idea of 11d M-theory itself, which for years now seems to have gone nowhere. Just as M-theory has led many physicists to pointless wanderings in 11-dimensions, it now seems to be leading mathematical physics away from rather rich mathematical areas into the complicated geometry of seven dimensions. Undoubtedly this will lead to some new mathematics, but it looks to me like it will be much less interesting than the mathematics emerging from string theory during earlier periods. The interaction between mathematics and physics remains dominated by the ideology of string/M-theory, and this is harming both subjects.

One aspect of the sad state of the interface between math and physics is that virtually no one from the physics department at Harvard seemed to be attending the JDG conference lectures. I’d been expecting to see at least Lubos Motl there, but he was down at Columbia attending a meeting on string cosmology. He reports on the talks here, here, and here, as usual covering very critically a talk on loop quantum gravity, quite uncritically one about the landscape and absurdly baroque constructions that try to make some contact with the standard model. I’m beginning to believe that his “leashing” did have something to do with his criticizing the landscape ideology too vigorously, since he seems to have stopped doing that.

For the latest on the landscape, see a recent talk by Lubos’s senior colleague Arkani-Hamed (whom he better not piss off too much) at the PHENO 05: World Year of Phenomenology symposium in Wisconsin, entitled The Landscape and the LHC. Arkani-Hamed’s talk begins with the usual strained historical analogy, this time a long and bizarre description of the calculation by Aristarchos of the distance to the sun by the method of parallax. The point of this is highly obscure, but seems to be that since Aristarchos was wrong to find unreasonable the huge distances to the stars implied by the lack of visible parallax, we’re wrong to find unreasonable the huge amounts of fine-tuning required by split supersymmetry.

He goes on much like Susskind for quite a while about the glories of the landscape idea, with the twist that supposedly split supersymmetry is “sharply predictive”. The only “sharp” predictions he mentions concern a relation between some coupling constants which haven’t been observed and likely never will, as well as that there may be a “long-lived” gluino. Not that he actually has a prediction for the mass or lifetime of this gluino.

Quite a few people have written in to point out to me a recent paper by some condensed matter physicists about the possibility of trapping a fermionic atomic gas in a vortex inside a Bose-Einstein condensate. As far as I can tell, about the only thing this has in common with superstring models of quantum gravity and elementary particles is that their abstract starts the same way as many superstring abstracts: “Supersymmetric string theory is widely believed to be the most promising candidate for a ‘theory of everything'”. This article has gotten wide attention in the press and on the internet at Slashdot which informs us that this will “(provide) the first experimental evidence to support superstring theory.” At Slashdot you can also read comments from large numbers of confused souls who now believe that experimental confirmation of superstring theory is right around the corner. Obviously this is about as absurd as believing that the existence of my shoelaces provides excellent experimental confirmation of the existence of open strings.

Another weird related phenomenon is the wide-spread idea that violin strings somehow have something to do with superstring theory. For some reason it always seems to be violin strings rather than, say, electric guitar strings. Maybe string theory would be more popular if it would make the connection with a more popular music form. The violinist Jack Liebeck has been going around with physicist Brian Foster, with Liebeck giving concerts in which he “demonstrates superstring concepts on his violin.” The performance ends “with a duet for two violins in which lecturer and soloist join forces to illustrate the production of mini Black Holes” at the LHC. I really think an electric guitar would be a lot better for this purpose.

These performances are taking place at dozens of locations around the world, are somehow part of “World Year of Physics 2005”, and supposedly educating people about science. They invoke the memory of poor Albert Einstein, implying that he has something to do with superstring theory since he played the violin and searched for a unified theory. Unfortunately Foster and Liebeck don’t seem to be coming to New York, although they were at Cornell this past weekend.

Along the same lines, for something truly weird, get a copy of Einstein’s Violin: A Conductor’s Notes on Music, Physics and Social Change, by Joseph Eger, the music director of the Symphony for United Nations. This book, besides also invoking poor Einstein, goes on in an extremely repetitive fashion about how superstring theory shows that music and fundamental physics are all the same thing. Eger has all sorts of original insights including for instance:

“Science had its heyday during Sputnik and then gradually faded until the eighties, when string theory came to the fore.”

“Religious fundamentalists, big business, and politicians, especially of the neo-conservative variety, have been quick to appropriate quantum mechanics and a perversion of the new music to sell their fundamentalist religion, anti-Darwin ideologies, and biological nightmares.”

“On this cosmological scale, and since we are postulating that the universe is music and that music expresses and explains the universe, then we can take the next logical step, that music could hold the key to a T. O. E.”

Evidently Witten is guilty of at least not discouraging the author, a sin for which I hope he is punished by having to read this book:

“One day in the eighties, driving with Ed to New York from Princeton, he responded to my question about what he was working on by excitedly telling me about string theory and its ten or more dimensions. Bewildered yet emboldened by this brilliant scientist, I tentatively spoke of my theory that the universe is made of music. Half expecting polite derision, he thought for a few seconds and calmly responded affirmatively.”

When I first started studying quantum mechanics I read quite a bit about the remarkable history of the subject, especially about the brief period from 1925-27 when the subject grew dramatically out of the incoherent ideas of the old quantum theory to the full quantum mechanical formalism that is still taught today. This was the work of a small group of physicists: especially Heisenberg, Born and Jordan in Göttingen, Schrödinger in Zurich, Dirac in Cambridge, and Pauli in Hamburg. Recently I’ve been reading again about some of this history, but paying attention especially to the interactions of mathematics and physics during these years. An excellent very recent article that covers some of this is by Luisa Bonolis, entitled “From the Rise of the Group Concept to the Stormy Onset of Group Theory in the New Quantum Mechanics”. (It seems that this link is inaccessible unless you’re at a university site that has a subscription. The article should also be available at most physics research libraries as vol 27, numbers 4-5 of the 2004 issue of Rivista del Nuovo Cimento.)

I’ve written a bit about this history before, especially about the mathematician Hermann Weyl’s role, but quite a few other mathematicians were closely involved, including Hilbert, von Neumann, Emmy Noether, and van der Waerden. Much of the interaction between mathematicians and physicists took place at Göttingen, where Hilbert was the leading mathematical figure, and Weyl was sometimes a visitor, with both of them lecturing on quantum mechanics. This period was very much a high point of the interaction of mathematics and physics, interactions of a sort that were not seen again until the 1980s. Heisenberg and his collaborators learned about matrices from Hilbert and the other mathematicians at Göttingen, and Weyl was responsible for educating physicists about group representation theory and turning it into an important tool in quantum mechanics.

The Bonolis article has some amusing quotes from physicists who were having trouble absorbing what the mathematicians were telling them. Heisenberg wrote to Jordan “Now the learned Göttingen mathematicians talk so much about Hermitian matrices, but I do not even know what a matrix is,” and to Pauli “Göttingen is divided into two camps, those who, like Hilbert (or also Weyl, in a letter to Jordan), talk about the great success which has been scored by the introduction of matrix calculus into physics; the others, like Franck, who say that one will never be able to understand matrices.” Pauli was scornful about this new, unphysical, mathematical formalism of matrices, drawing a testy response from Heisenberg: “When you reproach us that we are such big donkeys that we have never produced anything new physically, it well may be true. But then, you are also an equally big jackass because you have not accomplished it either.”

Immediately after having to get used to matrices, physicists were confronted by Weyl with high-powered group representation theory, which they found even harder to understand than matrices. Famously, Pauli referred to the group theory that mathematicians were talking about as the “Gruppenpest”, but the late twenties saw a very fruitful exchange of ideas between mathematicians and physicists around this topic. Weyl’s proof of the Peter-Weyl theorem and von Neumann’s work on representation theory grew out of quantum mechanics, and the Brauer-Weyl theory of spinor representations was inspired by Dirac’s work on the Dirac equation.

It’s also interesting to note how in the years just preceding this period, much interaction between math and physics had grown out of general relativity. Noether’s work on what is now known as the Noether theorem came about because she was asked questions by Einstein and Hilbert who were trying to sort out conservation laws in GR. Weyl took up representation theory as a result of his work on the symmetries of the curvature tensor.

An amusing story I hadn’t heard before that is in the Bonolis article was one told by Edward Condon about Hilbert. He claims that when Born and Heisenberg went to Hilbert to get help with matrices, he told them that “the only times that he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert did not know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger’s wave mechanics six months earlier if they had paid a little more attention to him.”

I’ve recently run across various interesting mathematically oriented sites, each with some connection to physics:

Alain Connes now has a web-site. He’s now a professor at Vanderbilt University as well as at the College de France. I can see him in Robert Altman’s movie “Nashville”. His site contains quite a few interesting things, including most of his research articles and some interesting survey articles about his work on non-commutative geometry. For instance, take a look at his “A View of Mathematics”, which starts off with a wonderful description of doing mathematical research and some interesting history of geometry, before surveying his recent work relating non-commutative geometry and physics.

David Ben-Zvi at Austin is organizing a new lecture series to be made available over the web called GRASP (for Geometry, Representations and Some Physics), which sounds promising although it is just getting started.

The MIT math department sponsors something called the Talbot workshops. Last year the topic was elliptic cohomology, this year geometric Langlands. Notes from the lectures are available courtesy of Megumi Harada who also maintains a useful website of geometry conferences, many of which have some sort of physics component.

Lubos Motl has taken to signing some of his postings with “leashed”, and Capitalist Imperialist Pig has speculated that “My dark suspicion is that he might have gotten caught in a PC violation in the Summers Affair, forcing him to do a T reversal to save his Lorentz invariant m ass”. Lubos wrote in to tell him “Unfortunately your intuition is perfectly correct, but I am not sure whether your imagination is big enough to imagine the scale.”

I have no idea who is responsible for the leashing of Lubos or what the reason for it is, but I figured this meant his blog would stop featuring the right-wing ideological political commentary he’s fond of. But today he has a posting about the Frist Center “filibustering” in which he says “I currently do not enjoy the freedom to tell you what I think about these things.” Actually he manages to make it pretty clear what he thinks about these things.

This leashing of Lubos is too bad, especially since I was finding myself more and more in agreement with his postings (not the ones about politics, but we seem to agree about the Landscape), and generally think the First amendment gives everyone the right to make a fool of themselves with crazed political rants if they feel like it. Lubos’s blog has also played another important role for me. Whenever people won’t believe me that string theorists can be smart and well-informed, but still crazed ideologues, all I’ve had to do is point them his way.

For the last couple days students at Princeton have been protesting the Republican’s plan to invoke the “nuclear option” and stop Democrats from filibustering a small number of Bush’s judicial nominees. This protest has taken the form of organizing a “filibuster” in front of the Frist Campus Center at Princeton, which was underwritten by Senator Bill Frist (Princeton ’74). Today Edward Witten and his wife, physicist Chiara Nappi, have joined the protest. I can’t tell what Chiara is reading from, but Ed is using a bullhorn to regale the crowd with passages from Introduction to Elementary Particles by David Griffiths.

Many thanks to my correspondent who wrote to me today to tell me about this.

Update: It seems that Josh Marshall of the Talking Points Memo weblog had something to do with this. Ed and Chiara got awarded a Privatize This! Talking Points Memo t-shirt, and there are still two more available.

According to a new article in New Scientist entitled The Theory of Everything: Are we nearly there yet? (unfortunately not available for free on-line), “The hunt for the theory of everything is turning into a road trip from hell – and don’t even ask who’s reading the map.” The article quotes Susskind and Weinberg as believing in the existence of a multiverse, even if this means that “all we can hope for from a final theory is a huge range of possibilities”.

Witten is referred to as a “string grandee”, and quoted as saying about string theory “More work has always given more possibilities – far more than anyone wanted… I hope that current discussion of the string landscape isn’t on the right track, but I have no convincing counter-arguments.” He’s welcome to my counter-arguments if he wants them: there’s not the slightest evidence for the landscape scenario pseudo-science, it’s incredibly ugly, not based on any kind of well-defined theory, explains nothing, and holds out no reasonable hope of ever explaining anything.

The article goes on to discuss the wishful thinking surrounding “M-theory”, quoting Witten as believing that M-theory may have a unique solution that fits our universe and explains the constants of the standard model. “Hope springs eternal” he says. Somebody seems to have given the writer the idea about M-theory that “theorists can prove that it exists as a mathematical construction, but they can’t actually write down its equations and there is no clear route towards doing so”, which is only true under a peculiar interpretation of the words “prove”, “exists”, and “it”. Lisa Randall is quoted as follows about M-theory: “We probably need fundamentally new principles… it’s not hopeless, but it’s going to require some deep new insight that we don’t really have.” She promotes her own work with Mukohyama on an alternate explanation of the cosmological constant.

The only person quoted in the article as thinking that there may be any problem at all with the way particle theory has been pursued for the last twenty years is Lee Smolin, who takes the absolute lack of any experimental evidence for string theory as a sign that the field may be off on the wrong track. He notes that “If you look back over the last 200 years, every decade or two there’s a dramatic advance, people always understand something new that couples theory and experiment… I suspect there is some right question that we’re not asking.”

Everyone in the particle physics community is avidly awaiting the startup of the LHC accelerator at CERN, scheduled for 2007. A new preprint by Gianotti and Mangano entitled LHC physics: the first one–two year(s) gives some idea of what to expect.

The design luminosity for the LHC is about 10³⁴cm^-2s^-1, which is about 100 times the current luminosity of the Tevatron. Current plans are to first cool down the machine in spring 2007, followed by commissioning single beams over the next few months, with first colliding beams in the second half of 2007. During 2007, most effort will be devoted to commissioning the machine, followed by a shutdown for a few months. A seven-month long physics run at luminosities of up to 2 x 10³³cm^-2s^-1 will take place during 2008. This is 20 times the current Tevatron luminosity and the Tevatron seems to be averaging a total of about 15 pb^-1 per week, so one could expect a total luminosity of up to about 10 fb^-1 to be collected during 2008. This is probably much too optimistic. Experience with the Tevatron when it was turned on at the beginning of its latest run was that for quite a while it was running at only a tenth of the hoped for luminosity. So perhaps 1 fb^-1 during 2008 is a more realistic expectation.

According to Gianotti and Mangano, 1 fb^-1 will be enough to see squarks and gluinos at masses of up to about 1.5 Tev. Seeing the Higgs is more demanding, especially if its mass is low. If its mass if above 180 Gev, it should require 5-10 fb^-1, if it is just above the LEP limit (114 Gev) it is likely to require more like 20 fb^-1.

Personally I think it’s quite unlikely the LHC will be seeing supersymmetric particles, so, of the things it is looking for, it will require good luck to get the data required to see the Higgs during 2008. Even if this does happen, I’d guess that analyzing the data would take us into 2009. If the LHC has trouble getting anywhere near design luminosity, things could take longer. Of course everyone hopes that something completely unexpected will be found. If this is dramatic enough, maybe there will be some exciting news in 2008.