Not Even Wrong

Via Slashdot, an article that seems quite relevant to the current situation of string theory.

Earlier this week Jonathan Dorfan, the director of SLAC, announced a reorganization of the structure of the laboratory. The new structure involves four divisions, two scientific and two operational. One of the scientific divisions will bring together particle physics and astrophysics. It will be led by Persis Drell who also will be a deputy director of the laboratory, a position previously held by her father, particle theorist Sidney Drell. The other scientific division will be called “Photon Science”, which will make use of the SLAC x-ray sources. At the moment SLAC produces intense x-ray beams at the SSRL, using synchrotron radiation from a ring which is a descendent of the original SPEAR electron-positron ring that was crucial in the “November Revolution” of 1974 (and which also provided me with a job one summer).

The main SLAC linac is being turned into a free electron X-ray laser to be called the Linac Coherent Light Source (LCLS), which will be operational in 2009. At that time the plan is for SLAC to be out of the accelerator based high-energy physics business, with the PEP-II collider also shut down. The last fixed target experiment using the linac, E158, recently reported the most accurate measurement of the weak mixing angle at relatively low energies (at LEP it was very accurately measured at the Z pole). This measurement shows the running of the ratio of coupling constants predicted by the renormalization group. For more about this experiment, see an article in the latest Nature magazine.

This week’s Science magazine also has an article about particle physics. It reports on the HEPAP meeting mentioned here earlier where a plan to evaluate whether to shut down PEP-II or the Tevatron early was put forward. On a more positive note, the House Appropriations committee has restored some of the cuts in the FY 2006 DOE budget proposed by the White House. The House committe added $22 million to the high energy physics budget, bringing it back to the FY 2005 level (which, accounting for inflation, would still be a cut, but a smaller one).

An article in New Scientist about the same House bill explains that money is being taken away from the ITER international project to build a fusion reactor and used to bring funding for domestic fusion research also back to FY2005 levels. This may have something to do with the fact that the latest news about ITER is that a deal has been reached that will site it in France.

Last Wednesday night, a paper appeared on the arXiv that spelled very bad news for the whole “Landscape” scenario of how to get physics out of string theory. This paper produced what appears to be an infinite number of possible vacuum states for string theory, ruining hopes for getting predictions out of the Landscape by doing a statistical analysis of vacuum states.

Tonight a new paper by a prominent Landscapeologist (Michael Dine) has appeared. The abstract gives no hint of trouble, claiming evidence of “distinctive predictions for the structure of soft breakings”, but the beginning and the end of the paper tell a different story. The second paragraph of the paper admits that the infinite number of states destroys this research program, but deals with this by saying that the author will just ignore the problem for now:

“If this (infinite number of states) is true, many of the ideas discussed in this paper will have to be reconsidered…. the discussion of this paper will be predicated on the assumption that the number of relevant states in the landscape is finite and naive statistical ideas can be applied.”

In the paper’s conclusion, Dine states:

“There are many ways, as we have indicated, in which the ideas described here might fail. Perhaps the most dramatic is that the landscape may not exist, or alternatively that there might exist infinite numbers of states, whose existence might require signficant rethinking of our basic understanding of string theory and what it might have to do with nature.”

I’m looking forward to Dine and others finally getting around to “rethinking what string theory might have to do with nature”. It’s about time.

The US High Energy Physics Advisory Panel (HEPAP) is meeting in Washington yesterday and today, and some of the presentations are already available on-line. These include one from the DOE Office of High Energy Physics which notes that, given budgetary constraints, the only way significant funds will become available for new projects (including significant work on the proposed ILC linear collider), is by shutting down operations at the Tevatron or PEP-II. The Tevatron is now scheduled to operate until 2009 (at which point it can’t compete with the LHC), PEP-II at SLAC until 2008. The DOE is asking the P5 committee to advise about whether or not it might be a good idea to shut these facilities down early, and redirect the funds that are freed up elsewhere.

There are also reports on the status of PEP-II and the Tevatron. PEP-II and other accelerators at SLAC were shut down after an accident last October, only turned back on last month. The plan now is to run the machine steadily until July 2006, with only a one-month break in October. Presumably it’s down today, since if you try and connect to the SLAC web-site, you get a message saying that power is out at SLAC due to a tree falling and severing the main power feed to the site.

The Tevatron is doing well this year, recently achieving record luminosity, and its integrated luminosity so far this year is running ahead of even optimistic projections. It seems highly unlikely to me that the P5 committee will suggest shutting it down early.

There’s also a report from the ongoing National Academy of Sciences EPP2010 study of the future of US particle physics. Presentations from a meeting earlier this week at Fermilab are now available. These include presentations dealing with what is going on outside the US, including ones from DESY in Germany and KEK in Japan.

The biggest issue facing US particle physics is what to do about the International Linear Collider (ILC) project. In the presentation of Michael Witherell (ex-director of Fermilab), he notes that the world is in a transition from having five major labs running the largest accelerators to possibly only two: CERN with the LHC, and wherever the ILC is sited, if it is built. For US experimental high energy physics to remain a world leader, it is crucial that the ILC be built, and built in the US. Witherell recalls how the US HEP budget has declined by $100-150 million in real dollars over the last few years, but then gives a plan for the future that involves this budget increasing by 4% over inflation every year, something I find hard to believe is going to happen. The EPP2010 site also contains feedback they have received from various members of the community in response to questions about plans for the ILC.

In other experimental HEP news, the Experimental High Energy Physics Job Rumor Mill has been revived, joining the Theoretical Particle Physics Jobs Rumor Mill. Send them both your inside information!

Shamit Kachru (described by Lenny Susskind as the “master Rube Goldberg architect”) and collaborators have a new paper out this evening on flux compactifications, one that in a rational world should finish off the subject completely. Recall that Kachru is one of the K’s responsible for the KKLT construction of these flux compactifications that stabilize all moduli, and for the last couple years debate has raged over whether this sort of construction gives 10¹⁰⁰, 10⁵⁰⁰ or even 10¹⁰⁰⁰ possible string theory vacuum states.

Susskind, Arkani-Hamed, and other anthropic principle aficionados have argued that the fact that this number is at least 10¹⁰⁰ is a great triumph because it means that there are so many vacua that at least some will have small enough cosmological constant to be consistent with our existence. But if there are too many, all hope of getting predictions out of string theory disappears. With 10¹⁰⁰⁰ vacua, you can find not only the cosmological constant you want, but probably any values of anything particle experimentalists have ever measured or ever will measure, and the theory becomes completely unpredictive.

Even so, the study of these vacua has become more and more popular over the last year or two, with many arguing that, no matter how big the number is, at least it’s finite, so you have improved over the standard model, which has continuously tunable parameters. This argument was made in the panel discussion at the Perimeter Institute a month or so ago. Also, a finite number of vacua allows you to study their statistics, by assigning a weight one to each possible vacuum state and getting a probability measure by dividing by the total number. You can then engage in wishful thinking that this probability measure will be peaked about certain values, giving a sort of prediction.

The new paper gives a construction of flux compactifications of type IIA string theory, and in this case the authors find an infinite number of possibilities. This should kill off any hopes of extracting predictions from string theory by counting vacua and doing statistics. The authors try and put a brave face on what has happened, writing:

“we should emphasize that the divergence of the number of SUSY vacua may not be particularly disastrous. A mild cut on the acceptable volume of the extra dimensions will render the number of vacua finite.”

but then they go on to puncture their own argument by noting that:

“one can legitimately worry that the conclusions of any statistical argument will be dominated by the precise choice of the cut-off criterion, since the regulated distribution is dominated by vacua with volumes close to the cut-off.”

With this new result, the infinitesimally small remaining hope of getting predictions out of the string theory landscape framework has now vanished. It will be interesting to see if this slows down at all the ever-increasing number of string theorists working in this field.

Update: Lubos Motl has some comments about this same paper.

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.”