Not Even Wrong

I’ve criticized the Templeton Foundation in the past for their endless attempts to blur the line between science and religion, supporting some of the most dubious research in cosmology and physics. To be fair to them, at least they are not promoting Intelligent Design, something they make clear in a statement released on Monday. The statement challenges a front-page Wall Street Journal story that referred to Templeton as a supporter of ID. Evidently one of the main pieces of evidence that the Wall Street Journal gave for this was Templeton’s support of IDer Guillermo Gonzalez as part of their Cosmology and Fine-Tuning Research Program.

So, if you’re interested in seeking funding from Templeton, you’d be aligning yourself with an organization controlled by right-wingers that wants to bring religion into science, but they’re not IDers. If you decide to go for it, it looks like Dec. 1 is the day when fq(x), a Templeton funded program run by highly reputable physicists, will announce how to apply for money from them. If you just want to extract money from Templeton for something completely flaky, I’d suggest considering another new program they are funding, Science and Theology Advanced Research Series (STARS), devoted to research “on the ways science, in light of philosophical and religious reflection, points towards the nature, character and meaning of ultimate reality.” It appears that, if you play your cards right, you can get a free winter break in Cancun, as well as grants of \$20,000 in walking around money and multiples of \$100,000 to look into this ultimate reality thing.

There’s an interesting guest posting from Lawrence Krauss over at Cosmic Variance. I think I’ll turn off the comment section on this posting here, since if people want to discuss this, it is probably best done over there.

Yesterday, Princeton University, as part of an effort to bring physics to a wide audience during the centennial of Einstein’s great work of 1905, sponsored a performance of Superstrings. This event featured a lecture by Oxford physicist Brian Foster as well as a performance by violinist Jack Liebeck, and it was one in a series of such events that have taken place around the world.

I’ve always wondered what non-physicists come away thinking after being exposed to things like this. There’s not much real scientific content, lots of wonderful music that has no real connection to the physics at issue, and many impressive analogies that could easily confuse listeners as to what the point of the analogy is. This time, one can see some of the effect the event had by reading an article about it in the Daily Princetonian.

The report recounts how the performers explained superstring theory:

“The concept of superstrings can be illustrated with a demonstration of quantum cookery,” Foster said, as Liebeck helped him into an apron. A mesh colander modeled the universe with very fine holes corresponding to fluctuations in the space-time continuum. Foster poured flour through the holes, exemplifying how point-like particles cannot be contained in the universe, making a “delicious mess” on the floor of the stage.

To complete the analogy, Foster introduced uncooked pasta in three different varieties, one for each generation of matter, which he nicknamed “quantum pasta” or “superpasta.” Although composed of the same ground-up grain as the flour, these “particles” avoided the problem of the point-like particles, staying contained within the colander.

Besides convincing at least some of the audience that supersymmetry is the idea of using uncooked spaghetti instead of flour, Foster did admit there was no evidence for any of this: “Superstrings may be purely philosophical and may have no measurable contributions to our universe”. It might have been more helpful if he’d mentioned that “purely philosophical” here really means “wrong”.

Some other facts about physics that the reporter learned yesterday are that:

gravity distorts the smoothness of Einstein’s continuum, a problem he attempted to resolve through quantum mechanics.

There are three “generations” of matter — the quark, lepton and boson.

Superstring theory will resolve the large discrepancies in the masses of these elementary particles.

All in all, it seems to me that these performances are not helping the public understanding of science, but rather signficantly setting it back. I’m sure that those bloggers who are highly concerned about the public understanding of science in general, and string theory in particular, will want to address this issue and demand the immediate cessation of events like this.

Last weekend Princeton held a Special Symposium in honor of Alexander Polyakov’s 60th birthday. Witten talked about his recent work on Langlands duality. He’ll also be speaking about this next week at Rutgers and December 1 and 2 up in Boston.

I hear from someone who attended the symposium that Gross gave a talk with title officially still TBA, but for which he said he’d use the title “Strings and Instantons”, since that is what all of Polyakov’s titles are. His theme was irresponsibility and he recalled around 1990 having dissuaded Polyakov from going to Santa Barbara and spending his time on the beach, getting him to come to Princeton instead. Of course Gross himself then soon left Princeton for Santa Barbara. Gross also said that, unlike his usual practice, he would end his talk on time since he didn’t have much to say due to being busy with the events of the past year.

On a completely unrelated topic, Fermilab recently held a celebration of the tenth anniversary of the discovery of the top quark, and the talks are on-line. Also on-line at Fermilab are some on-going lectures by Chris Quigg on The Electroweak Theory and Higgs Physics.

A wonderful long-promised paper by Dan Freed, Mike Hopkins and Constantin Teleman entitled Loop Groups and Twisted K-theory II has just appeared. They have advertised it in the past under various names such as “K-theory, Loop Groups and Dirac Families”, but their latest way of organizing their work seems to be to relabel the two-year old Twisted K-theory and Loop Group Representations (which recently has been updated, improved and expanded with new material) as “Loop Groups and Twisted K-theory III”. Working backwards it seems, they now advertise a “Loop Groups and Twisted K-theory I” as still to appear, hopefully in less than two years.

I don’t mean to give them a hard time about this. They are doing wonderful work, continually refining and improving on their results, and the paper is worth the wait. At the moment I don’t have time to do them justice by explaining much about their results or the conjectural relations that I see to quantum field theory, but I wrote a little bit about this a while back in another context. In the future I’ll try and find time to write some more entries about this material.

Also related to this is a new paper of Michael Atiyah and Graeme Segal called Twisted K-theory and cohomology which discusses the relation of twisted K-theory to twisted and untwisted cohomology.

Teleman has also recently made available on his web-site a preliminary version of notes from his fascinating talk at the algebraic geometry conference in Seattle this past summer, entitled Loop Groups, G-bundles on curves. He starts off with some philosophy he claims comes from lessons learned in working with moduli of bundles:

(i) K-theory is better than cohomology
(ii) Stacks are better than spaces
(iii) Symmetry

The first and third points I’m well aware of, and he has convinced me to spend some more time learning about stacks by his next point, which I hope may clarify some issues that confused me when I was writing my notes on Quantum Field Theory and Representation Theory. According to Teleman, the fundamental K-homology class of a classifying stack BG gives a notion of “integration over BG” in K-theory that corresponds precisely to that of taking the G-invariants of a representation. This idea has been a fundamental motivation for me for quite a while. It seems to me that one fundamental question about the path integral formulation of the standard model is “why are we looking at the space of connections and trying to integrate over it?” The K-theory philosophy gives a potential answer to this: we’re looking at the space of connections because it is the classifying space of the gauge group, and we’re integrating over it because we want to be able to pick out the invariant piece of a gauge group representation. I’ll try and write up more about this later, especially if learning some more about stacks ends up really clarifying things for me as I hope.

On a somewhat different topic, Teleman recently gave a very interesting talk at Santa Barbara entitled The Structure of 2D Semi-simple Field Theories.

John Baez has a very interesting new paper on the arXiv this evening entitled Calabi-Yau Manifolds and the Standard Model. In it he points out that the standard model gauge group (which he carefully defines as SU(3)xSU(2)xU(1)/N, where N is a six-element subgroup that acts trivially on the standard model particles) is the subgroup of SU(5) that preserves a splitting of C⁵ into orthogonal 2 and 3 dimensional complex subspaces. Furthermore, if you think of SU(5) as a subgroup of SO(10), then the spinor representation of SO(10) on restriction to the standard model group has exactly the properties of a single generation of the standard model.

Baez would like to think of SO(10) as the frame rotations in the Riemannian geometry of a 10d manifold X. The SU(5) is then the holonomy subgroup picked out by a choice of Calabi-Yau complex structure on the manifold. One way to get such an X is as the product of R⁴ and a compact 6-manifold M⁶, picking Calabi-Yau structures on both manifolds in the product. What is happening here is related to an old idea I wrote a paper about a very long time ago (see Nuclear Physics B, vol. 303, pgs. 329-342, from 1988). By picking an orthogonal complex structure on R⁴, one picks out a U(2) in SO(4) (the Euclideanized Lorentz group), and it is tempting to identify this with the electroweak U(2). This is one part of what is happening in Baez’s construction. It’s very hard though to see what to do with this within the standard gauge theory framework; this is true both for my old idea and for Baez’s newer one. Maybe string theorists can come up with some way of implementing this idea of thinking of the standard model gauge group in terms of the Riemannian geometry of the target space of a string. If so I might even get interested in string theory…..

I don’t immediately see from Baez’s paper why the hypercharge assignments come out right. I need to sit down and work that out, but it’s getting late this evening. There are some other issues his paper raises that I’d like to think about, and maybe I’ll finally get around to doing some work to see whether what I’ve learned about spin geometry in recent years has any use in this context.

I also noticed today that Baez is advertising for students to come to UC Riverside to study Quantum Mathematics. I like the term, and for many students who really care about mathematics and fundamental physics, this would be worth thinking about.

Please, commenters who want to write about their favorite ideas about standard model geometry, try and stick to any aspects of this directly related to Baez’s paper.

Lawrence Krauss has an essay in today’s New York Times about science, religion and string theory, covering much the same material discussed here in a recent posting. There are postings about this from Mark Trodden at Cosmic Variance and Lubos Motl on his blog. In comments at Cosmic Variance, Lubos tries to make the rather bizarre claim that the status of the theory of evolution is much the same as that of string theory. I don’t notice any string theorists writing in there to tell him that he is full of it.

Meanwhile, in the real world, the Kansas Board of Education has voted to change the definition of science. Krauss has been very involved in this controversy in recent years, fighting the good fight against Intelligent Design and Creationism. I suspect he’s all too aware of the danger posed by string theorists like Lubos intent on muddying the waters about the question of what is solid, testable science, and what isn’t.

Update: Over at Cosmic Variance, see some of the reaction Krauss is getting to his criticisms of string theory.

As a commenter here noted last night, and other commenters have discussed in the last posting, Steven Weinberg has just put on the arXiv an article entitled Living in the Multiverse. In it, he correctly points out that theoretical physics was immensely successful during the twentieth century as it adopted a fundamental paradigm of exploiting symmetries and quantum mechanical consistency conditions, using these to develop extremely powerful and predictive theories. Initial hopes for superstring theory were that it would lead to further progress along similar lines, but these have not worked out at all.

Faced with the failure of superstring theory to provide any new predictions based on a useful new symmetry principle or consistency condition, instead of drawing the obvious conclusion that it’s just a wrong idea about how to get beyond the standard model, Weinberg instead proposes to dump the lessons of the success of twentieth century physics:

Now we may be at a new turning point, a radical change in what we accept as a legitimate foundation for a physical theory. The current excitement is of course a consequence of the discovery of a vast number of solutions of string theory, beginning in 2000 with the work of Bousso and Polchinski.

What Weinberg sees as “excitement” is what some others have characterized as “depression and desperation”. His “radical change in what we accept as a legitimate foundation for a physical theory” seems to be to give up on the idea of a fundamental theory that predicts things and instead adopt the “anthropic reasoning” paradigm of how to do physics. Weinberg goes through various examples of his own recent work of this kind, announcing that the probability of seeing a vacuum energy of the observed value is 15.6% (this seems to me to violate my high school physics teacher’s dictum about not quoting results to insignificant figures, but I’m not sure how you’d put error bars on that kind of number anyway). He also quotes approvingly recent anthropic work of Arkani-Hamed, Dimopoulos and Kachru, as well as that of his colleague Jacques Distler. All he has to say about the underlying string theory motivation for all this is that “it wouldn’t hurt in this work if we knew what string theory is.”

In his final comments he acknowledges that this new vision of fundamental physics is not as solidly based as the theory of evolution. Describing the strength of his belief in it, he says “I have just enough confidence about the multiverse to bet the lives of both Andrei Linde and Martin Rees’s dog.” One can’t be sure exactly what that means without knowing how he personally feels about Andrei Linde, or cruelty to innocent dogs.

Weinberg’s article is based on a talk given at a symposium in September at Cambridge on the topic “Expectations of a Final Theory”. I haven’t been able to find out anything else about this symposium, and would be interested to hear any other information about it that anyone else has. The article will be published in a Cambridge University Press volume Universe or Multiverse?, edited by Bernard Carr (the president of the Society for Psychical Research), about which I’ve posted earlier here.

I’m curious whether this Cambridge symposium was one of the infinite number of such things funded by the Templeton Foundation. Next week the Vatican will be sponsoring a Templeton-funded conference held in the Vatican City on the topic of Infinity in Science, Philosophy and Theology. It will feature a talk by Juan Maldacena on “Infinity as Simplification”, and is part of a larger Vatican/Templeton project called Science, Theology and the Ontological Quest. This project is designed to promote the vision of scientific research outlined by Pope John Paul II in two encyclical letters, including the rule that scientific research must be “grounded in the ‘fear of God’ whose transcendent sovereignty and provident love in the governance of the world reason must recognize.”

Update: Lubos Motl has some comments on the Weinberg article. This is one topic on which we seem to be in agreement.

Update (much, much later, May 2022): Rereading this posting many years later, I decided to check on the question of Templeton funding raised here. The Weinberg article was published in the volume Universe or Multiverse?, and the Acknowledgements section there has:

First and foremost, I must acknowledge the support of the John Templeton Foundation, which hosted the Stanford meeting in 2003 and helped to fund the two Cambridge meetings in 2001 and 2005.

There’s a new paper out tonight by Nikita Nekrasov entitled Lectures on curved beta-gamma system, pure spinors, and anomalies. Motivated by questions about the covariant superstring quantization method being studied in recent years by Berkovits, Nekrasov considers a sigma model with target space the space of “pure spinors”. For more about pure spinors I suggest consulting “Spin Geometry” by Lawson and Michelson, but in general they are a subspace of the full spinor space with remarkable properties. In R²ⁿ, a pure spinor determines a complex structure on R²ⁿ, one that doesn’t change when you multiply the spinor by a complex scalar. Furthermore, modding out by the action of the complex scalars, the space Q(2n) of projective pure spinors is a Kahler manifold, isomorphic to O(2n)/U(n). This is a projective algebraic variety, and geometric quantization of it gives back the space of spinors. There’s quite a lot of beautiful geometry in this story.

Unfortunately, in the Berkovits story the target space of the sigma model is not Q(2n), which is smooth and has every nice property one could ask for, but the space of pure spinors themselves which is a cone over Q(2n), and has a singularity at the origin. How to handle this singularity is the problem Nekrasov is addressing. This is a rather technical business, one about which I’m no expert (and I’m not sure there are many experts out there on this topic other than Berkovits and Nekrasov).

At the end of his paper Nekrasov makes what appear to be some remarkable comments. He describes two ways to deal with the singularity. The first is to just remove it and work with a non-compact target space. In his paper he shows that this removes certain potential anomalies, but he comments that doing this causes “some unclear issues with the definitions of string measure”. The second way to deal with the singularity is to blow it up, working with the total space of a complex line bundle over Q(2n). Nekrasov claims that if you do this the superstring “would cease to be consistent beyond tree and one-loop level, thereby killing at once the landscape [48] problem.” The reference is to Susskind’s anthropic landscape paper, although Nekrasov refers to Susskind as “Sussking”.

I’m assuming this is some sort of perverse joke, since if the superstring is inconsistent on flat ten-dimensional space, there’s every reason to believe it’s also going to be inconsistent on curved 10d spaces and what gets killed is not just the landscape, but the whole idea of unification based on the 10d superstring. Nekrasov goes on to end with the comment that “This is of course one of the unrealized, so far, hopes to solve some pressing predictive issues of string theory by capitalizing on its unusual, from the conventional quantum field theory point of view, perturbation theory”, referring to a 1987 paper of Greg Moore that I don’t have access to at the moment.

I’m curious to hear what people more expert in this subject think of all this. There are various relevant blog entries: Robert Helling and Urs Schreiber on Nekrasov’s talk a couple weeks ago about this in Hamburg, a recent posting by Jacques Distler, and a report on a talk by Berkovits at the KITP in August by Andrew Neitzke. For some relevant papers on the arxiv, see a paper by Berkovits and Nekrasov from earlier this year as well as quite a few papers by Berkovits and other collaborators written over the last few years.

Update: A commenter wrote in to point out that the Moore paper is available on-line as a scan of the preprint at KEK.

After my post appeared, there were later posts on this topic by Jacques Distler and Lubos Motl. Lubos seems to agree with me that Nekrasov’s comment about an inconsistency in the quantization of the superstring in flat 10d killing the landscape is rather bizarre, since such an inconsistency would probably then hold in all backgrounds.

Funny, but if you look at trackbacks for the Nekrasov paper, they’re there for Distler and Motl’s blog entries but not mine, even though mine appeared earlier. I guess whatever the moderation policy is for trackbacks these days, I’m in a separate category.

Update: After inquiring with the arXiv about what was going on about this trackback, I just heard that it has been posted. It’s still unclear to me what their moderation system is.