Not Even Wrong

All sorts of news very recently on the science blogging front:

Seed’s ScienceBlogs site has been revamped, with 25 new blogs for a total of 43 science bloggers. First it was Cosmic Variance with 5 bloggers, now it is ScienceBlogs with 43. How can a single artisanal blog maker like myself compete with these massive blogging conglomerates? Still not very many physicists over at Seed. Besides Chad Orzel, one of the new ones is astrophysicist Steinn Sigurosson who has been running a blog called The Dynamics of Cats.

One physics blog I ran across recently, one that isn’t moving to Seed, is Angry Physics.

Besides Seed, Nature magazine has started up a site called NatureBlogs. They are running blogs on chemistry, genetics, and neuroscience, as well as a more general one on web technology and science. There’s also a newsblog for comments on news stories appearing in Nature, as well as a discussion blog related to a radical new concept in peer review that they are trying out: a blog where certain papers submitted to Nature are posted, asking for commentary on the paper, to be considered as part of the peer review process.

Nature also just launched another new project which I’d been hearing about for a while from my brother, called Nature Network Boston. It’s intended as a networking site for scientists in the Boston area, and has news, event listings, groups, and, guess what, more blogs. Maybe Lubos can start a string theory fanatic’s group there…

Finally, Jacques Distler is helping to provide access to these proliferating blogs with a new aggregation site he calls Planet Musings. As usual, Jacques is careful to make sure that anything he has control over censors links to people who disagree with him…

The latest issue of Seed magazine (not yet available online, as far as I know), contains responses from various well-known physicists who were asked what they hoped to learn from the LHC. Here’s the gist of what they had to say:

Lisa Randall: The magnificent thing is that we know there should be an answer to the question of the weakness of gravity, and that it should be revealed at the LHC.

Leon Lederman: The long-simmering concern over the weakness of Einstein’s gravity may well be confronted. However, what is for sure is that the LHC, with its awesome reach, will answer all of our current astro-particle problems…

Alexander Vilenkin: If no trace of supersymmetry is found, this would be – necessarily indirect – evidence for the existence of the multiverse.

Sir Martin Rees: I’m hoping that it will clarify the nature of the particles that constitute the “dark matter” in the universe.

Edward Witten: The LHC wil tell us whether this notion [electroweak symmetry breaking] is correct, and if so how it works.

Max Tegmark: Our theory of particle physics has 26 pure numbers in it. Why do they have these particular values? How did the universe begin? Did it?

Leonard Susskind: I see only two possible outcomes of the LHC project – either there will be low energy supersymmetry or there won’t. … the big question is whether the gauge hierarchy fine-tuning is similar to the cosmological constant fine-tuning, or if it has a more conventional supersymmetric explanation.

Steven Weinberg: What terrifies theorists is that the LHC may discover nothing beyond the single neutral “Higgs” particle.. We fervently hope for some complicated discoveries.

John Schwarz: There are many speculative ideas for possible discoveries at the LHC. These include indications of extra dimensions, black holes, strings, magnetic monopoles, etc. I believe that all of these exist, and I would be thrilled to have experimental confirmation – but I am pessimistic about the prospects for finding them in the LHC’s energy range… I could be wrong. That’s why it is important that these experiments be carried out.

Sean Carroll: The beauty of science is that we don’t know what surprises may await us in these domains.

Gordon Kane: The LHC could discover the superpartners in a supersymmetric world. In addition to strong theoretical evidence for Higgs physics, there is strong experimental evidence that Higgs particles do exist with a mass implied by supersymmetry… Probably the main thing we have learned in the past two decades is that any understanding of nature at the most fundamental level (beyond a description) will require extending our thinking to embed our world in extra dimensions… An optimist (like me) can make the defendable argument that the LHC could test supersymmetry, establish string theory and move on to the remaining “why” questions.

My predictions: The LHC won’t see supersymmetry and won’t tell us anything about dark matter, dark energy or why gravity is weak. Witten has it exactly right, what the LHC will do will be to start to tell us what is causing electroweak symmetry breaking. It’s possible that Weinberg’s worry will be borne out, and, at LHC energies, we’ll just see what appears to be an elementary scalar, which will be depressing. But I think it’s equally likely that symmetry breaking is not coming from an elementary scalar, but from something much more interesting, quite possibly something we haven’t thought of, and the LHC may start to give us evidence for what this is.

I’ll also predict that we are still a few years from finding out what the LHC will tell us. These will be completely wasted years for particle theory if people just give up on looking for new ideas and sit on their hands (or wander pointlessly in the landscape), waiting for the LHC to revive the subject.

Study of the string theory landscape seems now to have become the hot research topic that one should be working on in order to be taken seriously as a cutting-edge researcher in particle theory. Last week there was a workshop at Trieste on String Vacua and the Landscape that drew many researchers. Some of the talks from the workshop are available on-line.

Following on the heel’s of Susskind’s popular book promoting the landscape, which has received excellent reviews from particle and string theorists, there’s a new one on the same topic coming out later this month from cosmologist Alex Vilenkin, entitled Many Worlds in One: The Search for other Universes.

As string theorists in search of something to write papers about pour into the landscape, with its more than 10⁵⁰⁰ possible hot research topics to work on, Sean Carroll reports from a cosmology workshop at the Perimeter Institute that trouble may be ahead for the subject. Sean gives a short summary of the talks at the workshop, in the majority of cases ending with “Made fun of the landscape”, or “Made fun of the anthropic principle”.

The main argument for the landscape mania has always been that it justifies Weinberg’s “prediction” of the size of the cosmological constant. I’ve written elsewhere about why this is not a legitimate scientific prediction, and is off by at least an order of magnitude anyway. Evidently Steinhardt and Turok are about to put out a paper claiming that the situation is much worse than this, that if you take anthropic reasoning seriously, the natural “prediction” of the landscape is that:

the cosmological constant should be quite large (many times the matter density, although presumably not at the Planck scale), and we should live in a single lonely galaxy in an empty universe dominated by vacuum energy.

It will be interesting to see if landscapeologists will be willing to admit that the only supposed “prediction” of this subject doesn’t work at all, and that it is not only pseudo-science, but failed pseudo-science.

I ordinarily keep a short list on my desk of things I’ve seen recently that I’d like to write about here. The last few days this list has gotten way too long, so I’ll try and deal with it by putting as many of these topics as I can in this posting.

The June/July issue of the AMS Notices is out, with many things worth reading. The two long articles are one by Ken Ono about Ramanujan and one by Arthur Jaffe telling the story of the founding of the Clay Mathematics Institute and the million dollar prizes associated with seven mathematical problems. There’s also a book review of Roger Penrose’s The Road to Reality, news about the proposed US FY 2007 budget for mathematical sciences research, and an account of a public talk by Michael Atiyah, who evidently closed by explaining some of his very speculative ideas about how to modify quantum mechanics, then said:

This is for young people. Go away and explore it. If it works, don’t forget I suggested it. If it doesn’t, don’t hold me responsible.

The June issue of Physics Today is also out. In its news pages it reports that Robert Laughlin is out as the president of the Korea Advanced Institute of Science and Technology (KAIST), and will return to Stanford in July “where he plans to teach, research, and write ‘anything that brings income.'” The report gives conflicting reasons for why things didn’t work out for him at KAIST, but notes that “90% of KAIST professors gave him a vote of no-confidence and nearly all deans and department chairs quit their administrative posts to protest his continuing in the job.”

There’s an extremely positive review of Leonard Susskind’s The Cosmic Landscape by Paul Langacker, which ends:

The Cosmic Landscape is a fascinating introduction to the new great debate, which will most likely be argued with passion in the years to come and may once again greatly alter our perception of the universe and humanity’s place in it.

Why any particle theorist would want to encourage other physicists outside their field to read this book and give them the idea that it represents something theorists think highly of is very unclear to me.

Finally there’s an article by Jim Gates entitled Is string theory phenomenologically viable? Gates aligns himself with the currently popular idea that string theory doesn’t give a unique description of physics:

The belief in a unique vacuum is, to me, a Ptolemaic view – akin to that ancient belief in a unique place for Earth. As I wrote in 1989, a Copernican view, in which our universe is only one of an infinity of possibilities, is my preference, but there were very few Copernicans in the 1980s.

He seems to promote the idea that one should not use 10d critical string theory and thus extra dimensions, but instead look for 4d string theories, and that perhaps the problem is the lack of a “completely successful construction of covariant string theory.” For more about this point of view, see Warren Siegel’s website.

There are quite a few idiosyncratic things about Gates’s article, including the fact that he refers to non-abelian gauge degrees of freedom as “Kenmer angles”, after Nicholas Kemmer (not Kenmer) who was involved in the discovery of isospin.

Some of his comments about string theory are surprising and I don’t know what to make of them. He claims that “some aspects of string theory seem relevant to quantum information theory”, and the one supposed observational test of string theory he discusses is one I hadn’t heard of before and am skeptical about (observing string-theory-predicted higher curvature terms in Einstein’s equations through gravitational wave birefringence). His discussion of supersymmetry seems to assume that observation of superpartners is unlikely, since for reasons he doesn’t explain he expects their mass to be from 1 to 30 Tev. Finally, he worries that people will not investigate things like covariant string field theory since we are about to enter an “era that promises an explosion of data”. I certainly hope he’s right about the forthcoming availability of large amounts of interesting new data.

The Harvard Crimson has an interesting article about Ken Wilson.

John Baez is getting ever closer to having a blog in its modern form, now he has a diary.

Read about the tough summer life of theoretical physicists in Paul Cook’s report from Cargese (which reminded me of when I went there as a grad student), and JoAnne Hewett’s report from Hawaii (which reminded me of a very pleasant vacation I spent on the Big Island).

Science magazine has an article about progress on increasing luminosity at the Tevatron, hopes for getting enough events there to see the Higgs before the LHC, and the debate that is beginning about whether to run the machine in 2009.

Slides are available from the Fermilab User’s Meeting.

There’s a news story out from China (and picked up by Slashdot) about the new paper by Huai-Dong Cao and Xi-Ping Zhu soon to appear in the Asian Journal of Mathematics. This paper is more than 300 pages and is supposed to contain a proof of the Poincare conjecture and the full geometrization conjecture, filling in an outline of a proof due to Perelman, who used methods developed by my Columbia colleague Richard Hamilton. Other groups have also been working on this in recent years including my other Columbia colleague John Morgan together with Gang Tian; for another example, see the notes on Perelman’s papers recently put on the arXiv by Bruce Kleiner and John Lott. Cao and Zhu have evidently been explaining their proof in a seminar at Harvard run by Yau during the past academic year, and Yau will talk about this at Strings 2006 in Beijing later this month. When the paper appears it will be interesting to see what some of the other experts in the field think of it and whether there’s a consensus that the proof of Poincare and geometrization is finally in completely rigorous form.

Update: According to a blog entry from the Guardian, “Perelman seems to be active in string theory.”

I was up in Boston for a few days, and managed to attend a few of the talks at the conference in honor of George Lusztig’s 60th birthday. Lusztig started out his career in geometry and topology; his thesis was in the area of index theory, working with Michael Atiyah and using the families version of the index theorem. He soon turned his attention to representation theory, which is the field that he has worked in for most of his career, often from a quite algebraic point of view. His papers are dense and can be difficult to read, especially for someone like me who is not so algebraically inclined, but many speakers at the conference remarked on how their work had drawn important inspiration from one or another of these papers.

Among the things he is famous for are his work on quantum groups, on the representation theory of reductive groups over finite fields (called Deligne-Lusztig theory, for an introduction, see here), on a whole new field in Lie theory known as Kazhdan-Lusztig theory (for an introduction, see the article by Deodhar in the proceedings of the 1991 AMS summer institute on algebraic groups), and many other things.

Of the few talks I heard at the conference, two were really exceptional. One of these was by Michael Atiyah, with the title “Quaternions in Geometry, Analysis and Physics”. He began by explaining that not only was Lusztig 60, but, if he were alive, the Irish mathematician Hamilton would be 200. There’s a famous story about Hamilton’s discovery of the quaternions: this took place in a flash of insight on October 16, 1843, after which he supposedly engraved the defining relations of the quaternion algebra into a Dublin bridge. Atiyah described a piece of history I didn’t know, showing an extract from a 1846 paper of Hamilton’s in which he takes a square root of the Laplacian and essentially writes down the Dirac equation (in Euclidean signature, this was long before special relativity…).

Hamilton was very taken with quaternions as a generalization of complex numbers, and wanted to develop a “quaternionic analysis” that would be a generalization of complex analysis, a project he thought would take him at least ten years. It turns out that you can’t simply generalize the beautiful subject of complex analysis and algebraic geometry over the complex numbers to the quaternionic case. Because of non-commutativity, polynomials behave very differently. Atiyah explained that in his view the correct generalization of complex analysis to the quaternionic case was Penrose’s twistor theory. Here one considers all possible ways of identifying R⁴ with C², forming a 3 complex dimensional “twistor space”. Complex analysis on this twistor space is what Atiyah claimed should be thought of as the quaternionic analog of complex analysis (on the complex plane).

He reviewed the story of how solutions to various linear equations are related to sheaf cohomology groups on the twistor space, then went on to the non-linear case, where solutions of the anti-self-dual Yang-Mills equations correspond to holomorphic bundles on the twistor space. One can generalize twistor theory to what Atiyah claimed should be thought of as quaternionic analogs of Riemann surfaces: 4d Riemannian manifolds with holonomy in Sp(1)=SU(2), these are self-dual Einstein manifolds, what Penrose would call a “non-linear graviton” (although this is the Riemannian, not pseudo-Riemannian case). The twistor space of these 4d manifolds is a 3d complex manifold, and Atiyah considers complex analysis on this to be the quaternionic analog of complex analysis on a Riemann surface.

The quaternionic analog of higher dimensional complex manifolds are manifolds of dimension 4k, with holonomy Sp(k). Unlike in the complex case, there are few compact examples. Atiyah went on to discuss how examples (mostly non-compact) could be generated as quotients using the quaternionic analog of symplectic reduction. He described several different classes of examples, noting that this construction first appeared in work with physicists studying supersymmetric non-linear sigma models. While I was a post-doc at Stony Brook, Nigel Hitchin was visiting there and working with Martin Rocek and others on this, leading to the 1987 paper in CMP by Hitchin, Karlhede, Lindstrom and Rocek. Atiyah said that he wouldn’t try and describe the relation to supersymmetry, since “I don’t know much about supersymmetry, and if I tried to explain it, you would understand even less”. That Atiyah, after many years of working in this area, still finds supersymmetry to be something he can’t quite understand, is an interesting comment, reflecting the way the subject is still very imperfectly integrated into mathematician’s traditional ways of thinking about geometry and algebra.

Atiyah also commented that off and on over the years he had pursued the idea that quantum groups (which aren’t quite groups), are in some sense the quaternionification of a Lie group (which doesn’t quite exist). He said he hadn’t been successful with this idea, but still thought there was something to it, and hoped that someone else would take up the challenge of trying to make sense of it.

The second wonderful talk I heard was that of Igor Frenkel, from Yale, with the title “Quantum deformation, geometrization, categorification: What is next?”. Unlike Atiyah’s talk, which I pretty much completely understood, Frenkel’s covered much too quickly a lot of material I had never understood, but putting it into an intriguing perspective close to the unsolved problems that seem to me the most important ones for mathematicians and physicists to be looking at. Frenkel began by saying that for many years he had been trying to solve the problem of how to generalize the constructions of representations of loop groups that are related to 2d CFT to representations of 3d gauge groups that should be related to 4d QFT. Some of his thoughts about this are in the write up of his talk at the 1986 ICM. He described himself as having for a long time given up on this problem, moving on to simpler things that he could do: quantum groups which are deformations of the affine Lie algebra story. He went on to talk about “Geometrization”, by which he meant the principle that “all structure constants are Euler characteristics of some variety, all vector spaces are cohomologies”, then “Categorification”, to him the principle that “all structure constants are dimensions of vector spaces, all vector spaces the Grothendieck groups of an Abelian category”. Many of the examples he was using to flesh this out are not well-known to me, I need to do some serious work learning about them before I can say that I clearly understand exactly what he has in mind here.

The last part of his talk, the “What Next?”, went by way too fast but sounded fascinating. He claimed to have some new ways of thinking about the problem of what a representation of these higher dimensional analogs of loop groups should me. I hope to learn more from him in the future to get a better idea of what he has in mind here. He and collaborators at Yale have papers forthcoming, which I look forward to reading. When and if I ever better understand this stuff, I may try and write about it again here.