Not Even Wrong

Some quick links:

The Clay Mathematics Institute is now making available for free online the books whose publication it has sponsored. These include the Morgan-Tian exposition of the proof of the Poincare conjecture. Surveys in Non-commutative geometry, which contains two excellent articles by Jeffrey Lagarias and Paula Tretkoff explaining ideas about the Riemann Hypothesis that have been motivating Connes and others recently. Also the excellent huge group-effort expository volume on Mirror Symmetry, and a more recent volume on the topic, which includes a good review article by Michael Douglas about the string theory motivations for this work.

There’s an interview with Susskind here about his latest book. About anthropics and the multiverse he claims

…since I wrote “The Cosmic Landscape,” it has practically become the conventional view.

A couple of relatively new physics bloggers are Sunil Mukhi and Marco Frasca. P.P. Cook has revived his blog and is reporting from Eurostrings 2008 here and here.

Among the posts worth reading over at Secret Blogging Seminar, there’s a nice posting by A. J. Tolland explaining what a “stack” is. The comments contain a valuable discussion about the different versions of a “classifying space” that show up in this story.

Several things have come up recently that brought up the year 1985, the year the film “Back to the Future” came out.

This summer the IAS will be running a two-week program at the IAS on Strings and Phenomenology, designed to train a new generation of graduate students and postdocs in the details of compactification methods which mostly go back to 1985, quite possibly before some of the attendees were even born. No evidence that there will be any mention of the fact that 23 years of work on these topics has led simply to a dead-end: the landscape.

At SUSYO8, the first two speakers harkened back to the 1985 period, with Hans Peter Nilles (who also will be lecturing at Princeton) quoting his own words from 1984 (Physics Reports 110):

Experiments within the next five to ten years will enable us to decide whether supersymmetry at the weak interaction scale is a myth or reality

He notes that “This statement is still true today!”

Andrei Linde in his talk on cosmology crows about what he sees as Witten’s recent capitulation to the anthropic landscape point of view about string theory that Linde was pushing back around 1985 (actually 1986) when he wrote:

An enormously large number of possible types of compactification which exist e.g. in the theories of superstrings should be considered not as a difficulty but as a virtue of these theories, since it increases the probability of mini-universes in which life of our type may appear.

which he compares to this from the New York Times

Now, Dr. Witten allowed, dark energy might have transformed this fecundity from a vice into a virtue, a way to generate universes where you can find any cosmological constant you want. We just live in one where life is possible, just as fish only live in water.

At the same time, I’ve been reading and thinking about some papers written back in 1985 which deal with the mathematics of gauge theory and anomalies. At least some of these were never published, including one that I’ve seen references to (by Igor Frenkel and Iz Singer), but never a copy of (does anyone have a copy?). Looking at the history of this subject, it is clear that some very good people were working on this until 1985, at which point quite a few of them dropped it to take up the new fashion of string theory.

Perhaps the LHC will revive the subject of particle theory, by producing a wormhole that will take the world back to its other end, opened up in 1985 by a DeLorean in the movie, from there setting us off into a more promising part of the multiverse.

Sticking with the theme of the Riemann Hypothesis, the AMS has recently posted some articles to appear in an upcoming issue of the AMS Bulletin, one of which contains a long interview with Atle Selberg, who died last summer at the age of 90. Selberg had been a professor at the IAS and an expert in analytic number theory, responsible for some of the most important developments in the subject during the 20th century. A large part of the interview concerns in one way or another the Riemann Hypothesis, which is a central concern of Selberg’s mathematical research, with his work on it beginning during the German occupation of Norway when he was still a student, Some thoughts from Selberg on the subject:

“If anything at all in our universe is correct, it has to be the Riemann Hypothesis, if for no other reasons, so for purely esthetical reasons.” He always emphasized the importance of simplicity in mathematics and that “the simple ideas are the ones that will survive.”

About whether there is a spectral problem that gives the zeros of the zeta-function, useful for proving the RH:

That is certainly a thought that several people have had. In fact, there have been some people that have been able to construct such a space, if they assume that the Riemann hypothesis is correct, and where they can define an operator that is relevant. Well and good, but it gives us basically nothing, of course. It does not help much if one has to postulate the results beforehand—there is not much worth in that.

About his own attempts to find a proof:

Once I had an idea that I thought perhaps could lead to a proof….

[gives some details]

After a while I became more and more convinced that it would not work as I had thought initially. It just seemed unlikely to me. However, I have now and then seen that people have attacked a problem in a way that seemed “hare-brained”, to use an English term, but then it turned out that they could make it work. They have proven something that would not be easy to prove in another way. On the other hand, I have seen people have ideas that seemed absolutely brilliant, but the only problem is that if one follows these to the end one is not able to get anything out of it after all. So it works both ways: sometimes a good idea does not work, and what seems like a bad, even idiotic idea, may actually work.

About Connes’s work on the RH:

Yes, that is a new way to arrive at the explicit formulas—a new access, so to say—but it basically does not give more than what one already had. Connes undoubtedly believed to begin with that what he was doing should lead towards a proof, but it turned out that it does not lead further than other attempts. When I last talked with him he had realized this. This often happens with types of work that are rather formal. There was, for example, a Japanese mathematician, Matsumoto, who gave several lectures that made quite a few people believe that he had the proof.

and finally:

I think it is a good possibility that it will take a long time before it is decided. From time to time people have been optimistic. Hilbert, when he presented his problems in 1900, thought that the Riemann hypothesis was one of the problems that one would see the solution of before too long a time had elapsed. Today it is a little more than one hundred years since he gave his famous lecture on these problems. So one must say that his opinion was wrong. Many of the problems that he considered to be more difficult turned out to be considerably simpler to solve.

Last night a preprint by Xian-Jin Li appeared on the arXiv, claiming a proof of the Riemann Hypothesis. Preprints claiming such a proof have been pretty common, and always wrong. Most of them are obviously implausible, invoking a few pages of elementary mathematics and authored by people with no track record of doing serious mathematics research. This one is somewhat different, with the author a specialist in analytic number theory who does have a respectable publication record. Wikipedia has a listing for Li’s criterion, a positivity condition equivalent to the Riemann Hypothesis.

Li was a student of Louis de Branges, who also had made claims to have a proof, although as far as I know de Branges has not had a paper on the subject refereed and accepted by a journal. He describes his approach as using a trace formula and “in the spirit of A. Connes’s approach”. Li thanks

J.-P. Gabardo, L. de Branges, J. Vaaler, B. Conrey, and D. Cardon who have obtained academic positions in that order for him during his difficult times of finding a job.

but it is a little worrisome that he doesn’t explicitly thank any experts for consultations about this proof. If the arXiv submission of the preprint is the first time he has shown it to anyone, that dramatically increases the already high odds that there’s most likely a problem somewhere that he has missed.

I’m no expert in this subject, so in no position to check the proof or to have an intelligent opinion about whether his method of proof contains a new, promising idea. I suspect though that experts are already looking at this proof, and it appears to be written up in a way that should allow them to relatively quickly see whether it works. Given the history of this subject, I think the odds are against Li, but I’m curious to know what experts think of this.

This also has appeared on Slashdot. If your comment is like any of the ones there, please don’t submit it, but comments from the well-informed are strongly encouraged.

Update: It looks like a problem with the proof has been found. Terry Tao comments on his blog

It unfortunately seems that the decomposition claimed in equation (6.9) on page 20 of that paper is, in fact, impossible; it would endow the function h (which is holding the arithmetical information about the primes) with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry to make the adelic Fourier transform far more powerful than it really ought to be for this problem.

Update: Another Fields medalist heard from: Alain Connes comments as follows on his blog:

I dont like to be too negative in my comments. Li’s paper is an attempt to prove a variant of the global trace formula of my paper in Selecta. The “proof” is that of Theorem 7.3 page 29 in Li’s paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places).

Update: The paper has now been withdrawn by the author, “due to a mistake on pg. 29”.

This week there’s a Nobel Laureate Meeting in Lindau, devoted to physics. Many of the talks can be viewed on-line. From 3-5pm today (Lindau time) there will be a session devoted to a panel discussion of expectations for the LHC. Besides the Lindau web-site, a webcast will also be available here.

Blogging (in German) is going on here, including accounts of the late night activities there, featuring pictures of physicists dancing to the tune “Sex Bomb”.

Update: The panel discussion included two questions from the audience about the multiverse. At first Gross refused to address them leaving cosmologist Smoot to try and say something. Finally ‘t Hooft broke in to say that there were a lot of misconceptions being spread about the multiverse, but that the truth was that the LHC will never have anything to say about either the multiverse or string theory, and Gross did not disagree with him. ‘t Hooft explained that while in principle there could be indirect evidence for a multiverse (from direct evidence for aspects of a theory that implied multiple universes), at the moment the idea was completely untestable and the LHC would have nothing to say about it. Gross agreed, describing multiverse models and research as “very ill-defined”.

At the end, an argument between Veltman and others broke out over the selling of particle physics using astrophysics. He described claims that the LHC will “recreate the Big Bang” as “idiotic”, and as “crap”. He said that this is “not science”, but “blather”, and that the field would come to regret this, arguing that if you start selling the LHC with pseudo-science, you will end up paying for it. Gross and Smoot politely disagreed.

Update: See here for Gross’s talk on expectations of what will be seen at the LHC. He predicts definite observation of a Higgs particle, and says he has taken bets that supersymmetry will be seen, at 50-50 odds. Nothing about string theory at the LHC.

A workshop in Paris/Saclay is taking place this week entitled Wonders of Gauge Theory and Supergravity and the talks are now online. They show that some exciting new things have been happening in the study of gauge theory and supergravity amplitudes, and I’ll make the prediction that this field will attract a huge amount of attention in the coming years (at least until the LHC experiments announce results incompatible with the Standard Model…).

Perhaps the most remarkable part of this whole story is the mounting evidence that N=8 supergravity amplitudes are finite in perturbation theory. Remember the standard story about how quantum theory and general relativity are incompatible that has dominated discussion of fundamental physics for years now? Well, it turns out that this quite possibly is just simply wrong. See Zvi Bern’s talk on UV properties of N=8 supergravity at 3 loops and beyond for the latest about this. Bern shows that divergences everyone had been expecting to occur at 3 loops aren’t there, and gives evidence that they might also be absent at higher loops. He even sees this as a phenomenon not special to N=8 supergravity, but also occurring in theories with less supersymmetry, e.g. the N=5 and N=6 theories. Among the other talks, Nima Arkani-Hamed’s is also about this, advertising the idea that N=8 supergravity is the Simplest QFT.

Much of this story is about the N=4 SYM amplitudes and new insights into them and their relations to supergravity amplitudes, with some of this research growing out of and motivated by the AdS/CFT conjecture of the existence of a string dual to N=4 SYM. Quite a few of the talks are interesting and worth trying to follow, with a much higher proportion of new ideas than is usual at particle theory workshops in recent years.

To go out on a limb and make an absurdly bold guess about where this is all going, I’ll predict that sooner or later some variant (“twisted”?) version of N=8 supergravity will be found, which will provide a finite theory of quantum gravity, unified together with the standard model gauge theory. Stephen Hawking’s 1980 inaugural lecture will be seen to be not so far off the truth. The problems with trying to fit the standard model into N=8 supergravity are well known, and in any case conventional supersymmetric extensions of the standard model have not been very successful (and I’m guessing that the LHC will kill them off for good). So, some so-far-unknown variant will be needed. String theory will turn out to play a useful role in providing a dual picture of the theory, useful at strong coupling, but for most of what we still don’t understand about the SM, it is getting the weak coupling story right that matters, and for this quantum fields are the right objects. The dominance of the subject for more than 20 years by complicated and unsuccessful schemes to somehow extract the SM out of the extra 6 or 7 dimensions of critical string/M-theory will come to be seen as a hard-to-understand embarassment, and the multiverse will revert to the philosophers.

Many of the titles of the talks at Strings 2008 have recently been announced. The plenary talks will include several talks mostly not about string theory, including 3 about the LHC and one by Lance Dixon on the amplitudes story. It seems that the string theory anthropic landscape is a topic the conference organizers don’t want anything to do with, since the only person from the Stanford contingent speaking will be Kallosh on prospects for getting something observable out of string cosmology models of inflation. As for what is popular, it clearly helps a lot to be from one of my alma maters, with Princeton (7 speakers), and Harvard (3 speakers) the best-represented institutions.

Update: For an extensive rant about this, see here.

Update: Last week was Paris, this week it’s Zurich. Amplitudes are all the rage this summer.

Today’s Bloggingheads.tv diavlog features Sean Carroll and philosopher of science David Albert, discussing a variety of issues. Albert tells about his unfortunate experience with the What the Bleep? film, a good example of why it’s not always a good idea to get involved with people doing a supposedly science-related media project. He also discusses the hostility towards study of the quantum measurement problem from within the physics community over the years, a situation that has changed recently. The two also had a long discussion concerning Carroll’s claims about the arrow of time, about some of which Albert seemed to be rather skeptical.

The discussion of criticisms of string theory were on the whole ill-informed, misleading, and devoted to ferocious attacks on straw men. For some reason, only John Horgan was mentioned, with the existence of trained theoretical physicist critics and two recent books on the topic completely ignored. Albert insisted repeatedly on the idea that Horgan and other critics were not acknowledging the “spectacular predictive success” of string theory. He was referring to claims that string theory “predicts gravity”, since it contains a massless spin-two particle (ignoring the fact that it is in the wrong dimension; to quote Lisa Randall “string theory predicts gravity: 10d gravity”). Later on Carroll did explain the problem with this, that string theory seems to allow an infinite variety of ground states with different physics, many of which don’t have 4d gravity. Carroll told about having asked various string theorists if they could imagine any kind of experimental result at any energy that would be incompatible with string theory, and getting the answer “No” from at least some of them. This seemed to rather shock Albert.

There was no real discussion of the multiverse, a topic where philosophers of science might be able to perform a public service by taking a serious look at what physicists are up to and analyzing what they learn. Carroll launched the standard attack on string theory critics as having a “sophomore-level” understanding of the philosophy of science, unaware that there is anything to the problem of what is science and what isn’t other than Popper’s falsifiability criterion. He also claimed that string theory critics have created a “20 year statute of limitations” criterion, that theoretical work must lead to a falsifiable prediction within 20 years or cease to be science, chuckling with Albert about how ignorant people must be who think such a thing. This kind of willful misrepresentation of the views of people you disagree with seems to me to be less than honest. From what I remember of Lee Smolin’s book, there’s a long section about his engagement with the philosophy of science, and his sympathies are not with Popper, but with Feyerabend’s “anarchistic” views on the subject, which are very different. In my book there’s an entire chapter devoted to explaining what is wrong with just invoking falsifiability. I assume Carroll has read at least one of the two books, so it’s unclear why he thinks it’s acceptable to go on like this. He does make one more accurate accusation, that critics of the multiverse are stuck in an out-dated 1960s particle physics paradigm of what it means to test a theory. I suppose this is true enough. Not the first time I’ve been accused of being stuck in the 60s, which, if one has to be stuck somewhere, doesn’t seem like that bad a choice…

Update: Evolving Thoughts has a link to The Ideas of Quine on Youtube, an interview of the philosopher Willard Van Ormond Quine by Brian Magee. The relation of physics and philosophy was one of Quine’s main concerns, and one of the main topics of the interview. I suppose that to the extent my own philosophical views could be characterized by picking one philosopher I find most sympathetic, Quine would be a good choice. Perhaps he’s responsible for my “sophomore-level” philosophy of science, since I took a course from him as a sophomore.