Not Even Wrong

This evening a very interesting paper appeared on the arXiv, entitled Instantons Beyond Topological Theory I by E. Frenkel, Losev and Nekrasov. The authors are studying theories with a topological sector (supersymmetric quantum mechanics and 2d sigma models on a Kahler manifold, N=2 supersymmetric YM in 4d), but are interested in sectors of the theories that are not purely topological. I’m looking forward to reading the paper over the next few days, but it is a bit daunting. This paper is nearly 100 pages long, and it is only part I of three parts, and actually just the simplest part, that involving quantum mechanics.

HEPAP is meeting today and tomorrow, here’s the agenda. From the slides of the talk about NASA, the budget situation there for fundamental science missions doesn’t look good, and there is discussion of the upcoming NRC committee charged with figuring out which of the “Beyond Einstein” missions to allow to go forward. At Dynamics of Cats, Stein Sigurosson has been writing about this in terms of the missions being sent to Thunderdome, only one to emerge alive.

Slides from the talks last month at the conference in honor of Nigel Hitchin’s 60th birthday are available.

Joe Lykken has a nice review article about the standard model, in which he notes:

There is only one diagonal Yukawa coupling that is of order one, and that is the top quark Yukawa. But even this case is mysterious. The top Yukawa is not really of order one: it is equal to one! For example, using the 2005 combined Tevatron value for the pole mass of the top quark, the corresponding Yukawa coupling is 0.99 +/- 0.01. The entire particle physics community has chosen (so far) to regard this fact as a 1 per cent coincidence. I should point out that similar percent level equalities, e.g. supersymmetric gauge coupling unification or the ratio of the total mass-energy density of the universe to the critical density, have spawned huge theoretical frameworks bolstered by thousands of papers.

Difference is that, as far as I know, nobody has an idea why this Yukawa coupling should be one. Maybe this is a big clue…

Over at Backreaction, there’s an excellent posting about Does String Theory Explain Heavy Ion Physics?, one of the very few places to find a non-overhyped discussion of this topic.

Davide Castelvecchi has a well-done review of my book at his sciencewriter.org web-site.

At this week’s physics colloquium at Penn, Andre Brown reports that Robert Cahn emphasized that “half the particles needed for supersymmetry have already been discovered.” He also recalled a quote from another colloquium about supersymmetry: “Supersymmetry has stood the test of time. There is no evidence for supersymmetry.”

Update: A couple people have pointed out the following rather accurate cartoon.

Since string theory first became popular in 1984-5, attempts to connect it to particle physics have suffered from various problems. One of the most severe of these goes under the name of “moduli stabilization”. Six dimensional Calabi-Yau manifolds come in families, parametrized by “moduli”. The dimensions of these moduli spaces can be of order 100 or so.

Naively it might appear that string theories are characterized by a choice of a topological class of Calabi-Yaus (no one knows if the number of these is finite or infinite), and then a choice of each of the 100 or so parameters that fix the size and shape of the Calabi-Yau. According to the standard string theory ideology, this is not the right way to think, instead there is really only one string theory, with different moduli values corresponding to different states. The moduli parameters are supposed to be dynamical elements of the theory, not something parametrizing different theories.

The problem with this is that if you promote the moduli to dynamical fields, they naively correspond to massless fields, and thus give new long-range forces. So you have to explain away why we don’t see 100 or so different kinds of long-range forces, and the experimental bounds on such forces are very good. Some kind of dynamics must be found that will “stabilize moduli”, giving them a non-trivial potential. The moduli fields will then be fluctuations about the minima of this potential. If the quadratic piece of the potential is large enough, their mass will be high enough to have escaped observation.

One needs a potential with non-trivial minima, and has to ensure that the dynamics is not such that the moduli will run off to infinity. In recent years, ways of achieving this have been found that typically involve “flux compactifications”, i.e. choosing non-trivial fluxes through the topologically non-trivial holes in the Calabi-Yau. On the one hand, this seems to provide a long-standing solution to the problem of how to stabilize the Calabi-Yau, on the other hand, it appears that there is an exponentially large number of possible minima. This is the origin of the “Landscape” and the associated claims of 10⁵⁰⁰ or more possible vacuum states for string theory.

The constructions involved are famously exceedingly complex and ugly, with Susskind referring to them as “Rube Goldberg machines”, and one of their creators, Shamit Kachru, the “Rube Goldberg architect”. Very recently a new Reviews of Modern Physics article by Kachru and Douglas called Flux Compactification has appeared. It can be thought of as a manual describing how to construct and count these Rube Goldberg machines.

Many string theorists had long hoped that whatever method was found to stabilize moduli would have only a small number of solutions. Then, in principle one would get only a small number of possible models of particle physics for each topological class of Calabi-Yaus. If the number of these was finite and not too large (the known number of constructions is something like 10⁵-10⁶), then to see if string theory could make contact with particle physics, one would just have to do a moderately large number of calculations, check them against the real world, and hope that one matched. If it did, it would then be highly predictive.

The existence of the flux compactifications with stabilized moduli described in the Douglas-Kachru article has convinced many string theorists that this old dream is dead. Some have tried to claim that this is a good thing, that the exponentially large number of states allows the existence of ones with anomalously small cosmological constants, and thus an anthropic explanation of its value. The problem then becomes one of how to ever extract any prediction of anything from string theory. Small CCs are achieved by very delicate cancellations, and it appears to be a thoroughly calculationally intractable problem to even identify a single state with small enough CC.

Many string theorists are now claiming that this is not really a big deal. So what if there are lots and lots of string theory vacua, it’s just like the fact that there are lots and lots of 4d QFTs! For arguments of this kind, see recent comment threads here and here. There’s something fishy about this argument, since discussion of flux compactifications has from the beginning focused on whether it is possible to use them to make predictions, whereas no one ever was worrying about whether (renormalizable) QFTs were predictive or not.

The source of the problem lies in the combination of the large numbers of string theory vacua with their Rube Goldberg nature. Consistent 4d QFTs are characterized by a limited set of data (gauge groups, fermion and scalar representations, coupling constants), and it has turned out that among the simplest possible choices of such data lies the Standard Model. String theorists commonly describe the Standard Model as “ugly”, but it is among the simplest possible 4d QFTs, and is extremely simple and beautiful compared to something like the flux compactification constructions. One could hope that while flux compactifications are inherently rather complicated, one of the simpler ones might correspond to the real world. As far as I know there’s no evidence at all for this, such a hope appears to have nothing behind it besides pure wishful thinking. Some string theorists like Douglas and Kachru don’t seem to think this is possible, focussing instead on statistical counts of more and more complicated flux compactifications, hoping to find not a simple one that will work, but a statistical enhancement of certain complicated ones that would pick them out.

4d QFT is a predictive framework not because the number of possible such QFTs is small, but because our universe is described extremely accurately by one of a small number of the simplest of such QFTs. A few experiments are sufficient to pick out the right QFT, and then an infinity of predictions follow.

Is the QFT framework falsifiable? One could imagine that things had worked out differently, that instead of the Standard Model predictions being confirmed, each time a new experimental result came in, one could only get agreement with experiment by adding new fields and interactions to the model. It might very well be that the QFT framework could not be falsified, since one could always evade falsification by adding complexity. This happens very often with wrong ideas: they start with a simple model, experimental results disagree with this, but can be matched by making the model more complicated. As new experiments are done, if the original idea is wrong, it doesn’t get simply falsified, but the increasing complexity of the models needed to match experiment sooner or later causes people to give up on the whole idea.

This is very much what has happened with string theory. The simple models that got people excited about the idea of string theory unification don’t agree with experiment, with the moduli stabilization problem just one example. It appears one can solve the problem, but it’s a Pyrrhic victory: one is forced into working with a class of models so vast and so complicated that one can get almost anything, and never can extract any real predictions.

Douglas and Kachru do address the question of whether one can ever hope to get predictions out of this class of models, but their answer is that they can’t think of any plausible way of doing so. They mention various things that people have tried, but none of these ideas seem to work. The best hope was that counting vacua with different supersymmetry breaking scales would lead to a statistical prediction of this scale, but this has not worked out for reasons that they describe. In the end they conclude:

For the near term, the main goal here is not really prediction, but rather to broaden the range of theories under discussion, as we will need to keep an open mind in confronting the data.

This acknowledges that no predictions from this framework seem to be possible, and that continuing work in this area just keeps producing yet wider and wider classes of these Rube Goldberg machines. They are suggesting basically giving up not on string theory, which would be the usual scientific conclusion in this circumstance, but instead to for now give up on the theorist’s traditional goal of making testable predictions. They advocate not giving up on string theory no matter how bad things look, instead just continuing as before, hoping against hope that an experimental miracle will occur. Maybe astronomers will find evidence for cosmic superstrings, maybe the LHC will see strings or something that matches up with characteristics of one of the Rube Goldberg models. There’s not the slightest reason to believe this will happen other than wishful thinking, which has now been promoted to a new program for how to do fundamental science.

Update: Via Lubos, for those who don’t know what a Rube Goldberg machine is, two examples are here and here.

Bert Schroer has a new version of his paper that was discussed here earlier this year, now with the amended title String theory and the crisis in particle physics (a Samizdat on particle physics). He claims that the version reflects a change in viewpoint due to his participation in this and other weblogs, and I believe he would like the opportunity to discuss this further here. There’s also a posting about this at the weblog of Risto Raitio.

Update: Schroer, agreeing with his critics that his paper had too many typos, has sent me a corrected version, which is available here, for use until the arXiv version gets updated. He also agrees that an “s” should be a “z” in Samizdat…

Update: Schroer has a new paper out, which contains a review of AQFT and a discussion of light-front holography, with further comments on the relation to the Maldacena conjecture.

Penny Smith, a mathematician at Lehigh University, has posted a paper on the arXiv that purports to solve one of the Clay Foundation Millenium problems, the one about the Navier-Stokes Equation. The paper is here, and Christina Sormani has set up a web-page giving some background and exposition of Smith’s work. I should emphasize that I know just about nothing about this kind of mathematics, but I’m reporting on this here for two reasons:

1. It looks plausible that this really is important.

2. Penny Smith tells me that she is a regular reader of this weblog.

Update: There’s an informative news article about this on the Nature web-site.

There’s almost too much to keep track of the last couple days on the string theory controversy front:

Burton Richter of SLAC has a Reference Frame piece in the latest Physics Today entitled Theory in particle physics: Theological speculation versus practical knowledge. Richter shares my point of view that the Landscape studies currently popular in string theory are not science:

To me, some of what passes for the most advanced theory in particle physics these days is not really science. When I found myself on a panel recently with three distinguished theorists, I could not resist the opportunity to discuss what I see as major problems in the philosophy behind theory, which seems to have gone off into a kind of metaphysical wonderland. Simply put, much of what currently passes as the most advanced theory looks to be more theological speculation, the development of models with no testable consequences, than it is the development of practical knowledge, the development of models with testable and falsifiable consequences (Karl Popper’s definition of science)…

The anthropic principle is an observation, not an explanation… I have a very hard time accepting the fact that some of our distinguished theorists do not understand the difference between observation and explanation, but it seems to be so…

What we have is a large number of very good people trying to make something more than philosophy out of string theory. Some, perhaps most, of the attempts do not contribute even if they are formally correct.

The issue of Nature that just came out today has an article about the controversy by Geoff Brumfiel with the title Theorists snap over string pieces: Books spark war of words in physics. He describes Lubos Motl’s reviews of the Smolin book and mine on the Amazon web-site, and quotes Polchinski and Susskind. The reaction of string theorists to the books is said to be:

Few in the community are, at least publicly, as vitriolic as Motl. But many are angry and struggling to deal with the criticism. “Most of my friends are quietly upset,” says Leonard Susskind, a string theorist at Stanford University in California.

and

The books leave string theorists such as Susskind wondering how to approach such strong public criticism. “I don’t know if the right thing is to worry about the public image or keep quiet,” he says. He fears the argument may “fuel the discrediting of scientific expertise”.

Susskind will be giving a public lecture October 17 at UC Davis on String Theory, Physics and the “Megaverse”.

Polchinski avoids the problems associated with the failure of string theory as a unified theory, and promotes in a somewhat overhyped way the idea that string theory explains the RHIC data.

Finally, Smolin makes an offer to string theorists that I feel I should try and match, hoping they will read his book to better understand exactly what he has to say:

If they don’t want to buy it, tell them to get in touch with me and I’ll send them a copy.

One thing Brumfiel gets a bit wrong is that my problem with string theory is not quite what he says “a fear that the field is becoming too abstract and is focusing on aesthetics rather than reality.” The problems I see are rather different, with mathematical abstraction one of the few tools still available to theorists trying to make progress.

The same issue of nature contains an editorial Power and Particles lustily repeating much of the standard hype about string theory, noting that there are problems, but ending with:

Critical-mindedness is integral to all scientific endeavour, but the pursuit of string power deserves undaunted encouragement.

The editorialist definitely does not seem to be of the opinion that alternatives also deserve to be encouraged.

Finally, lots of reviews of Lee Smolin’s book:

Unburdened by proof by George Ellis, also in Nature. Ellis takes the opposite point of view from the Nature editorialist, calling for more research on alternatives to string theory.

A loopy view by Michael Duff, in Nature Physics. Duff is extremely hostile to Smolin’s book, sneering at Smolin and claiming that his book will “leave the reader rooting for strings” (funny, but this doesn’t seem to have been its effect on most reviewers…). Duff agrees that there are problems with string theory, but claims that the problems Smolin correctly identifies are exactly the ones that he himself first identified back in 1987. String theorists like Duff seem torn between claiming that criticisms of string theory are crackpot nonsense, and that they themselves made them first. He goes on to furiously attack various straw men, accusing Smolin of “denying that any progress has been made!” (something I don’t think Smolin does at all), and answering the criticism that string theory makes no predictions despite more than twenty years of effort by discussing how theories that did make predictions have sometimes taken a long time to be confirmed (or remain unconfirmed).

The string theorists were scammed! by Peter Shor on Amazon.

The Trouble With Physics by Sean Carroll at Cosmic Variance. If I can find the time, I may write about some of my problems with this review as a comment over there.

Back in April a paper appeared on the arXiv from string theorist Jacques Distler and collaborators that made a rather outrageously overhyped claim to have found a way to “falsify string theory”. The paper was entitled Falsifying String Theory Through WW Scattering, and was discussed extensively here. After the Wall Street Journal published an article in June about the problems of string theory, Distler wrote them to complain that the article was incorrect, because he and his collaborators had shown that string theory was falsifiable.

I had heard that this paper was going to be refereed, and was wondering whether a referee would really let the authors get away with the outrageous claim of their title. Well, it appears that the answer is no. A new version of the paper is now on the arXiv, with a new title: Falsifying Models of New Physics via WW Scattering. The abstract, which originally claimed that violations of the bounds they described “would falsify string theory” has now been modified to no longer make this claim; the new language is “would falsify generic models of string theory”.

The paper has acquired a new co-author and been extensively rewritten. I’m assuming many of the changes were made to satisfy a referee. Besides changing the misleading, overhyped title, criticisms of earlier work embedded in one reference have been removed, and nine new references to earlier work have been added.

Last week at the KITP, Keith Dienes gave a talk on A Statistical Study of the Heterotic Landscape. He gave a good idea of the state of the art of the investigation of the Landscape, focusing on one special type of models, heterotic models. The results he presented gave statistical distributions for just two very crude aspects of these compactifications, their gauge groups and cosmological constants. These models remain highly unrealistic, since the cosmological constants are of order the Planck scale and the compactifications are not stable.

The models studied have gauge groups of rank 22, and while many of them contain the standard model SU(3)xSU(2)xU(1), they also contain many more gauge group factors, with typically not one, but about seven SU(2) factors. These models, with their instabilities, far too large gauge groups and cosmological constants, are extremely far from anything like the standard model. It’s not at all clear what the point is in enumerating them and studying their statistics, but Dienes describes in detail various problems that arise with the whole concept of generating “random” models of this kind and trying to get sensible statistical distributions. He also looks for correlations between gauge groups and cosmological constants, finding that at small cosmological constant one is somewhat more likely to get many factors in the gauge group (although in his case, both the gauge group and the cosmological constant are very different than in the real world).

Despite the very crude state of these calculations, Dienes reports that a group of 17 prominent string theorists have banded together to form the “String Vacuum Project”, with the goal over the next few years of accumulating a database of 10s of billions of string models, with the hope of finding within this mountain of data about 100 models that have crude features of the standard model. I don’t at all see what the point of this is, but it certainly is a computationally intensive project that could keep many people occupied for a long time. It also appears to be just the beginning, with the longer term goal being to devote the next decades to expanding from 10s of billions farther into the 10^500 or whatever exorbitantly large number is thought to be the number of all string models.

The String Vacuum Project submitted a proposal to the NSF last year, which seems to have been turned down, and they appear to be planning to resubmit the proposal. They have a Wiki, with all sorts of details about the project. Most recent additions to the Wiki are from Bert Schellekens in August, who discusses a proposed “String Vacuum Markup Language” (SVML) format, with links to a web-page that produces data in this format for certain sorts of models. There’s also a European String Vacuum Project web-site.

Fewer and fewer science writers these days are credulous enough to keep promoting string theory, but there still are some around willing to keep writing overhyped stories about how theorists have finally found a way to get some sort of prediction of something observable out of string theory. One of these is Tom Siegfried, who has a new article in Science magazine entitled A Cosmic-Scale Test for String Theory? which reports that “some string theorists now believe they’ve found a way to make superstrings observable.”

Siegfried reports for Science from PASCOS 2006, where he finds two results worth writing articles about. One of these is the recent preliminary neutrino oscillation results from MINOS, which certainly are worth reporting, but the second is the cosmic superstring hype that has been around for nearly three years now, and which I’ve commented on in various places, including here and here. The hype surrounding this topic first got seriously going with a press release from UCSB more than two years ago, in which Polchinski claimed that cosmic superstrings were “potentially visible over the next year or two” at LIGO. Now that this time period is up, the hype has to be modified, and Siegfried informs us that:

LIGO may not be sensitive enough to detect them, but a planned set of three space-based gravitational wave detectors known as LISA would be a good bet.

As is always the case with string theory, there aren’t any real predictions here. The hype is based on the fact that, among the nearly infinitely complicated string theory models people have studied, it is in principle possible to come up with ones in which superstrings created in the early universe would expand to a very large “cosmic” scale and thus be observable. They would show up in various astronomical observations, but no one has yet seen the slightest evidence of such a thing. One can claim that it is logically possible that such things exist, with exactly the right properties to have escaped observation so far, but to be visible to the LISA experiment if it really does manage to get funded and operate sometime in the next decade. While this is logically possible, saying that “it would be a good bet” is pretty absurd; I doubt that any physicist would be willing to put money on this unless given very high odds.

The hype surrounding cosmic superstrings tends to completely confuse the kind of cosmic strings that occur as defects in the Higgs field in some GUT models (which have been studied for about 30 years now) with the kind that are supposed to come from elementary strings. Siegfried’s article includes a graphic purporting to show a “network of enormous ‘superstrings'”. As far as I can tell, this is nonsense, since the same graphic occurs here, in an article from 2000, long before the “cosmic superstrings”, where it is described as showing “cosmic strings form[ed] from a random initial distribution of phases of a hypothetical field called a Higgs field.”

Oh, and the fact that I think this is a pretty sad example of bad science reporting by someone completely taken in by the string theory hype machine has nothing to do with the fact that its author recently wrote an extremely hostile, unfair and inaccurate review of my book…

Update: For an example of the kind of misinformation spread by stories like this, see this blog entry by another science journalist, over at Seed’s ScienceBlogs.