Not Even Wrong

I recently noticed that, around the same time I was preparing my slides for a talk about Is String Theory Testable?, Michael Douglas was doing something similar, preparing a talk on Are There Testable Predictions of String Theory? There’s a certain amount of overlap in our presentations, and people might find it interesting to compare them.

Douglas goes over much the same story I do, but reaches different conclusions. For him, string theory does “make predictions”, just lots and lots of incompatible ones, so the problem is that:

none of the ideas which have been suggested so far are guaranteed signatures of string theory. We would be happier with one prediction, which could lead to a decisive answer either way.

This is the sort of thing I would call a prediction, so I guess we agree that they don’t exist. Douglas ends by noting that the one way he can think of to get such a prediction is through a statistical argument based on counting vacua and the dynamics of eternal inflation. He doesn’t mention the argument given in my talk that this is already falsified (by the lifetime of the proton), or that such arguments inherently lead to calculations that are inherently intractable and can never be done (this argument is due to him and Denef, it is surprising that he doesn’t mention it).

Along the way, Douglas does make a couple claims about things that he thinks the statistical anthropic landscape arguments disfavor, especially varying constants and large distance modifications to gravity. Seeing these would falsify our current theory, but would not falsify string theory, since it can accomodate them, although perhaps not within Douglas’s statistical framework.

One of the more surprising responses I’ve seen to my recent claims that string theory has failed as an idea about unification because it’s inherently untestable comes from Mark Srednicki, who writes (in the context of mentioning an MSNBC interview with Brian Greene):

We see that the big issue for Brian, and for just about all scientists (though with the apparent exceptions of Lee Smolin and Peter Woit), is what is TRUE. Not what corresponds to some philosophy of what science is or is not. Lee writes that the landscape must be rejected because “it would mean the end of our field” (page 165). It should be obvious that this is not the basis that is traditionally used for accepting or rejecting a theory! Peter’s (essentially the same) argument that string theory must be rejected because (at the moment) it does not appear to be sufficiently predictive (for Peter) is also irrelevant to the question of whether or not string theory is TRUE.

If the landscape is right, we may never get anything more than circumstantial evidence that it’s right. But that’s often the case in science. We’ve been spoiled in particle physics by having extremely precise data and highly predictive and quantitative theories for the past few decades. Most of the rest of science has not been so lucky. Perhaps we will not be so lucky going forward. The only way to find out is to do more work and see where it leads.

Srednicki’s reaction to the lack of testability of string theory seems to be that testability is not what matters. What matters is what is TRUE, and it’s perfectly logically consistent for string theory to be of such a nature that we can never test it. The problem with this point of view is that science is not so much about what is true as about how one knows what is true about the world. Religious believers are also interested in what is true and think they know what this is, but science is different since it provides a means for deciding what is true. Scientific ideas about the universe are true when they make predictions that can be checked in a convincing way. Ideas that can’t be experimentally checked in some way, directly or indirectly, may or may not be true, but they’re not scientific ideas, rather something of a different nature.

The LHC is the cover story on this week’s issue of Science magazine, with three articles on the topic here, here and here.

Also in this week’s Science is an article about the “spin puzzle”, the fact that accelerator experiments with polarized particles give results for protons that are different than what one would expect from a naive quark model. The general assumption seems to be that this is a QCD effect, one that is tricky to calculate. I’ve always wondered if there is any chance that there is some sort of spin-dependent behavior of quarks different than that predicted by QCD. I don’t know of any work by people trying to come up with such models, but maybe it’s out there. I’d love to hear from some expert on this about whether the experimental results really do point to a serious possibility of something going on other than standard QCD.

A new book of interviews of scientists has recently appeared, Candid Science VI by Istvan and Magdolna Hargittai. It contains interviews with David Gross and Frank Wilczek. The authors ask both of them about their interactions with Wigner, and what they think of various other famous Hungarian scientists. Wilczek explains why he has made various moves over his career, that he was quite influenced by Peter Freund as an undergraduate, why he thinks it took so long to get the Nobel prize, and that his motivation for working on the beta-function calculation was to know if the electroweak model had the same Landau pole problem as QED.

Gross talks about his background and relation to Judaism, and also about his Nobel prize work. He remains enthusiastic about string theory, and characterizes opposition to string theory in many physics departments as due to people not wanting to learn it because it is hard work, as well as fear that if they hire string theorists, all the good graduate students will go work with them. There may be something to what he says, but I think it’s out of date, and times are changing.

I hear from David Derbes, who put together Dyson’s 1951 Lectures on Advanced Quantum Mechanics that were mentioned here earlier, that World Scientific is publishing them as a book this month. Profits will go to the New Orleans Public Library, where David grew up.

The two new Fields medalist bloggers each have fascinating blog entries on Millenium problems. Terry Tao writes a long explanation of Why Global Regularity for Navier-Stokes is Hard. He also comments about the recent New York Times piece about him and about math education issues. The comment sections of his postings have some very interesting discussions going on.

Alain Connes has a wonderful posting about Le reve mathematique, especially his mathematical dream of proving the Riemann hypothesis using non-commutative geometry. He notes that the first goal is to come up with a non-commutative geometry version of a proof for the function field case. More about this in a recent posting on the same blog by David Goss.

This seems to be the month for string theory debates, with two a couple weeks ago in the UK involving Lee Smolin, and another featuring Lawrence Krauss and Brian Greene scheduled for next week in Washington D.C. The Washington Times has an article about this.

Smolin’s book has just appeared in the UK, and there have been lots of (very positive) reviews. See here, here, here, here, and here.

Besides talks (for a report on the one at Cambridge by a skeptical American physics student in England, see here), there were two debates. One featured Smolin, Philp Candelas, Simon Saunders and Frank Close and was held at Oxford; for a report, see here. It appears to have been a respectful and reasonable public airing of a few of the issues where string theorists and some of their critics disagree.

A couple days earlier though, a debate in London between Smolin and Mike Duff (also involving philospher Nancy Cartwright) had a very different nature. According to the report from one attendee, after Smolin started things out by arguing his case:

Smolin sat down. Duff stood up. It got nasty.

The trouble with physics, Duff began, is with people like Smolin…

Duff is described as “string theorist and man for whom, one imagines, the words ‘self’ and ‘doubt’ do not often rub shoulders”, and seemed to think it was a good idea to answer criticisms of string theory with vociferous ad hominem attacks. Lubos Motl and Clifford Johnson both found Duff’s behavior an excellent example for all string theorists, inspiring Clifford to write part VII of his extended attack on me, Smolin and our two books. He admitted somewhere around part V or VI that he actually hadn’t looked at the books and had no intention of doing so, and he’s pretty steadfast in that attitude. It never ceases to surprise me that people like Clifford don’t realize that, much as they may enjoy engaging in or listening to personal attacks on me and Smolin, this just doesn’t do a lot for the credibility of their field. String theorists often complain that Smolin portrays them as arrogantly dismissing any criticism, but they should realize that behavior like Duff’s doesn’t help them at all on this issue, quite the opposite.

Duff pretty obviously has a double standard for popular books about string theory. He’s quite capable of being polite, writing a very respectful review of Susskind’s The Cosmic Landscape for Physics World. His review of Smolin’s book in Nature Physics is something very different, much more like his performance at the debate. The review begins by misquoting Smolin, based upon something that was in the proof copy of the book he had (which the author hasn’t had a chance to look at), but was different in the published version. After the review, he had been informed about this, but still seemed to think it was a good idea to use this as ammunition in his personal attack on Smolin during the debate.

One of his main points was that it is ridiculous to claim that string theory has not made any progress since the 80s. Obviously there are some areas in which there has been progress in better understanding the theory, but, as far as the central issue, that of getting any predictions out of the idea of using strings to unify physics, it’s interesting to follow the link that someone with a waggish sense of humor at Nature put at the bottom of the page of Duff’s review. It’s a story from 1986 entitled Where Now With Superstrings?, and it reports on the views of string theorists at the time, roughly one year after the early developments that caused so much enthusiasm for string theory as a unified theory. The problem of too many vacua was something people were starting to worry about, but the feeling was that:

… another problem of non-uniqueness in superstring theory, the variety (thousands) of possible four-dimensional worlds it allows, is showing some signs of resolution.

The “progress” on this more than twenty years later is that instead of “thousands”, the number has moved up to the exponent, and we’ve now got the “Landscape” of 10¹⁰⁰⁰ or so possible four-dimensional worlds. Any “signs of resolution” of this are long vanished. Just as physicists are now waiting for the LHC next year, those of 1986 were waiting for the Tevatron to start up the next year, with Weinberg claiming that the mass range to be explored by the Tevatron was “a very plausible mass for them [superpartners] to have”. The reporter wrote that:

If the Tevatron sees no superparticles, supersymmetry will lose its value in the hierarchy problem, and hence half its motivation.

So, I guess Duff is right that it’s inaccurate to say that things haven’t changed with the prospects for string theory since 1986, since the situation now is a lot worse than it was then.

If you want to listen to the debate, audio is available on-line here, with a transcript to appear shortly. For another kind of audio showing what this is all about, see this posting from Sabine Hossenfelder.

Last Friday night when I was in Rome I received e-mails in quick succession from two science journalists asking what I thought about a new mathematical result, the “mapping of E8” that was going to be announced at a press conference on Monday. Information sent to journalists was embargoed until Sunday night at 11pm, but the first journalist sent me a copy of the brief press release and told me that there was a longer one available. Reading the press release left me still baffled about what this could be about: what was the “century old problem” that this group of 18 mathematicians had solved? The obvious interpretation of “mapping of E8”, mapping it as a geometrical object, didn’t make sense since that’s a well-understood problem. The group E8 is a 248 dimensional space, but its local geometry is the same everywhere and completely understood in terms of its Lie algebra. The global topology is interesting, but also well understood.

I wrote back to both journalists that the best person I knew to comment on this and its possible relation to physics would be John Baez, and asked to see the longer press release. It wasn’t much more enlightening, but it did have a link to a web-site with details. After spending a little time reading this I understood that “mapping of E8” was a calculation of the structure of representations of the split real form of E8, and decided that I was on vacation and not about to try and quickly write a blog posting about this.

Well, here are the press releases from MIT and AIM, and David Vogan did give a public talk about this yesterday at MIT. The media blitz was quite effective, getting the story into not just the usual suspects (there’s a good version of the story by JR Minkel at Scientific American), but also achieving a wide distribution in much less usual places such as today’s New York Times, the BBC, le Monde, and many, many others. I think this may be getting about as much attention as the proofs of Fermat’s Last Theorem and the Poincare Conjecture. There are also a huge number of blog postings, and I’m very pleased with myself to note that by far the best is the one by John Baez (crucially supplemented by the first comment there, from David Ben-Zvi), so I at least sent the journalists to the right place.

For mathematical details, John’s posting and the comments there are the best place to go besides the technical papers linked to from the AIM site.

While the calculation is a computational tour de force, and the computational methods may be useful elsewhere, the level of hype in the press releases, especially about the possible relations to physics, is somewhat disturbing. The AIM page on E8 and Physics contains statements such as

…once one adopts the basic principles of string theory, it can be argued that we live in the universe we live in because it is the only one that is possible.

as well as making the highly misleading claim that the new calculation has something to do with heterotic string theory.

What initially confused me about the press release is that, with the standard interpretation of what one means by “E8”, the “E8” that appears in heterotic string theory, there is no open problem to be solved. The group is well-understood, and so is its representation theory. As a compact Lie group, the representation theory of E8 is part of the standard Cartan-Weyl highest weight theory, and was worked out long ago. To read about this, there’s an excellent book by Frank Adams about the representation theory of E8 and other exceptional Lie groups, called Lectures on Exceptional Lie Groups. It is this representation theory that appears in the heterotic string story. For more about E8, and one of the stranger things I’ve seen in a math paper, you might want to look up a 1980 paper by Frank Adams called “Finite H-spaces and Lie Groups”, in the Journal of Pure and Applied Algebra.

What the new result is about is something quite different, the “split real form” of E8. The classification of compact Lie groups proceeds by classifying their Lie algebras, giving a well-known list, with E8 the largest of the exceptional cases. In doing this, one complexifies (works over the complex numbers), studying the complex semi-simple Lie algebras, which are the Lie algebras of the complexifications of the compact Lie groups. In the simplest example, one studies SU(2) by complexifying its 3d Lie algebra (R^3 with vector product), i.e. studying the Lie algebra of SL(2,C) instead. Finite dimensional unitary representations of SU(2) correspond to holomorphic representations of SL(2,C), and the same correspondence works in general between finite dimensional unitary reps of compact Lie groups and holomorphic representations of their complexifications.

Given the complexified group, one can ask if it has other “real forms”, i.e. subgroups other than the compact one which would have the same complexification. In the case of SL(2,C), there is another real form: SL(2,R). The representation theory of SL(2,R) is a vastly more complicated subject than the case of SU(2). One reason is that the group is non-compact. Geometrical constructions of representations like the Borel-Weil construction give infinite-dimensional irreducible unitary representations. The case of SL(2,R) is difficult enough (and a central topic in number theory), but the case of representations of general real forms of semi-simple Lie groups is extremely difficult and complicated. Representations are infinite-dimensional and labeled by “Langlands parameters” instead of highest weights. This theory has been pretty well worked out over the last 30-40 years or so, with the case of E8 one where it was known how to do calculations in principle, but they had so far been computationally intractable. Dealing with this is the new advance.

What actually is calculated are things called “Kazhdan-Lusztig” polynomials; for an explanation, see John’s blog. These tell one how to build arbitrary irreducible representations out of something simpler which one does understand, certain induced representations called “standard” representations. The numbers involved here also have a beautiful geometrical and topological interpretation. This is a generalization of what happens in the compact case, where the cell decomposition of the flag variety governs how irreducibles are built out of Verma modules.

So, this is a result about the structure of the irreducible representations of one of the real forms of E8 called the “split” real form. As far as I know it has nothing to do with heterotic string theory. The only thing I can think of that physicists have worked on that might make contact with this result is the work of people like Hermann Nicolai and Peter West trying to get physics out of Kac-Moody algebras like E10 and E11. I have no idea whether they have run into the split real form of E8 subalgebras and the representation theory of these in their work. In Pisa I had the pleasure of meeting blogger Paul Cook, a student of Peter West’s who is now a postdoc in Pisa and has worked on this kind of thing. Perhaps he would know about this.

Update: I hear from Jeffrey Adams that he has put together a web-page about this, aimed at mathematicians, and designed to explain the nature and significance of this result. It’s quite clear and does a good job of this, accessible if you have a bit of background in representation theory. If not, you may at least enjoy his comment on the media attention:

This leaves the question of why this story took off in the press. For us, that is harder to understand than the Kazhdan-Lusztig-Vogan Polynomials for E8.

I’ve been traveling in Italy for the past ten days, and gave talks in Rome and Pisa, on the topic “Is String Theory Testable?”. The slides from my talks are here (I’ll fix a few minor things about them in a few days when I’m back in New York, including adding credits to where some of the graphics were stolen from). It seemed to me that the talks went well, with fairly large audiences and good questions. In Pisa string theorist Massimo Porrati was there and made some extensive and quite reasonable comments afterwards, and this led to a bit of a discussion with some others in the audience.

I don’t think the points I was making in the talk were particularly controversial. It was an attempt to explain without too much editorializing the state of the effort to connect the idea of string-based unification of gravity and particle physics with the real world. This is something that has not worked out as people had hoped and I think it is important to acknowledge this and examine the reasons for it. In one part of the talk I go over a list of the many public claims made in recent years for some sort of “experimental tests” of string theory and explain what the problems with these are.

My conclusion, as you’d expect, is that string theory is not testable in any conventional scientific use of the term. The fundamental problem is that simple versions of the string theory unification idea, the ones often sold as “beautiful”, disagree with experiment for some basic reasons. Getting around these problems requires working with much more complicated versions, which have become so complicated that the framework becomes untestable as it can be made to agree with virtually anything one is likely to experimentally measure. This is a classic failure mode of a speculative framework: the rigid initial version doesn’t agree with experiment, making it less rigid to avoid this kills off its predictivity.

Some string theorists refuse to acknowledge that this is what has happened and that this has been a failure. Most I think just take the point of view that the structures uncovered are so rich that they are worth continuing to investigate despite this failure, especially given the lack of successful alternative ideas about unification of particle physics and gravity. Here we get into a very different kind of argument.

It was very interesting to talk to the particle physicists in Rome and Pisa. They are facing many of the same issues as elsewhere about what sort of research directions to support, with string theory often being pursued as an almost separate subject from the rest of particle theory, leading to conflict over resources and sometimes heated debates between them and the rest of the particle physics community. Many people were curious about how things were different in the US than in Europe, but I’m afraid I couldn’t enlighten them a great deal, mainly because I just don’t know as much about the European situation, although I’ve started to learn more about this on the trip. Several wondered if the phenomenon of theorists going to the press to make overhyped claims about string theory was an American phenomenon. I hadn’t really noticed this, but it does seem to be true. While the hype starts in the US, it does travel to Europe, with the US very influential in this aspect of culture as in many others. In the latest issue of the main Italian magazine about science, there’s an article explaining how certain US theorists have finally figured out how to test string theory with the new LHC…

John Horgan keeps moving his blogging activities to different locations, the latest one is here.

For a truly sad and distressing story about what has happened to Billy Cottrell (who was mentioned snarkily by me long ago here), see this LA Weekly article and a Clifford Johnson posting. The abuse of people going on in this country associated with labeling them “terrorists” is just appalling and deeply shameful.

More from Steinn Sigurdsson on Yarn Theory.

Cern Courier reports on the recent Axion workshop at Princeton and the 2006 Quark Matter conference in Shanghai.

Lee Smolin’s book is out in the UK, here’s a review from the Financial Times.

The latest London Mathematical Society newsletter has a review of Not Even Wrong.

David Ben-Zvi was here last week and gave a wonderful colloquium talk on Langlands duality, loop spaces and representations of real groups. Much of was somewhat general philosophy about a new way of thinking about these topics, and this was quite compelling, although I need to find a sizable chunk of time to sit down and really understand what he is doing. If I can do this, maybe I’ll then take a stab at trying to explain this here. He did convince me that one needs to think not only about stacks, but derived stacks. There’s a long foundational document about this by Jacob Lurie (see here), something more readable from Bertrand Toen.

This semester Edward Frenkel is running a seminar on Topics in the geometric Langlands program. The slides of a talk by Ben Webster that are there are wonderful. One problem with this field has always been how unreadable much of the material about is. People like Webster and Ben-Zvi are starting to do a great job of explaining what is going on in a form that others have some chance of following.

Later this month the IAS will have a conference related to this topic, next year a whole program.

I’ll be travelling most of the next week and a half or so, so blogging will be light to non-existent. Behave.

There’s a short memoir out this evening on the arXiv by Peter Freund about the algebraist Irving Kaplansky, universally known as “Kap”, who died last year at the age of 89. Freund worked with Kaplansky at Chicago during the mid-seventies on the classification of Lie superalgebras, and comments about the relations between math and physics at that time. He also claims that Kaplansky told him with assurance that Hopf algebras couldn’t possibly be of relevance to physics, and that Andre Weil was the greatest living mathematician, since he called all the courses he taught “mathematics”, and lived up to this title. Freund also tells a well-known story about a talk by Weil at Chicago that he heard about first-hand from Kaplansky.

Freund’s piece is based on his talk at the recent memorial event held for Kaplansky in Berkeley at MSRI. His student Hyman Bass has a wonderful presentation describing Kaplansky’s life and work.

I have my own personal recollections of Kap since he was director of MSRI the year that I was a postdoc there (1988-9), a year during which I unfortunately had only a few short conversations with him. The conversation with him I remember best was our first, which occurred on the phone. In early 1988 I was working part-time teaching Calculus at Tufts and had applied for several full-time mathematics jobs for the next year, not at all sure that there was any chance this would work out, since my Ph.D. and first postdoc had been in physics. When the call came from Kap offering me a job at MSRI for the next year I was elated, partly because Berkeley is one of my favorite places to live as well as being an excellent place to work in both mathematics and physics. During our conversation Kap told me a bit about his work on and continued interest in supersymmetry. I didn’t really have the heart to tell him that because my own inclinations are so geometric, I’d always found supersymmetry and superalgebras a tantalizing but very frustrating subject.

Many string theorists seem to have decided to react to the criticisms of string theory that have recently been getting a lot of attention by going to the press with claims to have experimental tests of string theory that can be performed in the very near future.

The latest of these claims has nothing at all to do with the aspect of string theory that has come under criticism, its failure as a unified theory of gravity and particle physics, but instead involves the conjectural use of string theory as an approximation method in QCD. The main problem with this idea so far is that it involves not QCD but a related theory (N=4 supersymmetric Yang-Mills), and it is very unclear exactly what the relation is between the calculation and the real world. For some earlier comments about this, see here. John Baez also has a summary, and the Backreaction blog of Sabine Hossenfelder and Stefan Scherer has a very extensive explanation here.

Last week the AIP Physics News site carried a story entitled String Theory Explains RHIC Jet Suppression, which dealt with recent work by Hong Liu, Krishna Rajagopal and Urs Wiedemann concerning the jet quenching parameter, which describes how charmed quarks move through a quark-gluon plasma. In the AIP story, Rajagopal claims that their calculation “agrees closely with the experimentally observed value”, and that other related calculations “make a specific testable prediction using string theory.” This story was picked up by Scientific American, which has a story by JR Minkel. According to Scientific American, “trying to fit the QCD-like theory to reality makes the results only semi-precise, Rajagopal says,” alluding to the problem of doing the calculation in the wrong theory. Maldacena is quoted about this as follows:

It’s like saying you are trying to study water, but instead you are studying alcohol… We certainly know it’s not the correct theory, but maybe it behaves in the same way.

Theorist Ulrich Heinz is even more skeptical:

Even if any of the numbers worked out by accident, I don’t think it would validate the approach… If they predict the color of an apple, and somebody looks at a pear and finds it has the same color, would you say that the prediction was correct?

Other recent claims by Shiu et al. and Distler et al. to be able to make predictions using the string theory approach to unifying physics are covered in the latest issue of Plus magazine, in a story entitled Stringent Tests. According to this story

It seems that string theory, so far the strongest contender for a physical “theory of everything”, may soon be put to the test for the first time. Two separate teams of physicists have just published work describing how to compare the theory’s predictions with reality….

Neither of the two new tests will be capable of verifying string theory once and for all. If the results concur with its predictions, then this is just some further evidence for its correctness, not absolute proof. But the tests’ ability to falsify string theory, or at least certain aspects of it, means that a philosophical barrier has been overcome.

On a somewhat related note, I’ll soon be traveling to Italy, giving talks in Rome and Pisa on the topic of “Is String Theory Testable?”.

The March issue of Physics Today is now available. It contains a piece by Steven Weinberg based on a banquet talk he gave to a group of postdocs. He describes his own memories of his time as a postdoc, writing that “Many of us were worried about how difficult it seemed to make progress in the state that physics was in then.” This was the heyday of S-matrix theory and he comments:

Some people thought that the path to understanding the strong interactions led through the study of the analytic structure of scattering amplitudes as functions of several kinematic variables. That approach really depressed me because I knew that I could never understand the theory of more than one complex variable. So I was pretty worried about how I could do research working in this mess.

He describes envying the previous generation of 10-15 years before his time, that of Feynman, Schwinger, Dyson, and Tomonaga, thinking that all they had had to do was sort out QED, and speculates that they in turn had envied the generation before them since quantum mechanics was even easier. I can see that he’s trying to provide encouragement, ending with

So the moral of my tale is not to despair at the formidable difficulties that you face in getting started in today’s research… You’ll have a hard time, but you’ll do OK.

Postdocs in high energy physics these days do need some encouragement, but I also think they need some recognition from their elders that they’re facing a different situation than that faced by earlier generations. Coming into a field that has not seen significant progress in about 30 years is a different experience than what Weinberg or previous generations of particle physicists had to deal with. High energy physics is now facing some very serious problems, of a different nature than those of the past, and I think these deserve to be mentioned.

In the same issue, Weinberg makes another appearance, in an exchange of letters with Friedrich Hehl about the torsion tensor in GR. Hehl takes him to task for his comments in a previous letter that torsion is “just a tensor”, pointing out that it can be thought of as a translation component of the curvature. Weinberg responds that he still doesn’t see the point of this:

Sorry, I still don’t get it. Is there any physical principle, such as a principle of invariance, that would require the Christoffel symbol to be accompanied by some specific additional tensor? Or that would forbid it? And if there is such a principle, does it have any other testable consequences?

Actually, Weinberg is rather well-known for taking the point of view that GR is just about tensors, and that their geometrical interpretation is pretty irrelevant, so it’s not surprising that he doesn’t see a point to Hehl’s comment. In his well-known and influential book on GR, he explicitly tries to avoid using geometrical motivation, seeing this as historically important, but not fundamental. To him it is certain physical principles, like the principle of equivalence, that are fundamental, not geometry. There’s a famous passage at the beginning of the book that goes:

However, I believe that the geometrical approach has driven a wedge between general relativity and the theory of elementary particles. As long as it could be hoped, as Einstein did hope, that matter would eventually be understood in geometrical terms, it made sense to give Riemannian geometry a primary role in describing the theory of gravitation. But now the passage of time has taught us not to expect that the strong, weak and electromagnetic interactions can be understood in geometrical terms, and too great and emphasis on geometry can only obscure the deep connections between gravitation and the rest of physics.

This was written in 1972, just a few years before geometry really became influential in particle physics, first through the geometry of gauge fields, later through geometry of extra dimensions and string theory. I recall seeing a Usenet discussion of whether Weinberg had ever “retracted” these statements about particle physics and geometry. Here’s an extract from something written by Paul Ginsparg, who claims:

back to big steve w., when he wrote the gravitation book he was presumably just trying to get his own personal handle on it all by replacing any geometrical intuition with mechanial manipulation of tensor indices. but by the early 80’s he had effectively renounced this viewpoint in his work on kaluza-klein theories (i was there, and discussed all the harmonic analysis with him, so this isn’t conjecture…), one can look up his research papers from that period to see the change in viewpoint.

There’s an article in this week’s Science magazine by Adrian Cho entitled Dreams Collide With Reality for International Experiment. It’s about DOE Undersecretary Orbach’s warning to HEPAP (mentioned here) that current plans were too optimistic about the time-scale for the ILC, leaving a potentially dangerously long period with few US HEP experiments in progress.

Some physicists who had proposals for experiments (BTeV and RSVP) that were canceled in favor of going ahead full steam with the ILC were not amused:

Meanwhile, Orbach’s call for a program of smaller projects evoked jeers from researchers whose experiments had been cut. “This is really stupid and very frustrating because we had a program,” says Sheldon Stone, a physicist at Syracuse University in New York who worked on an experiment called BTeV that would have run at the Tevatron collider at Fermilab.

While experimentalists are worrying about the short-term, string theorists seem to be taking the long view. In his talk on String Theory: Progress and Problems at the recent conference celebrating the centennial of Yukawa and Tomonaga, John Schwarz ends with the conclusion

Even if progress continues to be made at the current rapid pace, I do not expect the subject to be completely understood by the time of the Yukawa-Tomonaga bicentennial.

I don’t find his claims about a current rapid pace of progress very convincing, and the idea of the entire next century of theoretical particle physics being dominated by the kind of unsuccessful more and more complicated string theory constructions we’ve seen for the last 25 years doesn’t seem like something to look forward to.

Turning from the difficulties of the future, Howard Georgi gave a wonderful talk on The Future of Grand Unification at the same conference, which was actually mainly about the past, largely devoted to telling the story of how he and Glashow came up with the first GUT models. He emphasizes the kinds of manipulations of representations of Lie algebras that he and Glashow were masters of and used to construct many different kinds of models. There’s also an advertisement for his wonderful book on the subject, the text for his course where I first many years ago encountered this subject. This semester I’m teaching my own course on the same material, from a rather different point of view, emphasizing geometry. It remains one of the most beautiful and central parts of modern mathematics as well as physics.