Not Even Wrong

Shamit Kachru gave the physics colloquium at Rutgers yesterday. His title was “The Theory of More Than Everything” and I heard from people who attended that he was promoting research into the “Landscape” as a new model of how to do theoretical physics, especially cosmology.

I was down there today and heard two talks in the mathematical physics seminar, by Abhay Ashtekar and Tom Banks. Ashtekar’s talk was a standard exposition of a few of the basic ideas of loop quantum gravity, also reviewing an attempt to apply these ideas to cosmology. The talk by Banks was titled “Triumphs and Travails of String Theory”. The first hour was about the triumphs, giving a pretty standard survey of the supposed accomplishments of string theory. Banks emphasized the importance of supersymmetry, and described string theory as not quite background independent, but depending only on a choice of “asymptotic background”. He dealt with matrix models, holography, BPS states, dualities, getting gauge bosons out of string theory, and AdS/CFT.

His talk contained quite a lot of content, unlike some promotional talks of this kind, but it did come off a bit like an hour-long infomercial (“And, there’s even more! It slices, it dices, it ….”). The last five minutes were devoted to the travails of string theory, of which, according to Banks, there is really only one (although he did mention that the lack of observed supersymmetry is also a problem). The one travail is the fact that the cosmological constant seems to be positive, so the universe is de Sitter, not anti de Sitter or flat. This creates well known problems with defining an S-matrix. He went on to explain the “Landscape” idea with its de Sitter states that are only metastable, saying this “leads to a new philosophy of doing physics that many are exploring”. He didn’t seem interested in directly criticizing this new philosophy, but did end by promoting his own, different, ideas about how to deal with the cosmological constant problem.

During the question session afterward, someone asked if there was any overlap between loop quantum gravity and string theory. After some hemming and hawing by the speakers, Michael Douglas spoke from the audience, saying that since string theory was really 20 or so different kinds of approaches to quantum gravity, it was quite plausible that LQG was another related one.

A correspondent points out that this month’s Physics Today has a couple articles about ethical issues involved in how physics research is conducted in the U.S.

Most of this doesn’t really apply to the kind of research I know best, theoretical research in physics and research in math. One main issue considered is the trustworthiness of experimental data, and as far as I can tell, in elementary particle physics the data is quite trustworthy. Since the collaborations that produce these results are so huge, many people are involved in going over any published result of any interest, so even if someone were tempted to fake or manipulate data, it would be hard to get away with.

Another issue of concern is the treatment of young experimentalists, who are often overworked and under-recognized. But the situation of theorists is generally different. In most cases the problem for them is thesis advisors who ignore them, not ones who pay close attention to what they are doing and make them work too hard. There is a fundamental ethical problem in the treatment of young theorists by the physics community, that of producing far more particle physics Ph.D.s than there are jobs for. This creates a brutal situation for young people, while it is to some degree in the interests of those who are established in permanent positions to let this go on.

The main ethical problem in particle theory research these days, a fundamental lack of honesty in how the results of this research are evaluated, doesn’t seem to be addressed at all in the Physics Today articles.

Howard Georgi gave a colloquium at Fermilab last week, and the slides and video from his talk are now online. He has gathered quite a lot of interesting data about women in the various sciences at the undergraduate and graduate level, and he discusses his experiences at Harvard over the years as he became more aware of the problems experienced by women studying physics. As chair of the department and in other capacities, he has tried to understand why there are so few women studying physics, significantly fewer than in the other sciences, concluding that “Many of our women physics concentrators were trapped in an emotionally abusive relationship with the Harvard Physics Department!!!”. He also concluded that it was “past time to outgrow the hypermacho lone-ranger approach to physics”, and that this would make the field more fun for everyone.

The whole issue of why so few women study physics (and math) seems to me a complicated one since it is mostly about the very complex and tricky ways in which people deal with how others expect them to fit into certain behavior and roles appropriate to their gender. I don’t think the “emotionally abusive relationship” that Georgi describes the Harvard department as having with its students is limited to the female ones. While I can say that in many ways I very much enjoyed my time as an undergraduate there, the great majority of the faculty were less than friendly to the students (with Georgi a prominent exception), and the general level of social skills of both the faculty and many of one’s fellow students left a lot to be desired. According to Georgi, changes have been made to the culture of the place and it is much more encouraging of its students. This is part of a general trend at many US institutions, partly because of increased sensitivity to gender issues, partly just because the students are paying a lot more to be there than they used to, and their increased dollars get them increased attention and respect.

Then again, they now have Lubos Motl, so the Harvard department’s traditions of hyper-aggressive behavior have not totally been lost.

SLAC and Fermilab have joined forces and replaced their “FermiNews” and “Beam Line” publications with a new one called “Symmetry”. I like the title; it’s nice to see that the major US particle physics labs are supporting a publication about group representation theory.

One of the arguments often given for string theory is that it is somehow exceptionally “beautiful”. This has always mystified me, since that’s certainly not the way I would describe it. Over the years I’ve paid close attention whenever I see someone trying to explain exactly what it is about string theory that is so beautiful. Lubos Motl has just posted his own detailed answer to this question, something I read with interest.

As usual, Lubos is not exactly concise, so I won’t quote him extensively, but let me try and summarize his arguments for calling string theory beautiful, together with some of my own comments.

1. Symmetries are beautiful and just about every symmetry you can imagine gets used somewhere, somehow in string theory.

Even Lubos is not so sure of this argument, since he says ” I don’t really thing that we view symmetries as the most important reason why string theory is beautiful”. What is beautiful about symmetries is the way they constrain things. If your theory is based upon a simple symmetry principle (take for example gauge theory and the gauge symmetry principle), a huge amount of structure follows from a single, simple principle. String theory is not based on a simple symmetry principle, rather it is a complicated framework, into which you can fit all sorts of different symmetry principles. But because they are not fundamental, these symmetries don’t constrain the theory much if at all. This is very different than the standard model, where at a fundamental level the theory is built around a single symmetry principle, one that governs a large part of the structure of the theory and its physical predictions.

2. The way in which “miraculous” cancellations occur in string theory, constraining the theory by only allowing it to make sense for certain specific choices.

The most well known example of this is the way in which anomaly cancellation picks out 10 dimensions and SO(32) or E_8 times E_8 for the superstring. This was the main reason people got so excited back in 1984, when they thought that the anomaly cancellation principle would give them a nearly unique theory that could be used to make predictions. If the anomaly cancellation principle had picked out four dimensions and SU(3)xSU(2)xU(1), that certainly would have been a beautiful explanation of why the standard model is the way it is. In the standard model itself, anomaly cancellation for the chiral gauge symmetry does work in an impressive way. If you take just the leptons or just the quarks, you have an anomalous theory, but the anomalies of the one cancel those of the other.

In string theory, all anomaly cancellation does is pick out a much too large dimension of space-time and a much too large gauge group. You can certainly embed the standard model in this structure, but you could also embed just about anything you want in it because there is so much room. In the end you are stuck with some version of the “Landscape”, essentially an infinite number of different possibilities with no way to choose amongst them. The anomaly cancellation ends up providing very little constraint on what the structure of low energy physics looks like.

3. String theory is a unique theory that can predict everything about the physical world.

Lubos likes to go on about how unique and predictive string theory is. While I understand this is the dream of every string theorist, the reality of what they actually have is a long ways from what they hope is true. The vision of what they would like to be true may be beautiful, but the reality is something else. The reality is that there is no “unique” string theory that can reproduce the real world, just a dream that such a theory exists. And as for predictions of string theory, there are none. When Lubos says that “string theory predicts” things, what he really means is that if every thing he would like to be true actually were, then in principle you could predict things from string theory.

4. String theory manages to extend quantum field theory in a consistent way, something which is very non-trivial and the way this happens can be described as beautiful.

This seems to be Witten’s main argument these days for promoting the continued study of string theory and I have a certain amount of sympathy for it. There certainly is something of interest going on behind the complicated framework that people are studying under the name “string theory” and maybe it will someday lead to insight into something about physics, most likely the strong coupling behavior of gauge theories. But the fact that there is interesting structure you don’t understand doesn’t mean that this structure has anything to do with a fundamental unification principle for physics.

5. There are beautiful connections to new pure mathematical structures.

The relation of string theory to mathematics is a huge topic, and I’ll comment on it at length at some other time. In brief though, while I think string theory has been an utter disaster for theoretical physics during the past 20 years, it has lead to many interesting things in mathematics. However, most of these interesting things really come from 2d conformal QFT, and I would argue that it is QFT which is having a huge impact on mathematics, much more so than string theory. Witten’s Fields medal was for his work on the relation of QFT to math, not for anything he has done using string theory.

I was down in Princeton today and went to hear Witten’s physics department colloquium on the topic of “Supersymmetry: Pro or Con”. He spent most of the hour going over the 25 year-old hierarchy argument for supersymmetry (that supersymmetry provides a reason for the Higgs to be much lighter than the Planck scale, since it is paired with a fermion whose mass can be protected by an approximate chiral symmetry).

He gave the following arguments for believing in GUTs:

1. Can naturally get small neutrino masses via the see-saw mechanism.
2. Coupling constant unification to 1%
3. Tentative evidence from CMB that fluctuations come from GUT scale.

Actually none of these seem to me very convincing (and to claim 1% coupling constant unification I think he has to use 1-loop results, at 2-loops it is more like 5-10% off, but this may depend on exactly what you are comparing to what).

His points in favor of supersymmetry were:

1. Solves hierarchy problem.
2. Coupling constant unification again.
3. Prediction of top mass from supersymmetric SO(10) GUT.
4. Supersymmetry is consistent with all accelerator data.
5. Lowest mass superpartner a good candidate for dark matter.
6. Part of string theory.

Again none of these are really convincing. If you don’t believe in GUTs, the GUT scale is irrelevant, and since we don’t understand quantum gravity, the significance of the Planck scale is also unclear. I’m no expert on supersymmetric GUT “predictions”, but they seem to depend on lots of choices for the details of the GUT, how its symmetry breaks, and how fermions get masses from the symmetry breaking. Saying that supersymmetry is consistent with all accelerator data is kind of strange since the standard model without supersymmetry is consistent with all accelerator data and there is no evidence for supersymmetry. You can guess what I think of his last argument.

His points against supersymmetry were:

1. The Higgs mass bound is already embarassingly high, need some fine-tuning to get a Higgs that massive in a supersymmetric theory.
2. Supersymmetry spoils many of the experimental successes of the standard model since it generically has experimentally disallowed amounts of violation of CP, baryon and lepton number conservation, flavor-changing neutral currents.
3. No good picture of how to break supersymmetry.

Well, for me the con has it over the pro, but Witten still seems to hold out hope that supersymmetry will be found at the LHC. At the end of his talk, he discussed what he called the “worst case scenario”; that LHC sees a Higgs particle, but nothing else: no supersymmetry, no technicolor, no Little Higgs, no extra dimensions. He said that if this happens people will look for anthropic explanations of the hierarchy problem, whereas if the LHC found something that explained the hierarchy problem, they might be encouraged to look again for non-anthropic answers to the cosmological constant problem (which he claimed was analogous to the hierarchy problem). He did say “I hope it is wrong” about the anthropic explanation of the cosmological constant.

On the anthropic front, Michael Dine is claiming that maybe the statistical analysis of the landscape will “predict” that supersymmetry breaking is at a low energy scale. The arguments he gives sound to me like a complete joke, and from what I remember Michael Douglas was recently claiming that the same kind of analysis indicated that supersymmetry was broken at a high energy scale. One other funny thing about Dine: he doesn’t say that the landscape makes predictions, but that it is “the first predictive framework we have encountered”. This is a guy who for nearly twenty years has been giving talks on “superstring phenomenology” and claiming that any day now string theory would make predictions. I wonder why in all of those previous talks he neglected to mention that not only were there no predictions from string theory, there wasn’t even a “predictive framework”.

The latest issue of the Notices of the AMS contains several things very much worth reading. There’s the second part of a wonderful biographical article about Grothendieck written by Allyn Jackson (for some comments about the first part, see an earlier posting).

There’s also an excellent short expository piece by Barry Mazur that explains a bit about one of Grothendieck’s influential and still only partially understood ideas, that of a “motive”. In algebraic geometry the standard ways of defining topological invariants of topological spaces are of limited use, and one wants a much more algebraic notion of such an invariant. This is what a motive is supposed to somehow provide, but to even show that such conjectural motives have the properties one would like requires solving perhaps the biggest open problem in algebraic geometry, the Hodge Conjecture.

Finally there’s a thought-provoking piece called The Elephant in the Internet by Daniel Biss about the effect of the internet on the mathematics literature. It contains some comments about the difference between standards in physics and mathematics, including an analogy of mathematics as classical and physics as popular music. His conclusion that “our current relationship to the Internet has the undeniable effect of degrading the sacrosanct status of the mathematical text” seems to me excessive and it’s a shame that he feels “hesitant to post my papers online; it always feels a little like leaving my infant in a dumpster.” I have some sympathy for his worry that preprint archives and contact with the more journalistic physics literature may make the mathematics literature much less authoritative than it used to be (this was also the concern of a similar article by Jaffe and Quinn published in the AMS Bulletin in 1993). But the lost golden age that Biss yearns for was not so golden. Much of the math literature was written to very high standards of rigor, but often in ways that made such uncompromising demands on the reader that virtually no one who was not already an expert could hope to understand what was being said. The fact that the internet has provided venues for much sloppier, unpolished, but more expository articles also has its very positive aspects.

There’s a fascinating interview with Atiyah and Singer now on-line. It was conducted in May at the time they were awarded the Abel prize. The interview and Atiyah and Singer’s acceptance speeches are also available in video form.

The whole interview is very much worth reading and both Atiyah and Singer make extensive comments about the relation of mathematics and physics. Atiyah makes the provocative prediction that ideas from quantum theory will ultimately have a revolutionary effect on number theory, helping to understand why the Riemann hypothesis or Langlands conjectures are true. He notes that Wiles says this is nonsense. He also predicts that new progress in theoretical physics will come from a better understanding of classical four-dimensional geometry. By this I think he has in mind something like twistor methods. Singer’s comments about string theory are probably typical of the attitude of many mathematicians. He says that, because of the Landscape “you cannot expect to make predictions from string theory. Its inital promise has not been fulfilled”, but he still is an “enthusiastic supporter of superstring theory”, largely because of the interesting mathematics it leads to.

Singer also makes the following sociological comment about mathematics, but I think what he has to say is also very true in physics:

“I observe a trend towards early specialization driven by economic considerations. You must show early promise to get good letters of recommendations to get good first jobs. You can’t afford to branch out until you have established yourself and have a secure position. The realities of life force a narrowness in perspective that is not inherent to mathematics. We can counter too much specialization with new resources that would give young people more freedom than they presently have, freedom to explore mathematics more broadly, or to explore connections with other subjects, like biology these day where there is lots to be discovered.

When I was young the job market was good. It was important to be at a major university but you could still prosper at a smaller one. I am distressed by the coercive effect of today’s job market. Young mathematicians should have the freedom of choice we had when we were young.”

Over at Preposterous Universe Sean Carroll has some comments on the anthropic principle and the landscape.

He describes one extreme of the spectrum of opinion about this as people who think the whole thing is completely non-scientific, giving what he sees as being the two kinds of objections such people make, neither of which he thinks make sense. Since I’m one of these extremists, I think I should try and explain why and exactly what the nature of my objections are, since they’re not exactly the ones Sean mentions.

The first objection Sean attributes to extremists like myself is that of accusing users of the anthropic principle of “giving up” by assigning the parameters of the standard model to a selection effect instead of calculating them. This is very much David Gross’s objection, and while I would agree with it as a socio/psychological characterization of the behavior of Susskind et. al., my own version of this objection is a bit differerent. For any given supposed fundamental theory, some observables will be calculable from first principles, and others will be aspects of the particular state we are in, dependent on the history of how we got here. Given a particular observable, in some fundamental theories it may be calculable, in others environmental. But the theory is supposed to tell us which it is going to be. The standard model tells us that the earth-sun distance is environmental, and that the magnetic moment of the electron is calculable. It is silent about the origin of its 20 or so parameters, and whether they are environmental or calculable. It is one of the first jobs of any theory that purports to go beyond the standard model to give some sort of explanation of where these parameters come from, which of them are in principle calculable and which aren’t.

The problem with the whole Landscape idea is that it is so ill-defined that it can’t even tell you what things are calculable and what things are environmental. You don’t know what the fundamental M-theory is that is supposed to be producing the Landscape and governing the dynamics of how the universe evolves in it. String theorists would probably claim that while they don’t know exactly what the fundamental theory is, they may know enough about it to make conjectures about what the Landscape should look like, at least in certain limiting cases. The problem is that their conjectures not only don’t allow them to calculate anything, they don’t even allow them to determine what is going to be calculable. The problem with string theory is not that it can’t calculate the vacuum energy, it is that it can’t calculate anything. Some string theorists are now using the Landscape picture purely as an excuse to get them out of this embarassing situation. “Not our fault we can’t calculate anything beyond the Standard Model, because maybe nothing beyond the Standard Model is calculable”. If they had a well-defined fundamental theory which exhibited this behavior, one might take them seriously, but until they do, the whole picture is nothing more than an elaborate excuse for failure. A question that should be asked of anyone promoting this stuff: show us using string theory which of the Standard Model parameters are calculable and which are environmental. If they can’t do this they shouldn’t be taken seriously.

The second objection Sean attributes to the likes of me is that we object to the explanatory use of entities that are unobservable in principle, like multiple universes. This isn’t really my objection to the Landscape. If a compelling fundamental theory existed that made lots of correct testable predictions, and such a theory predicted lots of unobservable universes, I’d happily believe in their existence. But, absent such a compelling theory, people who go on about unobservable multiple universes are not behaving very differently from those theologians who supposedly took an interest in angels and pins. Science is about coming up with explanations for the way the world works, explanations that can in principle be tested by making more observations of the world. If you’ve been working on a theory for twenty years and it has totally failed to make any testable predictions, you should admit failure and move on, not engage in elaborate apologetics for why your theory can’t predict anything.