Not Even Wrong

It seems that the second most important web-site in the particle theory community (the first is obviously the arXiv ) has been shut down by the University of Washington. The Theoretical Particle Physics Jobs Rumor Mill has for years been a comprehensive source of information about who’s hot, who’s not, the hiring plans of all the theoretical particle physics groups in the United States and Canada, and the career moves of more established theorists. I hope a new home for the site can be found at a less fearful institution. I’d consider putting it up here, but I’ve got enough particle theorists annoyed at me already…

A more and more common argument one hears from string theorists these days (for one version see a recent anonymous comment posted here) goes more or less like this:

“A fundamental theory shouldn’t be expected to predict things like fermion masses or the standard model gauge group anymore than it should be able to predict the physical properties of the planets. Anyone who expects this is making the same mistake as Kepler, who tried to relate Platonic solids to planet orbits.”

The idea here is that many or even all of the things we don’t understand about the standard model are not fundamental aspects of the theory we should expect to be able to predict. Perhaps they are determined by the details of the history of how we ended up in this particular time and place, just as the properties of the planets were determined by the detailed history of the formation of the solar system.

As far as we can tell, the properties of the standard model hold uniformly throughout the observable universe, so to adopt this point of view one needs to postulate the existence of an unobservable “multiverse” of which we see only one small part. The so-called “landscape” of an unimaginably large number of possible vacuum solutions for string theory provides one realization of such a multiverse.

What are the problems with this idea? First of all, it is not so easy to dismiss out of hand. One can certainly imagine the possibility of the existence of an M-theory (maybe now the “M” is for “Multiverse”) with a local vacuum state that corresponds to our universe, and some dynamics that allows evolution from one universe to another. Perhaps tomorrow night a preprint will appear on arxiv.org containing a simple equation expressing a dynamics such that the possibility of a universe exactly like ours does arise as some part of a solution. Should we believe in such a new theory, whatever it is?

There seem to me to be two possible cases in which such a theory would be compelling. The first would be if the theory made experimentally testable predictions. Perhaps it would have only one solution that agreed completely with current experimental observations. Then the properties of this solution could be used to predict the results of experiments not yet done. If these predictions were accurate, the theory would have strong evidence in its favor.

Even if the theory had so many solutions that one couldn’t readily use it to make predictions, one still might find it compelling due to its “beauty” or “elegance”. If it were based on a very simple equation or idea, the fact that the relatively complex structure of the standard model could be made to fall out of a much simpler equation would again be strong evidence for such a theory. Just how compelling this would be would depend on how much simpler it was than the standard model. If the new equation was more or less as complicated as the equations which determine the standard model, it wouldn’t be compelling at all.

The current state of affairs in particle theory is that many people believe that they are on the road to finding such a compelling theory, but all the evidence is that this is nothing but wishful thinking on their part. There is no viable proposal for an M-theory based on a simple set of equations with a solution corresponding to the real world. This simply does not exist. An easy way to embarass a string theorist who is going on about the beauty of the theory is to ask them to write down a simple set of equations that characterize this beautiful theory. They can’t do it now and I don’t see any reason to believe they ever will be able to in the future.

What string theorists have now is not a single, consistent theory, but a set of several inconsistent fragmentary theories that they hope can be turned into a consistent whole. This circle of ideas is significantly more complicated than the standard model that it is trying to explain.

Even this complex of ideas might be compelling if it could be used to explain one or more not yet understood aspects of the standard model, or if it made new experimental predictions that could be checked. All the evidence of recent years is that this is impossible. If the whole framework makes any sense at all, it appears to predict nothing and explain nothing about the standard model. Not a single one of the parameters of the standard model can be calculated, not a single experimental prediction, at any energy scale, can be made. It is becoming increasingly clear that the circle of ideas known as “M-theory” is completely vacuous.

Strong evidence that this is the case comes from the fact that string theorists have no idea what, if anything, M-theory is supposed to be able to predict. Polchinski and others feel they have demonstrated that M-theory can’t predict the cosmological constant, but can’t come up with anything else it can predict and, increasingly, seem happy to live with the idea of promoting a theory that can’t predict anything. This wholesale abandonment of the scientific method upsets some physicists such as David Gross quite a bit, but more and more people seem to have no problem with this. Frankly I find this all bizarre, disturbing, and becoming ever more so all the time.

A while back when looking for theoretical physics related weblogs I ran across

The Search For A Theory of Myself: The Struggle Against String Theory

which at first sounded right up my alley. It turns out to be the weblog of a grad student at UCSB who is taking a course in string theory there from Polchinski. He’s working quite hard at doing well in the course, and seemed very worried about his final on March 15. After the final postings stopped, so I was kind of worried about what had happened to him. Yesterday he finally posted again. He got an 88 % and seems to be all right.

The news that next week’s “Science Times” will run an article by NYT reporter James Glanz in which several leading string theorists say that they are giving up on the idea is rapidly spreading throughout the particle theory community. Evidently Glanz recently went down to Princeton to interview Edward Witten, who took the opportunity to announce that he has changed his mind about whether string theory will ever be a “Theory of Everything”. When Glanz contacted other string theorists and read to them what Witten had said, almost all of them told him that they too had been having their doubts about the theory.

Glanz quotes Witten as follows:

“One night a few weeks ago I was sitting at my kitchen table trying to make sense of Douglas’s latest work on the KKLT proposal and all of a sudden it really hit me that this is a completely lost cause. If perturbative string theory has any relation to Planck scale physics, then KKLT or something like it should work and string theory is vacuous since it can never predict anything. If perturbative string theory isn’t useful then we really don’t have anything since we’ve never been able to come up with a non-perturbative version that makes sense. Twenty years of this is enough. It’s time to give up.”

When Glanz asked him what he intends to do now, Witten responded:

“I don’t really know. There are still promising ideas about using string theory to solve QCD, and I could keep working on those. Maybe I should take up something completely different, like biology. I’m starting to worry that John Horgan was right about the ‘End of Science’. Right now I just definitely need a long vacation.”

When Glanz read Witten’s statement over the phone to David Gross, Frederick W. Gluck Professor of Physics at UCSB and Director of the Fred Kavli Institute for Theoretical Physics, Gross thought for a moment and then told him “Yeah, despite my quote last year from Churchill, I’ve also been thinking of giving up. Not sure though how I’m going to break this to the two Freds.”

The news of Glanz’s article has had dramatic effects at many universities and research institutes. At MIT yesterday, Prof. Barton Zwiebach shocked students in his Physics 8.251 “String Theory for Undergraduates” class by announcing that he wasn’t going to collect the homework due that day and was canceling his lectures for the rest of the semester. He also asked Cambridge University Press to halt publication of his new undergraduate textbook called “A First Course in String Theory”, the release of which had been planned for next month.

Search committees at several institutions that hadn’t finished their hiring yet this season held new meetings to decide how to react to the news. A prominent theorist at a UC campus told me in an e-mail that “our chair had the phone in his hand and had already dialed the number of a string theory graduate student from Princeton we were going to offer a post-doc to. I ran into his office as soon as I heard the news and stopped him just in time. Last week we were sure that string theorists were the smartest guys around and considered only them for jobs, but now there’s no way we’re going to hire any more, ever!”.

At the Institute in Princeton this year’s “Summer Program for Graduate Students in String Theory” scheduled for July has been canceled, with one of its organizers remarking “what graduate student would now be crazy enough to show up for a program like this?” Next week’s conference on “The Status of M-theory” at the Michigan Center for Theoretical Physics has also been canceled on very short notice. The director there, Michael Duff, commented “We had to do this because the status of M-theory is all too clear. It’s passed on! This theory is no more! It has ceased to be! It’s expired and gone to meet its maker! … This is an ex-theory!”

The Abel prize is a new yearly prize in mathematics, intended to function somewhat like a Nobel Prize for mathematics. The first one was awarded last year to Jean-Pierre Serre and this year’s has gone to Sir Michael Atiyah and Isadore Singer, specifically for their development of the Atiyah-Singer index theorem.

Atiyah and Singer are great heroes of mine, especially Atiyah. They have both taken a great interest in the relation of mathematics and quantum field theory and are responsible for much of the fruitful exchange of ideas between the two subjects over the last 25 years. I consider much of my mathematical education to have come from a lot of time spent reading through Atiyah’s five-volume collected works. His interests have ranged over a wide swath of modern mathematics and his writing is always a model of clarity. A good case could be made that Atiyah has been the most important figure in mathematics during the second half of the twentieth century.

The Atiyah-Singer index theorem is perhaps the single most important theorem of the last half century. It links together analysis, topology, geometry and representation theory in a fundamental and surprising way, one that is dear to any physicist since it involves the Dirac operator. Very roughly, what Atiyah and Singer discovered was that the dimension of the space of solutions of certain PDEs on compact manifolds was a topological invariant, one that they could explicitly compute in terms of more well-understood topological invariants: the cohomology classes of the manifold.

They did this by noticing that the general case could be reduced to the case of the Dirac operator, twisted by the various possible vector bundles on the manifold. They actually rediscovered the Dirac operator for themselves in the course of their research. The natural abstract framework for these new topological invariants is K-theory, where classes are represented by vector bundles, much as cohomology classes are represented by differential forms.

Things get even more interesting if there is a symmetry group acting on the whole set-up. Then the space of solutions carries not just an integer, the dimension, but is a representation of the group. You can actually use the Atiyah-Singer index theorem to classify and construct geometrically the representations of many classes of Lie groups, or going the other way, use representation theory to get more powerful topological invariants. The explicit cohomological formulas you get in these cases often have versions which localize to fixed points of the group action; so you can find your answer just by locating the fixed points and looking at what happens in a neighborhood about them.

I hope Atiyah and Singer enjoy their shared $875,000!

One can keep track of what is going on in theoretical physics now by taking a look at conference websites. Often after the conference they put up speaker’s transparencies or even audio or video of the talk. Some very recent examples:

Strings and Cosmology

a conference last week at Texas A and M, and

Spring School on Superstring Theory and Related Topics

at the ICTP in Trieste. Among the Trieste lectures, Marcos Marino’s notes give a nice discussion of some things you can do with topological strings. Brandenberger’s notes on “Challenges in String Cosmology” include the peculiar statement that “String cosmology does not exist because non-perturbative string theory is not yet known”. That was my impression too, but this doesn’t really explain why he is lecturing on a subject that doesn’t exist or why people devote many conferences to it.

Among the new papers appearing at the arXiv is Witten’s latest:
Parity Invariance for Strings in Twistor Space

I’m still kind of not seeing why Witten and others are so interested in this. Using strings as a dual to QCD to understand its strong coupling behavior is obviously interesting, but why is reformulating something you understand well (perturbative Yang-Mills) in terms of strings in a super-version of twistor space so interesting? The interesting thing about twistors always seemed to me that they were naturally parity asymmetric, one chirality of spinors is tautologically defined. Witten’s latest paper seems to just be showing how to get rid of this natural chiral asymmetry in this case.

Another new paper is:

The Emergence of Anticommuting Coordinates and the Dirac-Ramond-Kostant operators

by Lars Brink. The Kostant version of the Dirac operator is pretty amazing and too little known, both among mathematicians and physicists. I’m not so sure what Brink is trying to do with it leads anywhere, but there are other applications of it I’ll try and write about some day.