Not Even Wrong

There’s a nice article this week in Nature about AdS/CMT, entitled String Theory Finds a Bench Mate. According to the article, the whole thing is (partly) my fault:

But in 2006, string theory took a public battering in two popular books: Not Even Wrong by Peter Woit, a mathematician at Columbia, and The Trouble With Physics by Lee Smolin, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Both books excoriated the theory’s isolation from experiment.

“It’s hard to say whether the interest in condensed-matter applications is a direct response to those books because that’s really a psychological question,” says Joseph Polchinski, a string theorist at the Kavli Institute for Theoretical Physics in Santa Barbara. “But certainly string theorists started to long for some connection to reality.”

The main point of the story is to tell about what is probably the hottest topic in hep-th these days, attempts to use AdS/CFT to say something about some models in condensed matter physics. For some idea of what this is all about, see the review article What can gauge-gravity duality teach us about condensed matter physics? by Subir Sachdev, and take a look at the online talks from the KITP workshop Holographic Duality and Condensed Matter Physics.

The article does go into the history of this in some detail, including its roots in efforts to use AdS/CFT to say something about heavy-ion physics phenomena observed at RHIC (for the string theory promotional campaign surrounding this, see e.g. here). I had expected to see a lot about this topic when higher energy results from heavy-ion collisions at the LHC were released earlier this year, but it seems to have gone quiet, perhaps because of the kind of comparison of data with AdS/CFT predictions that Sabine Hossenfelder points out here:

As the saying goes, a picture speaks a thousand words, but since links and image sources have a tendency to deteriorate over time, let me spell it out for you: The AdS/CFT scaling does not agree with the data at all.

My knowledge of condensed matter theory is minimal, and the hype level surrounding string theory makes it hard to know whether to take at face value many of the claims being made. On general principles, this looks a bit more promising than the heavy-ion case, since there are many different kinds of systems one might look at, and the connections are more to QFT than to string theory. Experts quoted in the Nature article give opinions ranging from:

Polchinski admits that the condensed-matter sceptics have a point. “I don’t think that string theorists have yet come up with anything that condensed-matter theorists don’t already know,” he says. The quantitative results tend to be re-derivations of answers that condensed-matter theorists had already calculated using more mundane methods.

to condensed matter theorist Andrew Green’s:

“Maybe string theory is not a unique theory of reality, but something deeper — a set of mathematical principles that can be used to relate all physical theories,” says Green. “Maybe string theory is the new calculus.”

Time will tell whether this suffers the same fate as in the case of heavy ions.

The latest New York Review of Books has an article by Steven Weinberg entitled Symmetry: A ‘Key to Nature’s Secrets’. It’s a bit unusual for the NYRB, since it is both scientifically more technical than usual for them (coming from a write-up of Weinberg’s talk at this conference), and doesn’t review any books. The printed version tells readers to go to the web version for footnotes, but some of these just note that things are being over-simplified. One of the footnotes is worse than useless: the editors have replaced x^3=x as an example of an equation with solutions that break a symmetry (x goes to -x) by “x 3 equals x”, an equation with the same symmetry but only a symmetric solution (x=0). The idea seems to have been to remove or replace any symbols in the equation that might upset people.

Weinberg tells the conventional story of how the Standard Model emerged during the 60s and early 70s out of the realization that non-abelian gauge symmetries were important and an understanding of what happens when symmetries are spontaneously broken. He tries to do some much more ambitious things, explaining the idea of “accidental symmetries” that are due to the limited number of possible renormalizable terms you can build out of a specified list of fields, but I’m not sure the typical reader of the NYRB is going to get much out of this.

The question of how to explain the notion of “symmetry” is an interesting one, and I thought a lot about it when writing Not Even Wrong, the book. To my mind, most such explanations mix up two conceptually distinct things: the group of symmetries (a group), and the action of the group on some other mathematical object (the representation: mathematically a homomorphism from the group to the group of automorphisms of something). It’s both the group and the representation that are important in the use of symmetries in physics, although often what is important is the trivial representation. From a mathematician’s point of view, the simplest representations to look at are unitary representations on a complex vector space, so the mathematical structure of quantum mechanics is very natural. To each symmetry generator you get a conserved quantity, and it appears in quantum mechanics as the thing you exponentiate (a self-adjoint operator) to get a unitary representation. In Weinberg’s piece, which aims at sophisticated issues in particle theory, the question of the basic relation of symmetries and conservation laws is relegated to a footnote which says only “For reasons that are difficult to explain without mathematics…”.

Weinberg ends with a landscape sort of picture, involving symmetries emerging only when a specific ground state emerges out of an initial chaotic inflation state. Philosophically this is a popular view of the future of the subject these days, but one that has so far led nowhere, and one that I think even in principle can never lead anywhere. Much more interesting would be to try and draw lessons from what has worked well in the past: exactly the gauge symmetries and spontaneous symmetry breaking phenomena that led to the standard model. We may very well soon find out there is no Higgs particle, turning this whole subject into a wide-open one. Future progress may come from exactly the same place as in the past: new ideas about how to exploit the mathematical structures inherent in quantum mechanical symmetries.

Update: The missing exponentiation in the on-line footnote has been fixed.

The graphic chosen years ago as the header for this blog is an event display from the UA1 detector in 1982, of historical importance since it was the first event found with a W candidate. To be honest, the reason it’s there is that I was looking for something quick to use at the interactions.org Imagebank, figuring these were graphics I could steal without getting sued. What I ended up with is a cropped, lower-resolution version of the much better image available here.

Even stripped of identifying info, UA1 experimentalist Jim Rohlf of course recognized it, and recently wrote me to tell me some more about it. He also tells me that he will soon be blogging at Quantum Diaries, and I look forward to seeing that. So, here’s the story behind that image:

The collision is Run 2958, Event 1279 and was the very first W candidate that was found. It was recorded in the Fall of 1982 with UA1. As a newly minted junior faculty member and CERN scientific associate, I was resident at CERN and the first round of the W event selection and analysis was completed during the CERN holiday shutdown. On 23 January 1983 we submitted the W discovery paper for publication (Phys. Lett. 122 B, 103 (1983)). The details of the events were given in this paper. Within a few days, I got a letter from Lev Okun who had become a good friend of mine due to his frequent visits to CERN and his great interest in the working details of our experiment. In this letter which was several pages long he referred to this event as a “monster” because it decayed in the “wrong direction” and asked if we could have made a measurement error. Then the obvious hit me instantly- nobody had thought of this before- we don’t measure the longitudinal momentum of the neutrino due to the singularity in the direction of beam pipe but we can solve it to a quadratic ambiguity knowing the W mass. Furthermore, I saw that the kinematics of a 80 GeV object being produced with a relatively low cm energy of 540 GeV gave a remarkable result: often one of the 2 solutions was kinematically forbidden and when it wasn’t, the two solutions were often close together. Therefore, we could solve for the longitudinal momentum of the neutrino and be able to transform to the rest frame of the W. Since the W was polarized because it was produced in proton-antiproton collisions, we could measure the angle of the decay wrt the spin direction. Very simple idea, but be the first to do it and it becomes interesting and fun. I immediately wrote this up as a UA1 internal note in which I acknowledged the contribution of Okun. This technique subsequently became a standard at the Tevatron and now at the LHC.
In the following months, we collected more data and the next international conference to come along was at Fermilab and I was told by Rubbia to give the talk which was published (J. Rohlf, “Physics at the Proton-Antiproton Collider,” Proceedings of the 12th International Conference on High Energy Accelerators, Fermilab, 619 (1983). I reported the first measurement direct observation of parity violation in (real) W decay and measurement of the spin. I attach a slide from a talk I gave at Fermilab 20 years later in 2003 where I pulled up some of my 1983 slides. (Notice I fit the W mass to 2% and got the right answer.) You can see the “monster” event in the bin at cos(theta) =-1. This W decayed in the wrong direction. We went on to collect about 300 W events in UA1. We never saw another one go in the wrong direction. We also could not find anything wrong with that original event 1279. So you see the event was “not even wrong”.

Update: A copy of the talk slide that Jim Rohlf refers to is here.

Update: Jim Rohlf’s blog at Quantum Diaries is now up here. His first blog entry is great, it’s about, independent of the Higgs issue, the fundamental problem the LHC hopes to investigate: what is causing electroweak symmetry breaking? He emphasizes that one way to study this is to try and see the self-interactions of Ws and Zs, which become strong at the TeV scale.

Back in 2004 I made my first venture into Nobel Prize predictions, then decided to retire from that business. This year I came out of retirement with another prediction. After the posting, I consulted with experts who assured me that the right names were Perlmutter, Riess and Schmidt, something I thought I mentioned in a comment, but it appears that I didn’t, instead leaving this to Shantanu.

Congratulations to Perlmutter, Riess and Schmidt. The theoretical significance of their tour de force observational work remains still controversial, but it richly deserves the Nobel prize.

Prospect magazine has an excellent new article by Philip Ball on recent developments in the fundamental problem of the interpretation of quantum mechanics: why don’t we see superpositions? Most popular discussions of this seem to me to be stuck back in debates from the 1930s, and ignore the main question. QM is a simple, beautiful mathematical structure that works perfectly experimentally, the confusing question is that of how classical behavior emerges during a measurement process (typically involving huge numbers of degrees of freedom, making analysis difficult).

At the end of the article, Ball mentions one particularly intriguing set of ideas, due to Wojciech Zurek, about “quantum Darwinism”. For more about this, see Zurek’s survey here.

There’s a new preprint out by Steven Weinberg on Collapse of the State Vector. Weinberg claims that “There is now no entirely satisfactory interpretation of quantum mechanics”, and refers for more detail about this claim to Section 3.7 of his Lectures on Quantum Mechanics, a manuscript that is “to be published”. I’m definitely looking forward to this book when it comes out. The sort of thing that Weinberg examines in the preprint though, modifying QM to take into account wave-function collapse, is the kind of idea I’ve never found promising. Why modify QM, it works perfectly and is mathematically extremely aesthetically compelling? Better to keep QM as is, and closely examine one’s understanding of what the problem really is.