Not Even Wrong

Last week I was in a bookstore and ran across a new book by Emanuel Derman called My Life as a Quant: Reflections on Physics and Finance. Derman got a particle theory Ph. D. here at Columbia in 1973 when he was one of Norman Christ’s first students. He then went on to post-docs at Penn, Oxford and Rockefeller and a tenure track job at Boulder. By 1980 he had decided he didn’t want to stay in Boulder, partly because his wife couldn’t get a job there, so he left academia for a job at Bell Labs.

In 1985 he went to work in the financial industry at Goldman Sachs, staying there until 2002, interrupted by a one-year stint at Salomon. He’s now back at Columbia, teaching in the Financial Engineering program run by the IEOR (Industrial Engineering and Operations Research) department of the Engineering school. This kind of master’s program is extremely popular; besides IEOR, the math and stat departments collaborate on a separate MA program in the Mathematics of Finance which has been wildly successful. Each year we get more and better applicants, and they seem to do very well on the job market when they get out.

The first half of Derman’s book gives a good view of what it was like to be a theorist of the phenomenological variety during the seventies and early eighties. The second half has a nice description of the mathematical problems involved in pricing options and mortgage-backed securities, as well as many comments on what it is like to work in the financial industry. He was one of the earliest particle theorists to do this, but many others have followed him there in recent years, some of whom are regular commenters here.

Over at sci.physics.strings there’s the scary sight of Lubos Motl agreeing with me in a posting about “Stringy Naturalness”. Well, maybe he isn’t directly saying he agrees with me, but “It would be too difficult for me to pretend that I disagree with these Woit’s remarks” is pretty close. Lubos is criticizing the new sort of “naturalness” critierion advocated by Miichael Douglas in a preprint reviewing his recent work on the “Landscape”. By this criterion a low energy effective QFT is more “natural” when there are more supposed string theory vacua that have this low energy limit. As Lubos points out, the danger with this criterion is that it tends to lead you to the conclusion that the most “natural” effective field theory is the one that is least likely to be able to predict anything new.

The posting immediately before Lubos’s is from Michael Douglas himself, responding to an earlier thread. In it he explains the goal of his work as follows. He wants to estimate N_SM, the number of vacua consistent with the observed known Standard Model behavior, then

“Based on this information, we can decide whether we should continue the search for the right vacuum directly (appropriate if N_SM <= a few), look for additional principles to cut down the number (if N_SM is large), or give up and start making anthropic arguments or whatever (if N_SM is ridiculously large)." The posting immediately before Douglas’s asks for “what would cause string theory to become nonviable and abandoned”, but hasn’t gotten any responses. An obvious response would be that if it becomes clear that string theory has so many consistent vacua that it can’t ever predict anything, the theory would have to be abandoned. Neither Douglas nor others working on the Landscape seem willing to mention this possibility in public, the closest he gets is the line about having to “give up and start making anthropic arguments or whatever”.

There’s an interesting new preprint by the historian of mathematics Erhard Scholz about the early history of the use of representation theory in quantum mechanics. Immediately after the beginnings of quantum mechanics in 1925, several people started to realize that the representation theory of the symmetric and rotation groups was a very powerful tool for getting at some of the implications of quantum mechanics for atomic spectra. One of the main figures in this was Eugene Wigner, who was trained as a chemical engineer, but worked on this topic with his fellow Hungarian, the well-known mathematician von Neumann.

Equally important was the role of the mathematician Hermann Weyl, who in 1925 had just completed his main work on the representation theory of compact groups, perhaps the most important mathematical work in a very illustrious career. Weyl was in close communication both with the group at Gottingen (Heisenberg, Born, Jordan) who were developing matrix mechanics, as well as Schrodinger who was working on wave mechanics. Weyl and Schrodinger both were professors in Zurich and knew each other well (Schrodinger’s first paper on quantum mechanics thanks Weyl for explaining to him some of the general properties of equations such as the Schrodinger equation). In 1927/8 Weyl gave a course on quantum mechanics and representation theory, which became the basis of his extremely influential book “The Theory of Groups and Quantum Mechanics”, first published in 1928.

Scholz has also posted another preprint about Weyl’s work, one that focuses on how his conception of the relation between matter and geometry evolved from 1915 to 1930. Weyl worked on general relativity and wrote an influential book about it (Space-Time-Matter, 1918). At that time he, Einstein and others believed that matter could somehow be described by a unified theory expressed in terms of some generalization of Riemannian geometry. Perhaps particles were some specific singularities or special solutions to the non-linear equations for the metric. The advent of quantum mechanics convinced Weyl (unlike Einstein), that this was a misguided notion, that matter should be described by a complex wave function. The right mathematics was not the geometry of a metric, but (in modern language) the geometry of gauge fields and of sections of a vector bundle with connection. The close connection between the basic ideas of representation theory and of quantum mechanics was quite clear to him, so, unlike Einstein, he enthusiastically adopted the new point of view of quantum physics.

One part of the close connection between Weyl and the history of quantum mechanics isn’t mentioned by Scholz. Weyl was not only a close friend of Schrodinger’s, he was Schrodinger’s wife’s lover. Schrodinger didn’t believe much in monogamy; it’s a well-known story that he discovered the Schrodinger equation while on holiday in the mountains with a girlfriend.

A new preprint by Michael Douglas indicates that, at least this week, the latest “predictions” from string theory are for:

1. No large extra dimensions.

2. No low scale supersymmetry.

So it looks like the “prediction” of the string theory “Landscape” will be that no physics related to string theory beyond that of the standard model will ever be observable. Thus the only “prediction” of string theory will be that you can never see any physics related to it. This kind of “prediction” is great since it proves string theory must be true. Either you don’t ever see any effects of string theory in which case you have confirmed its predictions so it must be true, or you do see effects of string theory, in which case string theory is even more true.

Nothing really new at Brian’s physics colloquium today. About 300 people showed up, which I think is probably a record for a physics colloquium. Brian doesn’t like Susskind’s “anthropic” arguments, which shows good sense. He still hopes that some new form of non-perturbative string theory will explain the standard model by picking out the right Calabi-Yau, but admits there’s no known reason for this to happen.

Thomas Larsson wrote in a comment mentioning a news story that appeared early this past summer in the Deseret Morning News (yes, that’s Deseret, not Desert; this is a name Mormons use to refer to Utah). The news story is about a conference on “String Geometry” held at Snowbird, Utah in June. Evidently at Andy Strominger’s talk at this conference someone actually mentioned that there were people who were skeptical about string theory and asked him to comment. His response was that “I hope they’re wrong, but I can’t prove it, and I bet my life work on their being wrong” , which I guess characterizes the attitude of many string theorists these days (“things don’t look good, but I’ve got too much invested in this to give up, so I’ll keep on engaging in wishful thinking even though I no longer have much of an argument for why I’m doing this”).

Many of the talks at the conference are online. These include a couple of interesting talks by Gukov and Spradlin about recent work on twistor theory and perturbative Yang-Mills amplitudes, as well as the usual Michael Douglas talk with its wishful thinking that analyzing the astronomically large “landscape” will somehow lead to some sort of prediction of something. There’s also a talk by Radu Tatar about non-Kahler superstring theory backgrounds. I’ve always wondered about this since I hear from an algebraic geometer colleague that although no one knows whether there are an infinite number of Calabi-Yaus in the Kahler case, if you relax the Kahler condition there definitely are an infinite number of them. If these non-Kahler backgrounds make sense, you can stop worrying about whether the landscape contains 10^100 or 10^500 possibilities.

Tomorrow here at Columbia my colleague Brian Greene is giving a colloquium on “The State of String Theory”. His abstract says he’ll “assess both its current shortcomings and major achievements”.

Lubos Motl has an interesting post on sci.physics.stringsthat gives a detailed explanation of the current state of string field theory.

One way of motivating quantum field theory is to start with a “first-quantized” quantum theory of particles (perhaps defined by integrating over paths), then “second-quantize” by considering a quantum theory of fields, where the fields are defined on the space the points in the path move in. The natural generalization to string theory would be to start with the “first-quantized” theory of strings given by doing path integrals over the possible worldsheets traced out by the moving strings (these are conformal field theories), then “second quantize” by quantizing fields defined on the infinite dimensional space of loops. It has always been a hope of string theorists that this would somehow give a true non-perturbative definition of string theory.

Lubos explains what some of the problems with this idea are. For one thing it is in conflict with the M-theory philosophy that a non-perturbative theory should involve on the same footing not just strings, but also higher dimensional “branes”. He goes on to speculate about what can be done about this problem, saying that perhaps one shouldn’t be trying to find a fundamental set of degrees of freedom and an action functional of them. Instead maybe one just needs to find a set of self-consistent rules, which will be obeyed by all sorts of different degrees of freedom. As he notes at the end, this is similar to the old “Bootstrap Philosophy” of Chew and others that dominated thinking about the strong interactions during the 1960’s. It didn’t work then, and I’ll bet it won’t work now.

This month is the 50th anniversary of the formal founding of the CERN laboratory near Geneva. There’s a very interesting article in Physics World about CERN and its future plans. LHC construction seems to be proceeding more or less on schedule, although there has been a delay in beginning to install the magnets in the tunnel due to problems with the distribution line that will provide liquid helium to the magnets.

Jos Engelen, the chief scientific officer of the lab, is quoted as wanting to see any decision about building a linear collider wait until 2010 or so. The scientific reason for this is that it may take that long to for the LHC to produce results, and the sort of linear collider one wants to build may depend upon these, e.g. on the mass of the Higgs. CERN has its own linear collider technology called “CLIC” which it is working on. CLIC is quite different than the TESLA superconducting cavity technology developed at DESY and recently endorsed by the ITRP committee charged with evaluating which technology to go ahead with. CLIC uses a second electron beam to accelerate the main beam and in principle is capable of higher accelerating gradients than TESLA. Whereas a machine using TESLA technology would probably have an energy of 500 Gev, upgradeable to 1 Tev, CLIC might be able to reach 3-5 Tev. CERN is now increasing the resources devoted to the CLIC project, and clearly hopes that a delay in the decision about whether to build the linear collider would give them time to develop and prove the viability of CLIC.

The latest issue of the Notices of the AMS contains the first part of a long biographical article about Grothendieck written by Allyn Jackson. Evidently Winfried Scharlau is writing a biography of Grothendieck, and Jackson’s article is partially based on materials he has gathered. Much of this material is brought together at a website maintained by the “Grothendieck Circle”.

This issue of the Notices also contains a short expository piece on one of the most abstract ideas due to Grothendieck, that of a “topos”. Illusie was a student of Grothendieck’s, and Jackson’s article has some of his reminiscences about what that experience was like. Illusie’s piece is not very accessible; a better place to try and get some feeling for these ideas is Pierre Cartier’s Bulletin article.