Wednesday, September 20, 2006

A Theory of Nothing?

String Theory dominates theoretical physics in most of the prestigious physics departments in the US. It aims and claims to be the long sought "Theory of Everything," explaining both particle physics and gravity. Thanks to talented proseletysers, especially Brian Greene, the theory has also captured the imagination of the scientifically literate public. Peter Woit has had the effrontery to step into this triumphal procession to announce that this emperor has no clothes. His new book Not Even Wrong is a frontal attack on String Theory and its pretensions. This non-expert reviewer will attempt to review both argument and book.

I took two main points from the argument: String Theory is a scientific failure, but it is a failure that has captured a grossly disproportionate share of the resources allocated for theoretical physics, especially in the US. In consequence of the concentration of power and prestige in the hands of a few top departments this String Theory dominance chokes off the opportunity for new and better ideas.

Why does Dr. Woit consider String Theory a failure? Firstly, because it makes no prediction that anyone has been able to test. Second, it fails to account for the known facts of particle physics. Finally, it lacks a coherent theoretical structure that could permit us to clearly ascertain what, if anything, it does predict.

It is perhaps a bit unfair to say String Theory predicts nothing. Since it only appears to be consistent in ten space-time dimensions, it could be said to predict that space has nine dimensions. Since we only observe three, it also "predicts" that six of them are curled up too tiny to be seen. No theoretical explanation is known for why six and just six of the dimensions should be so curled, so it can be considered an ad hoc assumption inserted to save the theory - and it is not the only such. Another such "prediction" is supersymmetry. I don't share Peter's distaste for supersymmetry, but it does have one undeniable flaw - it too is quite unobserved.

The other argument is that theoretical physics has gotten itself in a nasty box because all the leading physics departments have such a huge stake in String Theory that they can't afford to let it fail. String Theory is so complex and difficult that it takes many years to master, but aspiring theoretical physicists cannot get academic jobs if they study anything else.

It seems like a pretty brutal system. Of every ten theoretical physics PhD's produced by top universities, Peter calculates that only about one will get a similar job, and those jobs require an arduous post-doctoral apprenticeship - years of post-docs, more years for a sometime small chance of tenure. There is a very real chance that those who undertake the journey will find themselves middle-aged (35 or so), unemployed and with no obvious skills applicable to the real world.

I think Dr. Woit has made a powerful argument, and one I that I suspect may shake the towers of the mighty in theoretical physics. One reason I suspect that is that the criticism he has attracted so far seems curiously insubstantial. Of the major String Theorists, only Susskind has so far reviewed it, so far as I know, and his criticism was long on insult and short on refutation.

So much for the argument - how about the book? I didn't love every part of it - there were parts I could not follow - I suspect that might be true for everybody except experts in quantum field theory. I did end liking the book a whole lot, mainly for some of those parts I couldn't completely follow. He has a number of telling anecdotes and quotes. A lot of the most damaging come from leading String Theorists!

My favorite chapter was the one on quantum field theory and mathematics - it showed me glimpses of wonders I had never suspected.

I wrote some notes for an attempt at a chapter by chapter commentary on the book. I will append them here:

At one point Peter Woit offered to ask his publisher to send me a review copy of his new book, Not Even Wrong, but I didn't take him up on it. This was partly because I'm not an expert and couldn't give an expert review, but also partly because I wouldn't be able to look at a gift book impartially. So I bought a copy, which was slow, but at least I feel slightly more impartial.

The easiest thing to criticise a book for are those things that it isn't, and the material that it doesn't contain. Thus reviewer Aaron Bergman gave NEW a couple of knocks for being tendentious (Well, duh! Did you read the title?) and for not explaining why STers still love it. I myself have a list of things that Peter should have included, and I intend to send it to him if he ever announces plans to reissue NEW as a multivolume treatise. (In fact, let me start right here. That whole business of non-commutative rotations would be a lot clearer with just a little experimenting with 90 degree rotations of, say, a book, in different planes of rotation).

I prepared for this review by reading several other reviews, especially those by Motl, Aaron, Johnson, Chad Orzel and the Economist. The first thing I noticed was that, except for Aaron and Motl, none of those other reviewers seemed to be an expert either (I only saw excerpts from Susskind's review). Motl's review, of course, was a mixture of the trivial (planes of rotation generalize to dimensions other than three, axes of rotation don't), the misguided (criticizing British vs American spelling in the British edition), and the lunatic (declaring Peter to be a science hating Anti-Christ, and I'm only being slightly metaphorical here). Aaron's review was more balanced and thoughtful, but, while critical, scarcely layed a glove on any of Peter's central points. Working only from excerpts, Susskind's review seems both insubstantial and petty - ad hominen attacks are the lowest form of criticism in science. Having thus disposed of the experts, I have to modestly admit that, ignorant as I am, I still know a lot more physics than Easterbrook and the NYT science reporter.

Aaron and Chad, two talented writers and physicists that I greatly respect, both complain that Peter doesn't offer a good alternative. While it's true that he doesn't offer his own theory of everything, he does make several concrete suggestions: that there is more to gauge theory and representation theory than has yet been plumbed, that if ST wishes to continue without benefit of experiment, it needs to become more like pure mathematics, and that physics departments need to foster diversity of intellectual approach.

The epigraph to Chapter Two is from Karl Marx, in The Communist Manifesto:

The bourgeoisie cannot exist without constantly revolutionizing the instruments of production...

I don't know anything about Marx, and so I have no clue as to what his point was, but it certainly is apt for fundamental particle physics (bourgeoisie -> particle physics community). Should I read this as saying something about Peter's politics, or did he just like the statement, or did he put in in just to pimp Lubos? I don't know, but I like the last two theories. Woit has a way of putting the slyly humorous into his text in a fashion subtle enough that I can't quite tell when he is joking. The chapter is a very brief history of the "means of production," the accelerators which are used to study elementary particles.

Chapters three and four are devoted to quantum mechanics and quantum field theory. My guess is that it helps to know something about these subjects before you read the chapters. Notable features are his emphasis on the role of mathematician Hermann Weyl in elucidating the relationship of group theory to quantum mechanics and the relative estrangement of mathematicians from the development of quantum field theory.

One of my favorite aspects of the book are his inclusion of telling or otherwise interesting anecdotes. Mathematical physicist Res Jost:
In the thirties, under the demoralizing influence of quntum-theoretic perturbation theory, the mathematics required of a theoretical physicist was reduced to a rudimentary knowledge of the Latin and Greek alphabets.

In another vein are some quirky human aspects. While Schroedinger was holed up in a mountain retreat with his girlfriend, inventing his famous equation of quantum mechanics, his wife back in town consoled herself by banging his best friend, Weyl.

I found the brief chapter on gauge symmetry particularly clear, and the outline of the history of the guage principle outstanding. I would quibble with his rather stubborn mathematical disinclination to provide simple examples, even when available (eg, parallel transport on a 2-sphere). The final paragraph of the chapter is a nicely tantalyzing one:
The 1950s were a golden age of mathematics, especially in Princeton and Paris. Those years saw the development of a large number of fundamental ideas of modern mathematics that remain central to this day. It was also a time of minimal contact between physicists and mathematicians, with each of the two groups discovering things whose significance would become clear to the other only many years later.

My favorite chapter so far is the one on the standard model. This is mostly familiar material to me, but Peter's point of view is new to me, and I found much of the history illuminating. One puzzle: on page 78, he says "eight pions have been found that have the right properties to be the Nambu-Goldstone bosons for this symmetry..." I hope he is talking about psuedo-scalar mesons. Have they really taken to calling them all pions? Or is it just my inexpertise talking?

Awe and confusion is my reaction to chapter ten (New Insights into Quantum Field Theory and Mathematics. Most of the material in this chapter was new to me, and a lot is still beyond me. Witten is unquestionably the star of this chapter, and it gave me my first real appreciation of his contributions to mathematics, as well as teaching me a tiny bit about conformal field theory, mirror symmetry, dualities, and some of the uses of them that Witten's work made possible. One equation in one talk, for example, more or less detroyed the whole field of Donaldson Theory (by solving all the problems). The eight pions became nine in this chapter, so I was clearly on the wrong track wondering where the other five came from. I am probably confused, but I still think he may be referring to the psuedoscalar meson nonet.