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Mathematics & physics

Loose ends and Gordian knots of the string cult

Not Even Wrong

Can ever more abstruseness and distance from experimental results reveal physical truths? asks Nobel laureate Philip Anderson.

Four centuries ago Francis Bacon, in his Novum Organum , outlined the philosophy that came to be the distinguishing characteristic of modern science. This philosophy held that knowledge of the nature of things was to be gained by the acute observation of nature, not by the study of authoritative texts or of holy books, or from imaginative flights of human fancy. The resulting explosive growth in our understanding of the universe and of our ability to manipulate it cannot be gainsaid; whatever one may say about the technical ingenuity of the medieval Chinese or the early mathematical discoveries of the Indians and the Arabs, one has to concede that nothing remotely resembling modern systematic science developed in those cultures.

Many of us in the physics community have become increasingly disturbed by the growing hegemony in a major subfield of our subject of what we see as a revival of the medieval, pre-Baconian mode of thinking: that the universe is designed on some simple basic principle that can be discovered by the exercise of pure reason, unaided, in fact unencumbered, by experimental study. Such would seem to be the thinking of the community of "string theorists", who in the past two decades have achieved a dominant position in theoretical physics. Every research physics department worldwide with any pretensions looks to have its own string-theory group of at least two, since only a few string theorists talk physics to anyone else. String theory has produced at least three media superstars, whose books and TV interviews bring to physics departments flocks of students ambitious to join this brilliant enterprise, which, it has been said, reveals "the language in which God wrote the world".

Peter Woit, in a strongly argued and serious book, has taken on the task of analysing this situation. Woit, a mathematician at Columbia University, is neither a sour-grapes sorehead nor a sensationalist amateur, as he makes clear by describing the complex mathematics of string theory in what may be excessive detail for many readers without, so far as I can tell, many really serious errors. He is an admirer of Ed Witten, the fabulous mathematician-physicist who has been the guru of string theory for several decades. Woit took his degree at Princeton University, learning quantum-field theory from several of its most influential modern exponents, and he keeps in touch with the field through numerous contacts. Indeed, after spending several chapters on the history of modern particle theory, Woit adds a long and highly technical chapter praising the many exciting mathematical discoveries that have resulted from the complications of superstring theory - mathematical developments that, inter alia , earned Witten an unprecedented and well-deserved Fields Medal and contributed to the stellar career in mathematics of Sir Michael Atiyah, former president of the Royal Society.

How then can the enterprise on which all these unquestionably brilliant people are engaged have gone so far off the rails as to merit the physicist Wolfgang Pauli's famous put-down, "That's not even wrong!"? This needs a little history, which Woit describes in the early chapters. (The experimental bits are a bit shaky, though.) The history concludes with an unexpected and glorious success: the so-called standard model, which was constructed in roughly 1965-75, by many of the same theorists who carried on into string theory. This marvellous structure classifies all of the bewildering array of known "elementary" particles and fields by means of three families of four "particles" (fermions) each, and two "gauge" symmetry groups that imply two sets of "fields" (bosons) that are responsible for interactions of a particularly simple type among the particles.

The way in which this structural classification fell into place, and the great leaps of imagination involved, justifies a degree of hubris among the few dozen truly extraordinary individuals who discovered it. It has also the very special feature that the ostensible world picture we see at the ordinary chemical scale has very little resemblance to the underlying structure, but instead is emergent from it: for instance, neither nucleons nor light quanta are fundamental to the standard model (the electron happens to be). However, both this hubris, and the complexity of the result, fed the temptation to go on leaping, and to forget that each of these earlier leaps, without exception, had taken off from some feature of the solid experimental facts laboriously gathered over the years.

It is conventional to say that the standard model vitiated all of particle theory as we had come to know it because everything measured since 1975 has "agreed" with it. This is problematical; what is true is that measurements since 1975 have left the structure intact, but with modifications in detail. Some of these modifications are very ad hoc, such as those necessary to fit the observed weak-time asymmetry, and the neutrino masses and oscillations. As so modified, there remain at least 25 arbitrary constants that must be determined from experiment.

Woit begins the story of strings with a cautionary tale: the sad fate of the fad known as "particle democracy" that overtook the theory world in the 1960s. The hope it offered - as later did string theory - was that the mere structure of certain equations would lead to a unique theory of the world. The dream lives on in the minds of a few adherents and in a couple of books still popular among New Agers. It was in the course of fumbling around with this mathematics that the defining ideas of string theory emerged and eventually began to catch the fertile imaginations of the particle-theory community.

The main ideas behind string theory are these. First, that what we had been treating as particles (or fields defined at space-time points) are not that, but are little wiggly strings that define a surface in space-time as they move. Second, that (for reasons related to working out a consistent theory of these objects) space is really at least ten-dimensional, with most of the dimensions curled up so tightly we cannot see them. Third, that, by similar logic, the underlying symmetry of space-time must be supersymmetry, a generalisation of the ordinary relativistic symmetry that requires, among other things, that for every fermion there must be a corresponding boson (in strict supersymmetry, of the same mass) and vice versa, since the generators of the supersymmetry group switch the two. Hence, super strings.

I need hardly say that none of these ideas has any experimental basis. So why then are they taken seriously? Perhaps there are several reasons - reasons that do not include the possibility, or even the hope, of experimental confirmation.

At the outset, the main task was perceived as being to bring general relativity into the fold, a task at which ordinary quantum field theory has always failed. With this visionary postulate, it did seem possible to make a reasonable supergravity - in ten supersymmetric dimensions, of course.

Classical gravity is satisfactory all the way down to the "Planck" scale, 10¹5 smaller than we can at present measure, so we can imagine - and the string theorists do imagine - that all kinds of strange things, such as the disappearance of the extra dimensions and the breaking of supersymmetry, happen at the intermediate scales.

Gravity has always had a very special cachet among mathematically inclined theorists because of its gorgeous mathematical expression, accompanied by the myth that it sprang full blown from Einstein's brain (which it did not; he saw its outlines already in 1907 as a consequence of experimental arguments and spent eight years learning the maths to do it right). Even though we now know that there are other ways to converge gravity, one may nonetheless concede that it was a useful exercise to create an example of a theory that does not fail at the Planck scale.

To my mind, the most valid point in favour of string theory is that the standard model exhibits several "internal local symmetries". These receive a natural interpretation in string theory as rotations in the extra dimensions - an idea that dates back to Einstein's time.

I am far less sympathetic to a line of thinking in the theory that seems to be purely aesthetic. String theory (in some one of its many versions) has actually been justified as "just too beautiful not to be true". Woit is particularly dismissive of this claim, suggesting that intricacy, abstruseness and novelty are no substitutes for the simplicity of, for instance, the standard model. There is doubtless a fascination and excitement in being in possession of a particularly esoteric and complex body of knowledge or ritual. String theory has begun to seem an obsession, even a cult - the kind of thing that leads the young to wear T-shirts with slogans such as "Why be stuck with only four dimensions?"

The leading source of optimism, however, was the dream that superstrings would furnish a unique theory because of the constraints found on usable versions of the ideas. It is this dream that has evaporated as the mathematical understanding has increased - in fact, to the point that string theorists have come to accept that there are almost no uniqueness properties at all. In other words, one may have whatever universe one pleases. It may be said that there is so much freedom in string theory that our present universe, even at the elementary particle level, would be the result of historical contingency.

Finally, Woit points out, a motivation for pursuing superstrings is often quoted as "it's the only game in town". The implication is that if you want a job in theoretical physics or a position at a prestigious institute, or even a MacArthur genius award, you had better learn string theory. Woit notes that with string theory, physicists are getting perilously close to validating the thesis of radical sociologists of science that at least this portion of science is socially constructed.

It is time to sum up. What is Woit's argument? He is not accusing the string theorists of egregious mathematical error - of course they are superb mathematicians. Rather, he accuses them simply of doing pure mathematics in physics departments, of redefining "science". One could not possibly object to the existence of an active mathematical community pursuing such an exciting, original line of work. The objection is to the claim that this work is physics, that it possibly, or even probably, will tell us how the real world constructs itself. One may particularly cavil at the high level of hype around string theory, to the point of monopolising popular attention, and that the gigadollars of a number of philanthropists, as well as numerous physics department employment slots, are being farmed out to what is really an esoteric branch of algebraic geometry.

Not Even Wrong is written for the mathematically inclined. Woit seems to feel that it is essential for this very complex subject to be covered in a serious manner. The maths in the book may have been a mistake. It will open him to nitpicking on every issue he discusses and perhaps obscure the central issue, which may not be so very complicated: just what is the emperor actually wearing? He writes the non-mathematical parts of the book well and clearly, although not always without attitude. Still, as a solid-state theoretical physicist, I am pleased the book has been written and to have had the opportunity to speak my mind about its subject.

Philip W. Anderson is emeritus professor of physics, Princeton University, New Jersey, US. He was awarded the National Medal of Science by the US Government and is a Nobel laureate in physics.

Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics

Author - Peter Woit
Publisher - Cape
Pages - 290
Price - £18.99
ISBN - 0 224 07605 1

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