A critical evaluation of string theory

Excerpts from an article by Peter Woit,
Department of Mathematics, Columbia University
January 29, 2001

The strongest scientific argument in favor of string theory is that it appears to contain a theory of gravity embedded within it. It is not often mentioned that this is not yet a consistent quantum theory of gravity. String theory has lead to many striking new mathematical results. The concept of 'mirror symmetry' has been very fruitful in algebraic geometry.

Unfortunately the mathematically interesting parts of string theory have been pretty much orthogonal ( = statistically independent ) to those parts that attempt to connect with the real world. No one has managed to extract any sort of experimental prediction out of the theory other than that the cosmological constant should probably be at least 55 orders of magnitude larger than experimental bounds.

String theory not only makes no predictions about physical phenomena at experimentally accessible energies, it makes no predictions whatsoever. Even if someone were to figure out tomorrow how to build an accelerator capable of reaching Planck-scale energies, string theorists would be able to do no better than give qualitative guesses about what such a machine might see. This situation leads one to question whether string theory really is a scientific theory at all. At the moment it's a theory that cannot be falsified by any conceivable experimental result.

String theorists often attempt to make an aesthetic argument, a claim that the theory is strikingly 'elegant' or 'beautiful'. Since there is no well- defined theory, it's hard to know what to make of these claims, and one is reminded of a quote from Wolfgang Pauli. Annoyed by Heisenberg's claims that he had a wonderful unified theory (he didn't), Pauli sent his friends a postcard containing a blank rectangle and the text 'This is to show the world I can paint like Titian. Only technical details are missing.' Since no one knows what 'M-theory' is, its beauty is that of Pauli's painting.

From a mathematician's point of view, the idea that M-theory will replace the Standard Model with something aesthetically more impressive is rather suspicious. Two of the most important concepts of the Standard Model are that of a gauge field and that of the Dirac operator. Gauge fields are identical with connections, perhaps the most important objects in the modern formulation of geometry. Thinking seriously about the infinite dimensional space of all connections has been a very fruitful idea that mathematicians have picked up from physicists.

The Standard Model is dramatically more 'elegant' and 'beautiful' than string theory in that its crucial concepts are among the deepest and most powerful in modern mathematics. String theorists are asking mathematicians to believe in the existence of some wonderful new mathematics completely unknown to them involving concepts deeper than that of a connection or a Dirac operator. This may be the case, and one must take this argument seriously when it is made by a Fields medalist, but without experimental evidence or a serious proposal for what M-theory is, the argument is unconvincing.

During much of the twentieth century there were times when theoretical particle physics was conducted quite successfully in a somewhat faddish manner. Experimentalists regularly discovered new unexpected phenomena, each time leading to a flurry of theoretical activity and sometimes to Nobel prizes for those quickest to correctly understand the significance of the new data. Since the discovery of the J/Psi in November 1974, there have been no solid experimental results that disagree with the Standard Model. It is likely that this situation will continue at least until 2006 when experiments at CERN are scheduled to begin.

Graduate students, post-docs and untenured junior faculty interested in physics beyond the Standard Model are under tremendous pressures in a brutal job market to work on the latest fad in string theory, especially if they are interested in speculative and mathematical research. For them, the idea of starting to work on an untested new idea that may very well fail looks a lot like a quick route to professional suicide. Many physics researchers do not believe in string theory but work on it anyway. They are often intimidated intellectually by the fact that some leading string theorists are undeniably geniuses, and professionally by the desire to have a job, get grants, go to conferences and generally have an intellectual community in which to participate.

During the 1960's and early 1970's, quantum field theory appeared to be doomed and string theory played a leading role as a theory of the strong interactions. Could it be that just as string theory was wrong then, it is wrong now, and in much the same way: perhaps the correct quantum theory of gravity is some form of asymptotically* free gauge theory? As long as the best young minds of the field are encouraged to ignore quantum field theory and pursue the so far fruitless search for M-theory, we may never know.

* An asymptote is a straight or curved line which a curve will approach, but never touch.