The Elegant Universe

  • Brian Greene
Jonathan Cape: 1999. 428 pp. £18.99

A year ago, I fell into conversation with a young woman just embarked on a PhD stint at a British university. Her thesis adviser had assigned her a project in string theory, and I asked whether she believed that string theory would indeed answer all the questions of fundamental physics. “I don't think so,” she said, “but the mathematics is interesting.”

Agnosticism such as this (and worse) is rife. For much of the past 15 years, almost the only rejoinder to scepticism has been the observation that Ed Witten, the Princeton theorist who has stepped into Einstein's shoes at the Institute for Advanced Study, “is a believer”. But now the agnostics can read Brian Greene's remarkable book as well.

Greene is a regular physicist at Columbia, a practitioner of string theory of distinction and a proselytizer of the cause. (He is not to be confused with his near namesake, Michael Green, who with his colleague Julian Schwartz of Caltech caused a stir in 1984 by demonstrating that strings can reconcile quantum theory and relativity.) Greene's contention is that the account given by string theory of the properties of the particles of matter is too good not to be true.

To be fair, Greene repeatedly acknowledges, although with decreasing frequency as the pages turn, that his high hopes for string theory may be disappointed. Perhaps he has shrewdly calculated that the sceptics will either have been won over by the repetition of the refrain “Strings are the cat's whiskers!”, or that they will have fallen by the wayside before they reach the end — which is a long way from the beginning.

Greene starts with the frank declaration that quantum mechanics and general relativity are incompatible. That, in itself, is not a radical revelation: people have been trying to ‘quantize’ Einstein's equations for a quarter of a century without success. Greene prefers to explain this failure qualitatively: Heisenberg's uncertainty principle requires that quantum fluctuations increase without limit as the space accessible for the specification of physical variables shrinks indefinitely. That means that space itself, which is smooth on a macroscopic scale, is microscopically far from smooth — or “differentiable”, as mathematicians would say.

How does string theory resolve the difficulty? Elementary particles are no longer point-like objects, but tiny one-dimensional strings (which may be open with two loose ends or closed, like rubber bands) which, having tension, vibrate like piano strings. The energies of the normal modes of vibration then correspond to the masses of elementary particles (by the familiar rubric E = mc 2). They are all there. Electrons, quarks and the particles that transmit the various forces — photons, the heavy bosons of the electroweak theory and the gluons that mediate the strong nuclear force. And then, magic upon magic, there are also gravitons — the massless particles of spin 2 that are supposed to be the quantum particles of the gravitational field. That is how string theory unites gravitation with the other forces.

This picture, for outsiders, is also the stumbling block to understanding. A real string could not yield the riches of the known elementary particles. External disturbance of a vibrating string, perhaps by collision with another, would change a pure vibrational state into a mixture of all others, but photons do not turn into gravitons or into quarks of different kinds. Why do events of that kind never happen? Because the strings of particle theory vibrate in 10 dimensions — the four dimensions of relativistic space-time and six others of which we are unaware. Thus there is room for ample orthogonality to generate selection rules that prevent bizarre happenings between particles.

The most persuasive part of Greene's excellent book is that in which he persuades the reader that the problem of the six hidden dimensions is not a problem but a matter of perspective. A garden hose seen from a great distance looks like a one-dimensional object, but close up it is plainly a two-dimensional surface on which motion perpendicular to the length is perforce circular and repetitive. The length of the hose is Greene's analogy for an ordinary extended dimension; the perpendicular circular tracks stand for one of the six wrapped-up dimensions. If the radius of the circle (or of the garden hose) is small enough, it is recognizable only in close-up (which means at the highest energy).

How small are the compact radii? It seems to be agreed that the compact dimensions must be curled up with a radius in the neighbourhood of the Planck length, which is the constant with the dimensions of length formed from Planck's constant, Newton's gravitational constant and the velocity of light. Formally, the length is √(hG /c 3), where h and G are the quantum and gravitational constants and c is the velocity of light. Numerically, the length works out at 10−35 m, which is small enough for Greene's purposes.

This is the kindergarten stuff of string theory, but Greene shrinks from no obstacle in the path of understanding, instead turning each into an opportunity to make the field exciting. The doctrine of supersymmetry has become an intrinsic part of string theory — otherwise ‘superstring’ theory. The implication is that there are as many fundamental particles yet to be discovered as are now known, but all of them are much more massive. String theory will fall if it is ever shown that they do not exist.

The essential step forward, and the cause of Greene's rekindled enthusiasm, was taken by Witten in 1995. He showed that the five alternative string theories then defined are essentially equivalent. A weak coupling constant (or the strings' equivalent of electric charge) in one will be the equivalent of another theory with a strong coupling constant. So, says Greene, the road points ahead to the age-old dream of predicting both the contents of the Universe and the properties of those contents. Already there are people working on the notion that black holes are merely very massive elementary particles.

Even if the dream proves false, Greene has brought an absorbing field of enquiry to vivid life. The supposition that particles are not points but strings fits well with familiar phenomena. The fact that all particles of matter have intrinsic spin (which may be zero) has always provoked the question of whether spin is a property of particles or of space. The materialization of particles from apparently empty space is similarly provoking. String theory neatly answers them all.

So what lies ahead? Not even Greene is sure. String theory may not turn out to be the cat's whiskers he hopes. There are alternatives, such as Roger Penrose's twistor theory (which Greene reckons may say the same as strings). The most imaginative suggestion in this imaginative book is that the time has come to solve problems of quantum gravity in strictly quantum language and not by posing them in classical terms and then ‘quantizing’ them. Meanwhile, there is a whole raft of algebraic geometry to be done. The thousand and more people working in the field will need courage to do these largely thankless chores, but this splendid book will cheer them on their way.