String Theory | Research & Encyclopedia Articles

String Theory

Sometime in the fifth century B.C., the Greek philosopher Democritus introduced the atomic hypothesis--the idea that all matter is composed of extremely tiny, indivisible bits. (Hence the name, atom, which comes from the Greek atomos, "uncuttable.") That reductionist model, in which a few types of fundamental particles suffice to build everything that is, has, remarkably, lasted twenty-five centuries. But the current idea of which particles are actually fundamental has not. Since the turn of the last century it has been discovered that atoms have internal structure, a heavy nucleus surrounded by much lighter electrons. That nucleus is constructed of protons and neutrons, which, in their turn, are built of quarks.

Until 1967, it was thought that there were just four fundamental forces: the strong nuclear force, the weak nuclear force, the electromagnetic force, and gravity. But that year Steven Weinberg and Abdus Salam showed that the weak and electromagnetic forces were but different manifestations of a single "electroweak" interaction. Could it be that all forces derived, in a similar manner, from a single interaction? A number of theorists began the search for such a "Theory of Everything."

Meanwhile it was discovered that the strong nuclear force, which binds quarks together, behaved very strangely indeed. Rather than weakening with distance (like the inverse-square gravitational and electromagnetic forces), it became stronger as the separation between quarks was increased. The three quarks that bind together to form a proton, for example, behaved as if they were free--they did not interact with one another "inside" the proton. Yet they were permanently confined--no amount of energy could separate them. It was as if they were tied together by elastic bands; the attractive force needed to separate two quarks increased the further one tried to pull them apart.

In 1974 a new model for the strong interaction was introduced, in which the fundamental objects were not point particles, as in all previous models, but were, rather, one-dimensional-they were "strings." Particles were identified as "excitations" of the string (akin to the various frequencies with which, say, a plucked guitar string may vibrate). For a number of reasons, though, the model proved not to be a viable theory of strong interactions. In particular, though, there was present a massless, spin-2 excitation. There was no such strongly interacting particle in nature.

But there is a massless spin-2 particle in nature, the graviton, the carrier of the gravitational force. Gravity had been proving fiendishly difficult to quantize. All proposed models that united both quantum mechanics and Einstein's general relativity were beset by a major problem: non-renormalizability. All calculations of physical quantities led to infinite quantities which could not be removed; the models thus had no power to predict. It had not been possible to construct a consistent quantum field theory containing a graviton. Here, though, was a new quantum theory which contained both half-integral spin excitations (the fermions that constitute matter), and integral spin excitations (the bosons that mediate the fundamental interactions), including the spin-2 graviton. Joel Scherk and John Schwarz thus proposed string theory as a possible unified theory of all fundamental forces. The zero-dimensional particles of Democritus were to be replaced by one-dimensional strings.

String theory is "Planck scale physics." The size of the strings is of the order of the Planck length, 10-33 cm. A proton is about 10-13 cm in diameter. On any "reasonable" scale, then, and certainly on any scale that we are ever likely to be able to directly investigate experimentally, these extended objects "look like" point particles. But it is their extended, rather than point-like nature that allows string theories to be renormalizable.

By the early 1990s there were five consistent string theories that were acceptable as possible unified models. All were renormalizable and mathematically consistent, and contained the proper particles and forces. All were "supersymmetric"--they were invariant under a set of transformations that could interchange fermions and bosons. And all were wonderful examples of just how abstract fundamental physics had become by the dawn of the twenty-first century.

In all the models the strings live in a ten-dimensional space-time. (Ten dimensions are necessary in order for the theories to be anomaly-free.) To recover the four-dimensional space-time in which we live, six space-time dimensions must be "compactified;" that is, they are curled up very tightly. If we could travel along one of the compact directions, we would return to our starting point after traveling roughly one Planck length. (As an example, visualize a large two-dimensional space--a sheet of paper. Now roll the sheet up into a very long, very narrow soda-straw. The space is still two-dimensional, but one of the dimensions has been compactified.) Neither the mechanism by which compactification occurs, nor the geometry taken by the compact six-dimensional space is presently understood-a real problem for string theorists.

Theoretical physicists believe, to paraphrase Einstein, that "God had no choice," that there is only one unique way to construct a universe. That five consistent models could be constructed was truly an embarrassment of riches. It now seems, though, that there is an underlying theory of which all five are simply different aspects. It is called "M-theory," which is short for the "Mother of all theories," and is, at this writing, being intensively investigated.