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The Atlantic Monthly | April 1986

The Gospel of String

by Robert P. Crease and Charles C. Mann

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INCE THE SIXTH century B.C., when Thales of Miletus posited that all of nature is made of water, physicists have tried to construct a single theoretical edifice encompassing every aspect of matter and energy. Many times they have thought they were close, and have announced the imminent revelation of such a theory. Always they have been wrong. Never before today, however, has such an inquiry become the dominant pursuit of the discipline. Never before have so many physicists been persuaded that a Theory of Everything is nigh. by Robert P. Crease and Charles C. Mann

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Until now the grand steps by which physics has progressed have consisted of partial "unifications." In the seventeenth century, for instance, Isaac Newton made the far from obvious discovery that a single force—gravitation—holds the planets in orbit and makes apples fall to the earth. (The story that he was inspired by a falling apple is true. At the time, he was staying on his mother's farm, north of London, to escape the plague.) In the past century James Clerk Maxwell made another giant step by describing how electricity and magnetism are different forms of yet another force: electromagnetism.

But even as Newton and Maxwell simplified science's view of nature, other physicists began to complicate it. Once the atom was discovered to consist of a nucleus, made of protons and neutrons, surrounded by a cloud of orbiting electrons, scientists began to wonder what held the nucleus together and why it sometimes fell apart. Investigating these questions, they found two more forces, operating only on the submicroscopic scale, which they called the strong and the weak. The strong force clamps the nucleus together despite the mutual electrical repulsion of the protons inside it. The weak force is responsible for certain types of radioactivity and is essential to the fusion process, which makes the sun shine. At the beginning of this year a group of scientists from Purdue University, in Indiana, and Brookhaven National Laboratory, in New York, claimed to have found evidence of a fifth fundamental force; few scientists are convinced of its existence, however.

Throughout the 1950s and 1960s theoretical physicists concentrated on the strong force (so named because it is the strongest known force in the universe; indeed, over short distances it is a hundred times more powerful than electromagnetism). They found the strong force extraordinarily difficult to understand. Over the years, they made thousands of guesses about its nature, most of which were wrong. One of these guesses started, in a roundabout way, what has come to be called string theory.

N 1968 AN ISRAELI physicist, Gabriele Veneziano, devised an ingenious mathematical equation that seemed to sum up many of the properties of particles that are subject to the strong force. A year later several theorists—the first being Yoichiro Nambu, of the University of Chicago—discovered that Veneziano's abstract formula generated a picture both of subatomic particles and of the ways in which they combine, change into one another, and fall apart. Subatomic particles can interact in thousands of ways, and charting this multiplicity is one of the chief tasks of particle physics. If Veneziano's equation was right, subatomic particles would be like tiny strings rather than tiny dots. When particles collided forcefully enough, these strings would break, creating new strings in the process. These in turn could join to create a single string. A useful analogy is a shoelace: If you snap one hard enough, you get two little laces. Just as a shoelace can be put back together with a knot, the new strings, in Veneziano's theory, could be rejoined. Theorists hoped that the vast number of types of interactions among subatomic particles could all be viewed in terms of cutting and linking minute bits of string—an image that was intuitively pleasing and that hinted at an ultimate simplicity.

In addition to providing an amusing picture of particles, Veneziano's model allowed physicists to peek into a novel and fascinating type of mathematics. Several dozen theorists began developing variants of the model and exploring their ramifications. These theorists quickly discovered that the models were plagued with terrible problems. They seemed to predict the existence of such outlandish things as particles that went faster than the speed of light, violations of the laws of cause and effect, and objects whose chance of existing was, mathematically, less than zero. Several theorists found, more or less independently, that this set of problems could be evaded, but only by making assumptions of even more striking oddity. First and foremost, Veneziano's model required more dimensions than the usual trinity of length, width, and depth; in fact, many of the problems vanished only when space-time was endowed with twenty-six dimensions—a situation that one of Veneziano's colleagues described with some restraint as "obviously unworldly." Not knowing quite what to make of all these extra dimensions, string fanciers tended to treat them as abstract parameters and trusted that more work would either make sense of them or eliminate them from the equations.

At any given time there are not that many original ideas floating around in science. Thus a goodly number of physicists continued to work on this one. However, their interest flagged in the early 1970s, when a theory of the strong force known as quantum chromodynamics was demonstrated to work quite nicely. At about the same time, several theorists—principally Sheldon Glashow, of Harvard University, Abdus Salam, of the International Centre for Theoretical Physics, in Trieste, and Steven Weinberg, now of the University of Texas, all of whom shared the 1979 Nobel Prize for Physics—developed a theory that linked the weak and electromagnetic forces. Glashow and a Harvard colleague, Howard Georgi, took the next step, unifying the strong, weak, and electromagnetic forces into a single structure, referred to portentously as a Grand Unified Theory.

Despite the considerable excitement engendered throughout the late 1970s by quantum chromodynamics and Grand Unification, the formal elegance of string theory was enough to keep a few brave scientists at work on it—notably John Schwarz, now of the California Institute of Technology, in Pasadena, Andre Neveu and, later, Edward Witten, of Princeton University, and the late Joel Scherk, of the Ecole Normale Superieure, in Paris. Just before the triumph of quantum chromodynamics, Schwarz and Neveu had managed to come up with a version of Veneziano's model which economized on the number of dimensions, reducing it to ten. Then, in 1974, Schwarz and Scherk came to a realization that would launch the entire modern string movement, although few paid attention in the burst of excitement over quantum chromodynamics. Schwarz and Scherk suddenly understood that they had spent years on the wrong problem. String theory was not a theory merely of the strong force. Instead, it seemed able to describe every known force, including gravitation.

HE CONTEMPORARY theory of gravitation was general relativity, put together by Albert Einstein in 1915, after a long struggle. An imposing and beautiful structure, relativity remained aloof from the other great achievement of twentieth-century physics—quantum mechanics. Relativity shows its effects at great speeds, quantum mechanics at minute distances. All efforts to subsume relativity within quantum mechanics—to produce a quantum-mechanical theory of gravitation—eventually foundered on the rocks of mathematical absurdity.

Loosely speaking, present-day quantum theories argue that the universe has two fundamental components: particles of matter, like electrons, protons, and neutrons; and particles associated with forces, which are known collectively as gauge particles, from the jargon describing their properties. The best-known example of a gauge particle is the photon, the particle of light, which is associated with electromagnetism. A less familiar example is the gluon, which is associated with the strong force. By 1974 all known forces except gravitation had been explained in terms of particles. Although physicists had assumed that a particle was associated with this force and had given such a particle a name (the graviton), making a theory with gravitons turned out to be very hard. All attempts produced impossible answers, in somewhat the same way that dividing by zero creates trouble for beginning algebra students.

Schwarz and Scherk realized that the string theory they were staring at was the first theory capable, as far as they knew, of incorporating not only gluons but also particles that could be identified as gravitons. To their surprise, this theory was not beset by as many difficulties as its less ambitious predecessor. The strong force has nothing to do with the geometry of space and time, but, as Einstein showed, gravitation does. Thus, if mathematics compelled you to work with a peculiar number of dimensions, a theory encompassing gravitation would be the place to do so. Schwarz and Scherk suggested that the extra six dimensions curl up, so that only four—three spatial and one temporal—can be observed in the everyday world. (The process is called compactification by string theorists and topologically inclined mathematicians.) In other words, string theories lead to the startling idea that at every point of ordinary space is a submicroscopic six-dimensional ball. The minute size of the balls and the strings that inhabit this strange space means that for all practical purposes most of us can go on thinking that we live in a three-dimensional world made of dot-like particles.

A measure of the audacity of the new string view is that at first it was dismissed; most theorists believed in eventual unification but considered unification just then to be a pipe dream. Scherk died in 1980, and with considerable intellectual courage the remaining members of the small string band kept on. What kept them going was the fact that string theory seemed to be as roomy and inflexible as a Victorian mansion. Schwarz thought that he might be able to derive the entire universe mathematically from the equations of string theory, just as Euclid was able to derive the capacious whole of his geometry from a few simple axioms and the strict rules of deduction.

In the summer of 1984, after years of intense effort, Schwarz and Michael Green, of the University of London, proved that the new way of looking at things avoided most of the mathematical pitfalls that had trapped previous investigators. Word passed quickly in seminars and lecture halls all over the world; suddenly, theorists everywhere were listening to the gospel of string. Once again, they hoped that the Theory of Everything might be around the corner.

Such a theory—a unification theory—would have to show that particles of mass (such as electrons) and particles of force (such as photons) somehow stem from the same thing. In the picture of matter provided by string theories subatomic particles consist of minute rings as much smaller than an atom as an atom is smaller than the solar system. Each tiny loop can vibrate, undulate, and be besieged by little ripples that travel around its circumference. The theories hold that only ripples of particular wavelengths can go round and round the circle without eventually canceling themselves out. Subatomic particles are differentiated by the number of ripples on them. Last spring a group of Princeton University theorists—David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rhom—took this scenario a step further and, in doing so, came up with a plausible candidate for the unification theory that the physics world has been waiting for. The Princeton scientists suggested that combinations of clockwise and counterclockwise waves account for everything in nature.

String theories are associated with a branch of mathematics known as group theory, and the various models are named for the mathematical groups that describe them. (These groups were catalogued and named at the turn of the century by the French mathematician Elie Cartan.) Theorists believe they have narrowed the candidates down to just one: E

HE IDEAS OF Gross and his fellow string theorists are plagued by a difficulty that afflicts other unification theories as well: nobody yet has the faintest notion of how to test them. If strings exist, they can be seen only at energies so high and distances so small that experimental equipment may never be up to the task. Unable for the moment to count on direct verification of their ideas, string theorists are relying on the demands of mathematical consistency to guide their work. The calculational juggling act is so difficult—a unification theory has to satisfy the dictates of relativity and quantum mechanics, as well as account for the vast range of information that experimenters now have about the real world—that many theorists think that only one theory can possibly do the trick. That survivor will be the Theory of Everything. (When we asked Schwarz what predictions string theory makes, he said, "Well, it predicts that gravity exists, whereas all other theories predict that it doesn't. There will be many more testable consequences when we work out the mathematics.")

Skeptics doubt that mathematics is restrictive enough to hold the field of candidates at one. They envision several different Theories of Everything, each of which will work on paper and none of which can be proved by observation. Howard Georgi, for instance, says that string theory is doomed to be nothing but "recreational mathematical theology." His collaborator, Sheldon Glashow, considers string theories to be simply "an interesting sociological example of the tendency for physicists to jump on a theoretical bandwagon." If the skeptics are right, string theorists may one day find themselves in the painful position of having achieved the goal of Thales—a complete explanation of all matter and energy in terms of a single principle—but unable to substantiate their accomplishment with the proof hitherto expected of all empirical science.

The attempt to construct a Theory of Everything is necessarily based on the confident assumption that all major aspects of nature have been identified and that the remaining task is merely to link them together. Thus any important new experimental discovery runs the risk of—so to speak—upsetting the string applecart. For example, if the fifth force that scientists claim to have discovered does exist, it is not clear whether string theory will be able to accommodate it.

Even without a surprise from experimenters, string theorists may simply be wrong. In this event the quest for unification will not die; other theorists have been working on a welter of alternative approaches, which have names like supersymmetry, supergravity, and Kaluza-Klein. But so far string theory remains the most ambitious and mathematically elegant of the contenders. (It is so elegant, in fact, that mathematicians, who need not worry about its truth, have been using it to push back the frontiers of their own discipline.)

Enthusiasts of string are not worried about what the future holds for their theory. As Murray Gell-Mann, of the California Institute of Technology, an ardent booster of E

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