Aesthetic Science
Chris Quigg

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. By Brian Greene. W. W. Norton & Company, New York and London, 1999 ($27.95).

Making connections is the essence of scientific progress. For monumental examples in the realm of physics, think of the amalgamation of electricity and magnetism and light; of the recognition that heat is atoms in motion, which brought together thermodynamics and Newtonian mechanics; and of the realization that the chemical properties of substances are determined by the atomic and molecular structure of matter.

These advances, and much of our recent progress in particle physics and cosmology, came about in large measure through the creative resonance between experimental discovery and theoretical insight, sometimes one taking the lead, sometimes the other. Another path to theoretical progress focuses on foundational issues of internal logic and self-consistency. The most recent strides—many would say leaps and bounds—along that path have attended the development of string theory, the subject of Brian Greene's thoughtful and important book, The Elegant Universe. Greene, a professor of physics and mathematics at Columbia University, and an adjunct professor at Cornell University, is a leading contributor to string theory and a key agent in the growing reunion of physics and mathematics. The Elegant Universe presents the ideas and aspirations—and some of the characters—of string theory with clarity and charm. It is both a personal story and the tale of a great intellectual movement.

The conceptual tension that faces physics at the millennium has been building for half a century. All of modern physics rests on two pillars. One is Albert Einstein's general relativity, which describes the world on the largest of scales—stars, galaxies and the immensity of the universe itself. The other is quantum mechanics, which describes the world on the smallest of scales—atoms, nuclei and quarks. Experiments have confirmed the predictions of both general relativity and quantum mechanics to a remarkable degree. But—as we currently understand these two theories—they cannot both be right. The violent fluctuations on ultramicroscopic scales implied by the uncertainty principle of quantum mechanics are at odds with the smooth geometry of spacetime that is the central feature of general relativity.

Why has this battle of titanic ideas not paralyzed physics? At most of the distance scales that physicists contemplate, from less than a billionth of a billionth of human scale out to the farthest reaches of the universe, the dissonance between quantum mechanics and general relativity does not arise. That is why many physicists are content to note the problem and go—productively—about their business. But when we consider stupendously short distances to analyze the earliest history of the universe, we run up against the fundamental incompatibility between general relativity and quantum mechanics.

Over the past three decades, an intrepid band of theoretical physicists and mathematicians—first in tiny groups, now in a veritable army—have concluded that the time is ripe to address this grand conflict between the two great pillars of our understanding. The picture they are developing is called string theory. It holds that the fundamental constituents of the universe are not the elementary particles that we idealize as having no size, like geometric points, but tiny strings. The resonant patterns of vibrations of the strings are the microscopic origin of the masses of what we perceive as particles and the strengths we assign to the fundamental forces. Because strings have a finite, though fantastically tiny, size, there is a limit to how finely we can dissect nature. That limit—set by the size of strings—comes into play before we encounter the devastating quantum fluctuations that rend spacetime. Thus, the conflict between quantum mechanics and general relativity is resolved

Searching for Symmetry

String theorists undertake their campaign to reconcile general relativity and quantum mechanics even without detailed experimental results, which Greene calls "the shining light of nature," to guide them from one step to the next. Lacking experiment's guiding hand, it is possible that one or more generations of physicists will devote their careers to string theory without getting any experimental feedback. They risk investing a lifetime of effort for an inconclusive result.

Why take the risk? The string theorists are not simply sticklers for rigor. They are animated by ambition, by the hope that resolving the conflict between general relativity and quantum mechanics will resolve at a stroke many other issues—explaining the properties of the elementary particles and forces, plumbing the true nature of a black hole. "In his long search for a unified theory," Greene writes, "Einstein reflected on whether 'God could have made the Universe in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.' With this remark, Einstein articulated the nascent form of a view that is currently shared by many physicists: If there is a final theory of nature, one of the most convincing arguments in support of its particular form would be that the theory couldn't be otherwise."

Early in the study of string theory, physicists learned that the theory does not make sense if spacetime is made up of the three space dimensions plus one time dimension of ordinary experience. String theory also requires extra space dimensions that apparently must be curled up to a very small size to be consistent with our never having seen them. Whether we can probe them directly or not, these extra curled-up dimensions—six of them, in most forms of string theory—have physical consequences. As Greene explains it, "a tiny string can probe a tiny space. As a string moves about, oscillating as it travels, the geometrical form of the extra dimensions plays a critical role in determining resonant patterns of vibration. Because the patterns of string vibrations appear to us as the masses and charges of the elementary particles, we conclude that these fundamental properties of the universe are determined, in large measure, by the geometrical size and shape of the extra dimensions. That's one of the most far-reaching insights of string theory."

String theory is still a work in progress. In fact, the equations of string theory seem so complicated that physicists have managed to write down only approximate versions. Within the past few years, string theorists have realized that all the approximate formulations might be seen as different limiting cases of an 11-dimensional theory whose fundamental entities include two-dimensional membranes. Although it is only partially understood, this new theory, termed M-theory, has given unforeseen unity to the approximate versions of string theory that previously seemed distinct and unrelated [see "The Theory Formerly Known as Strings," by Michael J. Duff; Scientific American, February 1998].

If string theory arises from metaphorical travel to the realm of infinitesimal distances and unattainably high energies, how can we hope to test it? Edward Witten of the Institute for Advanced Study in Princeton, N.J., urges that string theory already can claim experimental confirmation for its prediction of gravity. As Greene explains, "Both Newton and Einstein developed theories of gravity because their observations of the world clearly showed them that gravity exists. On the contrary, a physicist studying string theory … would be inexorably led to it by the string framework."

One reason that string theory appeals so powerfully to theoretical physicists is that it is the most symmetrical theory ever devised. Symmetry is the concept physicists use to relate phenomena and circumstances that seem—on first examination—to be different. James Clerk Maxwell showed that such disparate phenomena as light, electricity and magnetism are fundamentally intertwined; Einstein showed that all states of motion are related. String theory encompasses these symmetries and more. It incorporates the grandest symmetry that physicists have imagined: supersymmetry, a quantum-mechanical extension of space and time. Supersymmetry relates the two quantum-mechanical categories of elementary particles, so that each of the known fundamental particles must have a superpartner whose spin differs by half a unit. Intensive searches for supersymmetry—or for indirect indications of the existence of supersymmetry—preoccupy many particle physicists around the world. Although supersymmetry can exist without string theory, the discovery of supersymmetry would supply extremely strong encouragement for string theory.

String theory might also be able to resolve one of the great puzzles of cosmology. Astronomical observations have shown that Einstein's cosmological constant, which governs the cosmic evolution of the motions of distant galaxies, is quite small, if not exactly zero. Yet according to our current understanding of the fundamental interactions, quantum fluctuations throughout space tend to create a cosmological constant that is many, many times larger than observation allows. Can string theory show why the cosmological constant is tiny?

The Significance of Scale

For most of the 20th century, physicists have been living through—no, making—a change in the way humans think about their world. Physicists have known since the 1920s that to explain why a table is solid, or why a metal gleams, we must explore the atomic and molecular structure of matter. That realm is ruled not by the customs of everyday life but by the laws of quantum mechanics. The recognition that the human scale is not privileged, that we need to leave our surroundings the better to understand them, has been building since the birth of quantum mechanics. As it emerges whole, fully formed, in our unified theories and scale-changing shifts in perspective, the notion seems to me both profound and irresistible. I find it fully appropriate to compare this change in perception with the shifts in viewpoint we owe to Copernicus and Einstein. And just as the realization that we are not at the center of the universe ultimately enlightened and empowered—not diminished and dispirited—us humans, so, too, the recognition that our size is not the only, or the most important, scale for comprehending nature will be a source of insight and inspiration.

If string theory succeeds, its success will represent the culmination of the idea that we understand the universe best when we consider it on many scales. Here is Greene's summation: "Although we are technologically bound to the earth and its immediate neighbors in the solar system, through the power of thought and experiment we have probed the far reaches of both inner and outer space. During the last hundred years in particular, the collective effort of numerous physicists has revealed some of nature's best-kept secrets. And once revealed, these explanatory gems have opened vistas on a world we thought we knew, but whose splendor we had not even come close to imagining."

Will string theory succeed? We do not know. After all, no one yet understands completely what string theory is, and the tools needed to extract its predictions are still being developed. It is certainly not the only fruitful path to follow: experiments at the great accelerators and surveys at the great observatories, together with the theoretical developments that motivate or respond to them, will surely bring dramatic advances in our understanding of what nature is and how it works. But the insights that string theory has already brought illustrate anew the power of the question "Why not?" to open our eyes to new possibilities. String theory is a beautiful dream, beautifully told in The Elegant Universe.

CHRIS QUIGG is a theoretical physicist at Fermi National Accelerator Laboratory in Batavia, Ill. He is the author of Gauge Theories of the Strong, Weak, and Electromagnetic Interactions (Perseus Books, 1997).

Published in Scientific American 280, (4) 101 (April 1999).