A THEORY OF EVERYTHING

DESPITE HIS thick glasses, rumpled jacket, a tie that barely reaches past his sternum and the obligatory chalk-covered pants of a professor, he cuts a handsome figure. Striding across the room in long, sure steps, he conducts his lecture like a maestro, the rat-a-tat-tat of the chalk on the board providing a counterpoint to his high, breathy, sometimes inaudible voice. He talks of ''vector bundles,'' ''spin groups,'' ''Dirac operators,'' ''connected Lie groups,'' ''trivial modules,'' ''free loop spaces.'' At one point he pauses: ''We've been living in a finite dimensional world. Now I'm inviting you to jump into a world of infinite dimension.''

He is Edward Witten of the Institute for Advanced Study in Princeton, N.J. At the age of 36, he is among the foremost physicists of his day, and he is in New York lecturing the Columbia University mathematics department on, of all things, the applications of physics to mathematics. Math - which has to do with abstract, intangible relationships - has always been an important tool in physics - which has to do with concrete forces and objects in the actual world. Witten has turned things upside down, attempting to show how physics can provide new insights into math. Turning things upside down is something he seems to do as a matter of course.

''We shouldn't toss comparisons with Einstein around too freely,'' says Sam B. Treiman, a member of the physics department at Princeton, ''but when it comes to Witten. . . .'' His hands open in a gesture of helplessness. ''He's head and shoulders above the rest. He's started whole groups of people on new paths. He's started whole new fields. He produces elegant, breathtaking proofs which people gasp at, which leave them in awe.''

Harvard physicist Sidney Coleman calls Witten, simply, ''smarter than anyone else. He's brought light where there was darkness. Everything he does is golden. If you go to any theoretical physics department in the world, you can see that people are touched, and touched deeply, by Ed's work.''

Witten is everywhere at once, publishing papers and lecturing on cosmology, mathematics and many different aspects of physics. When Witten talks, physicists listen. In particular, they perked up their ears several years ago when he began to pay serious attention to a seemingly bizarre and long-forgotten theory that turns our current picture of the physical universe on its head. Although it is nearly impossible to put a finger on the single contribution that has made Witten such a force in physics, his passion for this controversial theory makes him a leading proponent of what may be the most revolutionary idea in physics in more than half a century - as revolutionary, claims Witten, as relativity; as revolutionary as quantum theory.

If the theory is right, as Witten believes it may ultimately prove to be, it could provide entirely new answers to fundamental questions asked by philosophers, poets and theologians since the beginning of human time: Why is the universe the way it is and what is the origin of matter? (Box, page 24.) Although the term makes Witten uncomfortable, some people call it a ''theory of everything.''

''String theory,'' as it is commonly known (some scientists call it ''superstring theory''), does away with the familiar image of a universe composed of billiard-ball-like particles pushed and pulled by familiar forces like gravity and electricity. Quantum theory had already revealed in the 1920's that the billiard balls have curious wave-like properties: they are more like vibrations than well-defined points in space. Now string theory is proposing that these points, in fact, are tiny loops, or closed ''strings,'' that the universe is built not of Grape-Nuts but of Cheerios. The strings, too, vibrate invisibly in subtle resonances. These vibrations, so the theory goes, make up everything in the universe - from light to lightning bugs, from gravity to gold.

These strings are not, of course, visible, nor are they like rubber bands or pieces of twine. Impossible to detect by any means known to science today, they are mathematical curves. Talking about strings, like talking about billiard balls or waves, is a crude way of trying to comprehend the unfamiliar in familiar terms. But then, physics has always had to resort to metaphor. As the late Niels Bohr, the father of quantum theory, once put it, ''When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images.''

Previous scientific theories describing the universe have not yet been able to create an image that fits all the pieces of the universe together within a single conceptual framework. Physicists have opened the atom, like a series of Russian dolls, to reveal, first, electrons, protons and neutrons - then, more exotic entities like neutrinos and quarks. They have learned how nuclear, gravitational and electromagnetic forces mold these particles into molecules and galaxies. But nobody knows why, among other things, there should be electrons at all, or why particles are affected by gravity. String theory, according to its adherents, has the potential of offering a single consistent explanation for everything from the inner workings of the atom to the structure of the cosmos.

Unfortunately, string theory contains what some scientists consider to be a major flaw. The mathematical consistency that makes it so compelling is revealed only if we are willing to suspend our belief in a world fashioned from the familiar four dimensions of height, breadth, width and time, and instead suppose the existence of six additional hidden dimensions - a total of 10 in all.

Imagine a closed string - a loop -of some kind of fundamental stuff. Now imagine that the loop rotates, twists and vibrates not only in the three familiar spatial dimensions (plus one dimension of time) but also in six other dimensions we can't perceive. As the loop wriggles, it resonates in many different modes, like a 10-dimensional violin string sending out cosmic versions of A or E flat. These vibrations, if string theory is correct, determine all the possible particles and forces of the universe.

Pressed for further explanation, Witten smiles and shrugs. ''Nobody understands this much better than I just explained it to you,'' he says.

Ten dimensions don't bother Witten in the least: ''These extra dimensions aren't stranger than a lot of other things physicists think about.'' Still, the notion of a 10-dimensional universe and the absence of any experimental data that could offer proof of it have caused many physicists to be highly skeptical. ''It's not obvious how string theory explains certain striking facts about the universe,'' says Frank A. Wilczek, of the Institute of Theoretical Physics at the University of California, Santa Barbara.

To be sure, string theory has a great deal to explain. For example, it will have to show just how it is that six extra dimensions remain invisible to us. String theorists imagine these dimensions to be ''rolled up'' tightly around themselves on scales billions of times smaller than the nucleus of an atom. But they do not yet know how, why or when the six hidden dimensions rolled up. Perhaps, some theorists say, they simply failed to expand billions of years ago when the rest of the universe began doing so.

Such doubts do not in any way diminish Witten's conviction. ''It is very possible that a proper understanding of string theory will make the space-time continuum melt away,'' Witten says. ''String theory is a miracle through and through.''

WITTEN STARTED GETTING OFFERS of professorships within a few years of completing graduate school at Princeton, where he became a full professor at 28. He's received a plethora of prizes from all over the world, including a MacArthur Fellowship and, most recently, the National Science Foundation's Alan T. Waterman Award for best young researcher.

That medal, along with other prestigious awards, is piled ingloriously in the corner of a bookcase in a spare bedroom Witten uses as a study, sharing it with his wife, Chiara Nappi, also a Princeton physicist. Their house could be anybody's suburban ranch. The few pictures on the walls are mostly children's crayon drawings (they have two daughters). There is an Exercycle in the kitchen and a pool in the backyard where, on a recent sunny Wednesday, the Wittens gave a party for 40 first graders. While children in wet bathing suits ran in and out of the living room, Witten discussed the status of string theory.

In physics, the yearning for an ultimate explanation has always been evident. Time and time again, physics has advanced when seemingly diverse phenomena have turned out to be different aspects of the same thing. Newton's great discovery, for instance, was that the same force that pulled the apple to the ground also held the moon in its orbit around the earth and the earth in its orbit around the sun. Magnetism, electricity and light were long thought to be completely unconnected - until Maxwell and Faraday found that all were manifestations of electromagnetism. Einstein's theory of relativity grew out of his efforts to reconcile electromagnetism with classical mechanics.

Most recently, physicists have been obsessed with trying to unify, or find connections among, the known fundamental forces of nature: gravity, electromagnetism, the ''strong'' force that holds particles together within the nucleus of an atom and the ''weak'' force that accounts for, among other things, radioactivity, the spontaneous disintegration of the nucleus that results in the emission of energy. (Recent research has raised the question of whether there is another force in the universe that somehow counteracts gravity.) Electromagnetism, the strong and the weak forces, and all the known particles in the universe can be described in terms of quantum theory, a fact Witten considers ''magic.'' The theory has given rise to an entire field of scientific inquiry to which Witten himself has made several important contributions. According to quantum theory, everything results from the interactions of fields of energy. The fields vibrate, but only in certain patterns or resonances that correspond to specific quantities (hence the term ''quantum'') of energy. These resonances are the familiar particles and forces of the everyday world. In fact, physicists who use giant accelerators to smash atoms and search for exotic particles have been known to call their work ''resonance hunting.''

Quantum theory managed to clear up a host of questions and led to an understanding of subatomic processes that has since produced everything from lasers to semiconductors. Nevertheless, quantum theory cannot account for gravity. Mathematical calculations that try to fit gravity within that framework yield unworkable results.

''If it weren't for gravity,'' says Witten, ''we'd probably think we already knew everything fundamental about nature. But gravity doesn't fit. It's a clue that something is wrong with our understanding. Why gravity doesn't fit is the big mystery of mysteries.'' Yet gravity interacts with every kind of energy in the universe - even a light beam falls under its influence. So gravity has to obey the same laws of nature. The question is, what are they?

FOR MUCH OF HIS CAREER, EINSTEIN struggled to unite gravity with electromagnetism to explain all of nature in terms of one ''unified field.'' He never succeeded. But in 1919, he got a letter from an obscure German-born physicist named Theodor F.E. Kaluza suggesting that electromagnetism could be understood as a fifth-dimensional manifestation of gravity. Kaluza didn't explain why the fifth dimension remained unperceived. But in 1926, a Swedish mathematician, Oskar Klein, suggested this was so because the fifth dimension was rolled up so tightly - existed on such a tiny scale - that it did not affect anything as large as even a subatomic particle.

String theory is a resurrected form of the Kaluza-Klein theory, although vastly more sophisticated. Just as Klein's fifth dimension shriveled up into invisibility, so the extra six dimensions in string theory somehow ''compacted.'' If we accept the idea of those six hidden dimensions, string theory proposes, mathematical inconsistencies that have plagued previous attempts to reconcile quantum theory and gravity wondrously disappear.

But it's not clear that string theory accurately represents reality. No evidence apart from mathematical consistency supports the existence of six extra dimensions. Still, mathematical consistency, Witten says, has been ''one of the most reliable guides to physicists in the last century.''

Even if it has mathematical consistency, what string theory is still missing are underlying concepts. ''Vibrating strings in 10 dimensions is just a weird fact,'' says Witten. ''An explanation of that weird fact would tell you why there are 10 dimensions in the first place.''

''I wish I had a bigger role in all this,'' says Witten, somewhat puzzled by all the attention he's been getting lately. ''To be honest, it's not clear that I'm newsworthy.''

Formal, quiet, withdrawn, Witten is hesitant to talk about his accomplishments. At times, he seems so other-worldly that one can easily understand why his graduate students call him (with great respect and admiration) ''the Martian.''

Sidney Coleman, the Harvard physicist, remembers visiting Witten in Princeton just after Witten had moved there from Cambridge. (Witten was a member of the Harvard Society of Fellows for several years before taking his first job as professor.) Coleman asked him how he compared living in quiet, suburban Princeton with his previous existence in the bustling Boston area. Witten responded: ''In Princeton, I sit at my kitchen table at night doing physics instead of going down to Nassau Street. At Harvard, I sat at my kitchen table at night doing physics instead of going to Harvard Square.''

To some extent, the world of the theorist is by definition a private one. The work requires no lab, no test tubes, no cyclotrons, no supercomputers, no equipment of any sort apart from a pencil and paper, and sometimes not even that. Although Witten has graduate students, he is reluctant to involve them in his more speculative projects. ''It would be gambling their futures,'' he says.

He rarely even sits down at a desk to write, according to his wife. ''He thinks. He lies down on the bed. He sits like this,'' she says, resting her chin on her wrist. ''He never does calculations except in his mind. I will fill pages with calculations before I understand what I'm doing. But Edward will sit down only to calculate a minus sign, or a factor of two.''

If you listen to Witten, becoming a physicist was almost a casual thing. Although his father, Louis Witten, is a gravitational physicist (now at the University of Cincinnati), he says he wasn't all that influenced by his family. ''I came within a whisker of doing other things.''

Witten grew up in Baltimore and got his undergraduate degree in history at Brandeis, where his real interest, however, was linguistics. Before he entered graduate school at Princeton, he wrote articles for The Nation, The New Republic and other publications. For a six-month period during 1972, he worked on George McGovern's Presidential campaign as aide to one of the candidate's legislative assistants. McGovern wrote him a recommendation for graduate school. Still, Witten feels, he lacked the qualities necessary for a career in writing or politics, foremost among them, ''common sense.'' When he entered graduate school at Princeton, he came very close to choosing mathematics before settling on physics.

WITTEN'S COLLEAGUES TEND to give him far more credit than he gives himself, especially when it comes to his role in bringing string theory out of the closet.

Physicists didn't set out to look for string theory, nor did they seriously follow up Kaluza-Klein. Rather, they tripped over string theory in the dark and have been trying to figure out exactly what it is ever since. ''I don't think that any physicist would have been clever enough to have invented string theory on purpose,'' says Witten. ''Luckily, it was invented by accident.''

In 1968, an Italian physicist named Gabriele Veneziano was investigating the strong force (the glue that holds particles together within the nucleus) when he stumbled upon what Witten describes as ''a formula that had a few curious properties.'' It was a few years later, through the work of Yoichiro Nambu of the University of Chicago and others, that people ''realized that silly formula described vibrating strings.''

For a few years, string theory generated a great deal of interest. By the mid-1970's, however, it had been largely abandoned, partly because other lines of thought seemed more promising, and partly because it required the unacceptable idea of extra dimensions.

''When people found out that it only made sense in 10 dimensions,'' says Witten, ''most people left the field.'' His own interest in it was sparked primarily by the work of the physicists John H. Schwarz of the California Institute of Technology, and Michael B. Green of Queen Mary College in London. Witten remembers going through a ''few rough months to learn about it. It was unlike anything anyone had seen before. There was no encouragment from anybody.''

By all accounts, it was a series of papers written by Schwarz and Green in the early 1980's that resuscitated the theory. In 1984, they published an important paper that, according to Nobel Prize-winning physicist Steven Weinberg of the University of Texas, answered a question that had also been posed by Witten.

The question had to do with anomalies that appeared in theories that tried to put gravity together with quantum field theory. Anomalies are defects in a theory that yield absurd results and make the theory meaningless. Witten, along with Luis Alvarez-Gaume of Harvard, discovered a new class of anomalies. Even more important, he showed that the origin of the anomalies was topological - that is, related to geometric properties that do not arise in four dimensions but do arise in 10.

Topology, the study of the properites of geometric figures as they are distorted or deformed in various dimensions, is, for Witten, ''basic.'' The thought that lay people might not be familiar with topology strikes him as funny. ''That's like saying they don't know how to speak in prose,'' he says. A cup with one handle, for instance, is topologically equivalent to a doughnut. If the cup were made of malleable clay, it could be reshaped into the doughnut without tearing the material. ''It's so obvious,'' Witten says. ''There are properties of things that change when you break them, but not when you bend them.'' He sighs: ''Physicists didn't use to take topology seriously either.''

Topology is critical to Witten because the question of whether the real world can be explained by string theory depends not only on whether the extra dimensions exist, but also on the forms they take in space - whether they are, say, rolled up like tubes or have holes like doughnuts or are spheres.

Appealing to extra dimensions actually makes some problems simpler. Consider a riddle: A pair of explorers walks due south for one mile, then due east for one mile, then due north for one mile, only to find themselves back at the starting point. Question: What color are the bears?

This riddle makes no sense as long as the explorers are walking on a flat, two-dimensional surface, as on a conventional map. But the earth is a three-dimensional sphere. Its surface curves. Taking this into account, the answer to the riddle becomes obvious: The explorers' starting point was the North Pole. The bears are white. In his Victorian science fiction classic ''Flatland,'' Edwin Abbott demonstrated eloquently that what seems puzzling and obscure in one dimension can become crystal clear in another. In his hypothetical world of two-dimensional triangles and squares, a three-dimensional sphere was an incomprehensible object. As it passed through this flattened space, it would first appear as a point, then as a widening circle that finally shrank back to a point and faded away. A two-dimensional creature can see only one two-dimensional slice of a sphere at a time. It takes a three-dimensional onlooker to see a sphere in its entirety.

And if we could see the universe in its 10-dimensional entirety, string theory presumes, a new symmetry would appear and the puzzling array of forces and particles would be revealed as different facets of one cohesive whole.

Unfortunately, this tantalizing symmetry inherent in 10-dimensional space is not easy to translate into four-dimensional particles and forces. To be comprehended, it requires incredibly subtle mathematical tools, ones that probably haven't even been invented.

SEVERAL YEARS ago, Witten had a conversation with a colleague that struck him deeply. ''He was talking about a very talented physicist who wasn't as productive as he might have been. And he said it was because he never worked on the kinds of problems for which he was really suited.''

Witten has been serious about taking his colleague's implied advice. What he's suited for, he says, is ''taking a physics problem and finding a solution based on bizarre mathematics. String theory is going to require a lot of new mathematics -and applying bizarre mathematics to physics is what I'm good at.''

During the past several years, Witten has been one of the leaders in a new liaison that string theory has forged between physicists and mathematicians. ''In my book, he's the leader,'' says I.M. Singer, a mathematics professor at the Massachusetts Institute of Technology. ''He's one of two people I call if I get stuck. His intuition is fantastic.'' Of his most important contributions, Witten describes several as contributions not to physics, but to mathematics. ''He's got more mathematical muscles in his head than I like to think about,'' says Weinberg of the University of Texas.

Close liaisons between physics and mathematics have marked most of the major advances in our understanding of the universe. Newton needed to invent a new kind of mathematics -calculus - to complete his theory of gravity. Einstein's general relativity relied on a geometry of curved space invented by Georg F.B. Riemann in the mid-1800's. Quantum theory required a tool called ''functional analysis.''

String theory, Witten says, ''brings us to the frontiers of mathematics.'' But that doesn't deter him: ''I realized I could actually turn it around, and get some surprising insights about mathematics from physics.''

The new marriage between physics and mathematics has made physics truly difficult for the first time for Witten. That's one reason he has accepted an invitation to join the prestigious Institute for Advanced Study next door to Princeton, where he'll be free from teaching obligations. ''I want to work in a more ambitious way on half as many things.'' All of them are aspects of string theory.

Witten's work cannot now, nor for the foreseeable future, be tested in a lab. In fact, it is so far removed from observable reality that a lifetime or more may be required before its value - or any possible application - is known. Theoretical physics is a risky business. ''It's extremely important to believe in what you're doing,'' Witten says. ''But it's difficult to have faith when things are so speculative. I remember when my smallest daughter was learning to crawl. It was clear that she could do it, but she didn't seem to realize that it was a worthwhile thing to pursue. It reminds me of my own efforts.''

''One lesson you can learn,'' he continues, ''is don't make mistakes. But that's not very useful. Another lesson is, don't give up on right ideas. But how do you know they're right?''

Because string theory is so speculative, a good many physicists regard it with suspicion and even disdain. Harvard Nobel laureate Sheldon L. Glashow co-authored an article in Physics Today with his colleague Paul Ginsparg - entitled ''Desperately Seeking Superstrings?'' - in which they wrote: ''A naive comparison suggests that to calculate the electron mass from superstrings would be a trillion times more difficult than to explain human behavior in terms of atomic physics.''

Witten describes such criticism as ''manifest silliness. It's not always so easy,'' he says, ''to tell which are the easy questions and which are the hard ones. In the 19th century, the question of why water boils at 100 degrees centigrade was hopelessly inaccessible. If you told a 19th-century physicist that by the 20th century you would be able to calculate this, it would have seemed like a fairy tale. . . . Quantum field theory is so difficult that nobody fully believed it for 25 years.''

Witten points out that neutron stars and gravitational lenses - large concentrations of matter in outer space that produce, for earthly observers, double images of stars - were considered science fiction, pure speculation, until they were suddenly found in the skies. ''The history of science is littered with predictions that such and such an idea wasn't practical and would never be tested. The history of physics shows that good ideas get tested.''

String theory, for Witten, is too good not to be true. If it seems difficult and complicated, that only means it's not well understood. For now, string theory remains ''a piece of 21st-century physics that fell by chance into the 20th century,'' he says. What physicists are working with today is but ''a few crumbs from the table compared to the feast which awaits us.''

Still, he worries at times that it might be too difficult. ''There are long odds against its leading anywhere in the next few years, but I feel I would be missing the point if I didn't try.''

John Ellis, a theoretical physicist at the European Center for Nuclear Research, the international laboratory in Geneva, recently wrote, ''Superstring phenomenology is still a very young subject. There are many open questions and technical problems, and it is easy to ridicule superstring advocates for their totalitarian fervor. However, in the words of a candy wrapper I opened a few years ago: 'It is only the optimists who achieve anything in this world.' ''

Or, as Witten says, ''To test string theory, we will probably have to be lucky. But in physics, there are many ways of being lucky.''