In string theory, beauty is truth, truth beauty. Is that really

It is the best of times in physics. Physicists are on theverge of obtaining the long-sought Theory of Everything. In a few elegantequations, perhaps concise enough to be emblazoned on a T-shirt, this theorywill reveal how the universe began and how it will end. The key insight is thatthe smallest constituents of the world are not particles, as had been supposedsince ancient times, but “strings”—tiny strands of energy. By vibrating indifferent ways, these strings produce the essential phenomena of nature, theway violin strings produce musical notes. String theory isn’t just powerful;it’s also mathematically beautiful. All that remains to be done is to writedown the actual equations. This is taking a little longer than expected. But,with almost the entire theoretical-physics community working on theproblem—presided over by a sage in Princeton, New Jersey—the millennia-olddream of a final theory is sure to be realized before long.

It is the worst of times in physics. For more than a generation, physicistshave been chasing a will-o’-the-wisp called string theory. The beginning ofthis chase marked the end of what had been three-quarters of a century ofprogress. Dozens of string-theory conferences have been held, hundreds of newPh.D.s have been minted, and thousands of papers have been written. Yet, forall this activity, not a single new testable prediction has been made, not asingle theoretical puzzle has been solved. In fact, there isno theory so far—just a set of hunches and calculations suggesting that a theorymight exist. And, even if it does, this theory will come in such a bewilderingnumber of versions that it will be of no practical use: a Theory of Nothing.Yet the physics establishment promotes string theory with irrational fervor,ruthlessly weeding dissenting physicists from the profession. Meanwhile,physics is stuck in a paradigm doomed to barrenness.

So which is it: the best of times or the worst of times? This is, after all,theoretical physics, not a Victorian novel. If you are a casual reader ofscience articles in the newspaper, you are probably more familiar with theoptimistic view. But string theory has always had a few vocal skeptics. Almosttwo decades ago, Richard Feynman dismissed it as “crazy,” “nonsense,” and “thewrong direction” for physics. Sheldon Glashow, who won a Nobel Prize for makingone of the last great advances in physics before the beginning of thestring-theory era, has likened string theory to a “new version of medievaltheology,” and campaigned to keep string theorists out of his own department atHarvard. (He failed.)

Now two members of the string-theory generation have come forward withexposés of what they deem to be the current mess. “The story I will tell couldbe read by some as a tragedy,” Lee Smolin writes in “The Trouble with Physics:The Rise of String Theory, the Fall of a Science, and What Comes Next”(Houghton Mifflin; $26). Peter Woit, in “Not Even Wrong: The Failure of StringTheory and the Search for Unity in Physical Law” (Basic; $26.95), prefers theterm “disaster.” Both Smolin and Woit were journeyman physicists when stringtheory became fashionable, in the early nineteen-eighties. Both are nowoutsiders: Smolin, a reformed string theorist (he wrote eighteen papers on thesubject), has helped found a sort of Menshevik cell of physicists in Canadacalled the Perimeter Institute; Woit abandoned professional physics formathematics (he is a lecturer in the mathematics department at Columbia), whichgives him a cross-disciplinary perspective. Each author delivers a bill ofindictment that is a mixture of science, philosophy, aesthetics, and,surprisingly, sociology. Physics, in their view, has been overtaken by acutthroat culture that rewards technicians who work on officially sanctionedproblems and discourages visionaries in the mold of Albert Einstein. Woitargues that string theory’s lack of rigor has left its practitioners unable todistinguish between a scientific hoax and a genuine contribution. Smolin adds amoral dimension to his plaint, linking string theory to the physicsprofession’s “blatant prejudice” against women and blacks. Pondering the cultof empty mathematical virtuosity, he asks, “How many leading theoreticalphysicists were once insecure, small, pimply boys who got their revenge bestingthe jocks (who got the girls) in the one place they could—math class?”

It is strange to think that such sordid motives might affect something aspure and objective as physics. But these are strange days in the discipline.For the first time in its history, theory has caught up with experiment. In theabsence of new data, physicists must steer by something other than hardempirical evidence in their quest for a final theory. And that something theycall “beauty.” But in physics, as in the rest of life, beauty can be a slipperything.

The gold standard for beauty in physics is Albert Einstein’stheory of general relativity. What makes it beautiful? First, there is itssimplicity. In a single equation, it explains the force of gravity as a curvingin the geometry of space-time caused by the presence of mass: mass tellsspace-time how to curve, space-time tells mass how to move. Then, there is itssurprise: who would have imagined that this whole theory would flow from thenatural assumption that all frames of reference are equal, that the laws ofphysics should not change when you hop on a merry-go-round? Finally, there isits aura of inevitability. Nothing about it can be modified without destroyingits logical structure. The physicist Steven Weinberg has compared it toRaphael’s “Holy Family,” in which every figure on the canvas is perfectlyplaced and there is nothing you would have wanted the artist to do differently.

Einstein’s general relativity was one of two revolutionary innovations inthe early part of the twentieth century which inaugurated the modern era inphysics. The other was quantum mechanics. Of the two, quantum mechanics was themore radical departure from the old Newtonian physics. Unlike generalrelativity, which dealt with well-defined objects existing in a smooth (albeitcurved) space-time geometry, quantum mechanics described a random, choppymicroworld where change happens in leaps, where particles act like waves (andvice versa), and where uncertainty reigns.

In the decades after this dual revolution, most of the action was on thequantum side. In addition to gravity, there are three basic forces that governnature: electromagnetism, the “strong” force (which holds the nucleus of anatom together), and the “weak” force (which causes radioactive decay).Eventually, physicists managed to incorporate all three into the framework ofquantum mechanics, creating the “standard model” of particle physics. The standardmodel is something of a stick-and-bubble-gum contraption: it clumsily joinsvery dissimilar kinds of interactions, and its equations contain about twentyarbitrary-seeming numbers—corresponding to the masses of the various particles,the ratios of the force strengths, and so on—that had to be experimentallymeasured and put in “by hand.” Still, the standard model has proved to besplendidly useful, predicting the result of every subsequent experiment inparticle physics with exquisite accuracy, often down to the eleventh decimalplace. As Feynman once observed, that’s like calculating the distance from LosAngeles to New York to within a hairbreadth.

The standard model was hammered out by the mid-nineteen-seventies, and hasnot had to be seriously revised since. It tells how nature behaves on the scaleof molecules, atoms, electrons, and on down, where the force of gravity is weakenough to be overlooked. General relativity tells how nature behaves on thescale of apples, planets, galaxies, and on up, where quantum uncertaintiesaverage out and can be ignored. Between the two theories, all nature seems tobe covered. But most physicists aren’t happy with this division of labor.Everything in nature, after all, interacts with everything else. Shouldn’t therebe a single set of rules for describing it, rather than two inconsistent sets?And what happens when the domains of the two theories overlap—that is, when thevery massive is also the very small? Just after the big bang, for example, theentire mass of what is now the observable universe was packed into a volume thesize of an atom. At that tiny scale, quantum uncertainty causes the smoothgeometry of general relativity to break up, and there is no telling how gravitywill behave. To understand the birth of the universe, we need a theory that“unifies” general relativity and quantum mechanics. That is the theoreticalphysicist’s dream.

String theory came into existence by accident. In the latenineteen-sixties, a couple of young physicists thumbing through mathematicsbooks came upon a centuries-old formula that, miraculously, seemed to fit thelatest experimental data about elementary particles. At first, no one had a cluewhy this should be. Within a few years, however, the hidden meaning of theformula emerged: if elementary particles were thought of as tiny wrigglingstrings, it all made sense. What were these strings supposed to be made of?Nothing, really. As one physicist put it, they were to be thought of as “tinyone-dimensional rips in the smooth fabric of space.”

This wasn’t the only way in which the new theory broke with previousthinking. We seem to live in a world that has three spatial dimensions (alongwith one time dimension). But for string theory to make mathematical sense theworld must have nine spatial dimensions. Why don’t wenotice the six extra dimensions? Because, according to string theory, they arecurled up into some microgeometry that makes them invisible. (Think of a gardenhose: from a distance it looks one-dimensional, like a line; up close, however,it can be seen to have a second dimension, curled up into a little circle.) Theassumption of hidden dimensions struck some physicists as extravagant. Toothers, though, it seemed a small price to pay. In Smolin’s words, “Stringtheory promised what no other theory had before—a quantum theory of gravitythat is also a genuine unification of forces and matter.”

But when would it make good on that promise? In the decades since itspossibilities were first glimpsed, string theory has been through a couple of“revolutions.” The first took place in 1984, when some potentially fatal kinksin the theory were worked out. On the heels of this achievement, fourphysicists at Princeton, dubbed the Princeton String Quartet, showed thatstring theory could indeed encompass all the forces of nature. Within a fewyears, physicists around the world had written more than a thousand papers onstring theory. The theory also attracted the interest of the leading figure inthe world of theoretical physics, Edward Witten.

Witten, now at the Institute for Advanced Study, in Princeton, is held inawe by his fellow-physicists, who have been known to compare him to Einstein. Asa teen-ager, he was more interested in politics than in physics. In 1968, atthe age of seventeen, he published an article in The Nationarguing that the New Left had no political strategy. He majored in history atBrandeis, and worked on George McGovern’s 1972 Presidential campaign. (McGovernwrote him a letter of recommendation for graduate school.) When he decided topursue a career in physics, he proved to be a quick study: Princeton Ph.D.,Harvard postdoc, full professorship at Princeton at the age of twenty-nine,MacArthur “genius grant” two years later. Witten’s papers are models of depthand clarity. Other physicists attack problems by doing complicatedcalculations; he solves them by reasoning from first principles. Witten oncesaid that “the greatest intellectual thrill of my life” was learning thatstring theory could encompass both gravity and quantum mechanics. Hisstring-theoretic investigations have led to stunning advances in puremathematics, especially in the abstract study of knots. In 1990, he became thefirst physicist to be awarded the Fields Medal, considered the Nobel Prize ofmathematics.

It was Witten who ushered in the second string-theory revolution, whichaddressed a conundrum that had arisen, in part, from all those extra dimensions.They had to be curled up so that they were invisibly small, but it turned outthat there were various ways of doing this, and physicists were continuallyfinding new ones. If there was more than one version of string theory, howcould we decide which version was correct? No experiment could resolve thematter, since string theory concerns energies far beyond those which can beattained by particle accelerators. By the early nineteen-nineties, no fewerthan five versions of string theory had been devised. Discouragement was in theair. But the mood improved markedly when, in 1995, Witten announced to anaudience of string theorists at a conference in Los Angeles that these fiveseemingly distinct theories were mere facets of something deeper, which hecalled “M-theory.” In addition to vibrating strings, M-theory allowed forvibrating membranes and blobs. As for the name of the new theory, Witten wasnoncommittal; he said that “M stands for magic, mystery, or membrane, accordingto taste.” Later, he mentioned “murky” as a possibility, since “ourunderstanding of the theory is, in fact, so primitive.” Other physicists havesuggested “matrix,” “mother” (as in “mother of all theories”), and“masturbation.” The skeptical Sheldon Glashow wondered whether the “M” wasn’tan upside-down “W,” for Witten.

Today, more than a decade after the second revolution, the theory formerlyknown as strings remains a seductive conjecture rather than an actual set ofequations, and the non-uniqueness problem has grown to ridiculous proportions.At the latest count, the number of string theories is estimated to be somethinglike one followed by five hundred zeros. “Why not just take this situation as areductio ad absurdum?” Smolin asks. But some stringtheorists are unabashed: each member of this vast ensemble of alternativetheories, they observe, describes a different possible universe, one with itsown “local weather” and history. What if all these possible universes actuallyexist? Perhaps every one of them bubbled into being just as our universe did.(Physicists who believe in such a “multiverse” sometimes picture it as a cosmicchampagne glass frothing with universe-bubbles.) Most of these universes willnot be biofriendly, but a few will have precisely the right conditions for theemergence of intelligent life-forms like us. The fact that our universe appearsto be fine-tuned to engender life is not a matter of luck. Rather, it is aconsequence of the “anthropic principle”: if our universe weren’t the way itis, we wouldn’t be here to observe it. Partisans of the anthropic principle saythat it can be used to weed out all the versions of string theory that areincompatible with our existence, and so rescue string theory from the problemof non-uniqueness.

Copernicus may have dislodged man from the center of the universe, but theanthropic principle seems to restore him to that privileged position. Manyphysicists despise it; one has depicted it as a “virus” infecting the minds ofhis fellow-theorists. Others, including Witten, accept the anthropic principle,but provisionally and in a spirit of gloom. Still others seem to take perversepleasure in it. The controversy among these factions has been likened by oneparticipant to “a high-school-cafeteria food fight.”

In their books against string theory, Smolin and Woit view the anthropicapproach as a betrayal of science. Both agree with Karl Popper’s dictum that ifa theory is to be scientific it must be open to falsification. But stringtheory, Woit points out, is like Alice’s Restaurant, where, as Arlo Guthrie’ssong had it, “you can get anything you want.” It comes in so many versions thatit predicts anything and everything. In that sense, string theory is, in thewords of Woit’s title, “not even wrong.” Supporters of the anthropic principle,for their part, rail against the “Popperazzi” and insist that it would be sillyfor physicists to reject string theory because of what some philosopher saidthat science should be. Steven Weinberg, who has a good claim to be the fatherof the standard model of particle physics, has argued that anthropic reasoningmay open a new epoch. “Most advances in the history of science have been markedby discoveries about nature,” he recently observed, “but at certain turningpoints we have made discoveries about science itself.”

Is physics, then, going postmodern? (At Harvard, as Smolinnotes, the string-theory seminar was for a time actually called “PostmodernPhysics.”) The modern era of particle physics was empirical; theory developedin concert with experiment. The standard model may be ugly, but it works, sopresumably it is at least an approximation of the truth. In the postmodern era,we are told, aesthetics must take over where experiment leaves off. Sincestring theory does not deign to be tested directly, its beauty must be thewarrant of its truth.

In the past century, physicists who have followed their aesthetic sense inthe absence of experimental data seem to have done quite well. As Paul Diracsaid, “Anyone who appreciates the fundamental harmony connecting the way Natureruns and general mathematical principles must feel that a theory with thebeauty and elegance of Einstein’s theory has to be substantially correct.” Theidea that “beauty is truth, truth beauty” may be a beautiful one, but is thereany reason to think it is true? Truth, after all, is a relationship between atheory and the world, whereas beauty is a relationship between a theory and themind. Perhaps, some have conjectured, a kind of cultural Darwinism has drilledit into us to take aesthetic pleasure in theories that are more likely to betrue. Or perhaps physicists are somehow inclined to choose problems that havebeautiful solutions rather than messy ones. Or perhaps nature itself, at itsmost fundamental level, possesses an abstract beauty that a true theory isbound to mirror. What makes all these explanations suspect is that standards oftheoretical beauty tend to be ephemeral, routinely getting overthrown inscientific revolutions. “Every property that has at some date been seen asaesthetically attractive in theories has at other times been judged asdispleasing or aesthetically neutral,” James W. McAllister, a philosopher ofscience, has observed.

The closest thing to an enduring mark of beauty is simplicity; Pythagorasand Euclid prized it, and contemporary physicists continue to pay lip serviceto it. All else being equal, the fewer the equations, the greater the elegance.And how does string theory do by this criterion? Pretty darn well, one of itspartisans has facetiously observed, since the number of defining equations ithas so far produced remains precisely zero. At first, string theory seemed thevery Tao of simplicity, reducing all known particles and forces to the notes ofa vibrating string. As one of its pioneers commented, “String theory was toobeautiful a mathematical structure to be completely irrelevant to nature.” Overthe years, though, it has repeatedly had to be jury-rigged in the face of newdifficulties, so that it has become a Rube Goldberg machine—or, rather, a vastlandscape of them. Its proponents now inveigh against what they call “the mythof uniqueness and elegance.” Nature is not simple, they maintain, nor shouldour ultimate theory of it be. “A good, honest look at the real world does notsuggest a pattern of mathematical minimality,” says the Stanford physicistLeonard Susskind, who seems to have no regrets about string theory’s having“gone from being Beauty to the Beast.”

If neither predictive value nor beauty explains the persistence of stringtheory, then what does? Since the late eighteenth century, no major scientifictheory has been around for more than a decade without getting a thumbs-up or athumbs-down. Correct theories nearly always triumph quickly. But string theory,in one form or another, has been hanging on inconclusively for more thanthirty-five years. Einstein’s own pursuit of a unified theory of physics in thelast three decades of his life is often cited as a case study in futility. Havea thousand string theorists done any better?

The usual excuse offered for sticking with what increasinglylooks like a failed program is that no one has come up with any better ideasfor unifying physics. But Smolin and Woit have a different explanation, onethat can be summed up in the word “sociology.” Both are worried that academicphysics has become dangerously like what the social constructivists have longcharged it with being: a community that is no more rational or objective thanany other group of humans. String theorists dominate the country’s top physicsdepartments. At the Institute for Advanced Study, the director and nearly allof the particle physicists with permanent positions are string theorists. Eightof the nine MacArthur fellowships awarded to particle physicists over the yearshave gone to string theorists. Since the fall-off in academic hiring in thenineteen-seventies, the average age of tenured physics professors has reachednearly sixty. Every year, around eighty people receive Ph.D.s in particlephysics, but only around ten of them can expect to get permanent jobs in thefield. In this hypercompetitive environment, the only hope for a youngtheoretical physicist is to curry favor by solving a set problem in stringtheory. “Nowadays,” one established figure in the field has said, “if you’re ahot-shot young string theorist you’ve got it made.”

Both authors also detect a cultlike aspect to the string-theory community,with Witten as the guru. Perhaps, it has been joked, physicists might have aneasier time getting funding from the Bush Administration if they representedstring theory as a “faith-based initiative.” Smolin deplores what he considersto be the shoddy scientific standards that prevail in the string-theorycommunity, where long-standing but unproved conjectures are assumed to be truebecause “no sensible person”—that is, no member of the tribe—doubts them. Themost hilarious recent symptom of string theory’s lack of rigor is the so-calledBogdanov Affair, in which French twin brothers, Igor and Grichka Bogdanov,managed to publish egregiously nonsensical articles on string theory in five peer-reviewedphysics journals. Was it a reverse Sokal hoax? (In 1996, the physicist AlanSokal fooled the editors of the postmodern journal SocialText into publishing an artful bit of drivel on the “hermeneutics ofquantum gravity.”) The Bogdanov brothers have indignantly denied it, but eventhe Harvard string-theory group was said to be unsure, alternating betweenlaughter at the obviousness of the fraud and hesitant concession that theauthors might have been sincere.

These two books present the case against string theory with wit andconviction, though Smolin’s book is by far the more lucid and accessible. Woithas too many pages full of indigestible sentences like “The Hilbert space ofthe Wess-Zumino-Witten model is a representation not only of the Kac-Moodygroup, but of the group of conformal transformations as well.” (Distressingly,he goes on to confess that this is “a serious oversimplification.”) Let’sassume that the situation in theoretical physics is as bad as Smolin and Woitsay it is. What are non-physicists supposed to do about it? Should we form asort of children’s crusade to capture the holy land of physics from thestring-theory usurpers? And whom should we install in their place?

Smolin furnishes the more definite answer. The current problem with physics,he thinks, is basically a problem of style. The initiators of the dualrevolution a century ago—Einstein, Bohr, Schrödinger, Heisenberg—were deepthinkers, or “seers.” They confronted questions about space, time, and matterin a philosophical way. The new theories they created were essentially correct.But, Smolin writes, “the development of these theories required a lot of hardtechnical work, and so for several generations physics was ‘normal science’ andwas dominated by master craftspeople.” Today, the challenge of unifying thosetheories will require another revolution, one that mere virtuoso calculatorsare ill-equipped to carry out. “The paradoxical situation of string theory—somuch promise, so little fulfillment—is exactly what you get when a lot ofhighly trained master craftspeople try to do the work of seers,” Smolin writes.

The solution is to cultivate a new generation of seers. And what, really, isstanding in the way of that? Einstein, after all, didn’t need to be nurtured bythe physics establishment, and Smolin gives many examples of outsiderphysicists in the style of Einstein, including one who spent ten years in arural farmhouse successfully reinterpreting general relativity. Neither Smolinnor Woit calls for the forcible suppression of string theory. They simply askfor a little more diversity. “We are talking about perhaps two dozentheorists,” Smolin says. This is an exceedingly modest request, for theoreticalphysics is the cheapest of endeavors. Its practitioners require no expensiveequipment. All they need is legal pads and pencils and blackboards and chalk toply their trade, plus room and board and health insurance and a place to parktheir bikes. Intellectually daunting as the crisis in physics may be, its practicalsolution would seem to demand little more than the annual interest on therounding error of a Google founder’s fortune.

“How strange it would be if the final theory were to be discovered in ourown lifetimes!” Steven Weinberg wrote some years ago, adding that such adiscovery would mark the sharpest discontinuity in intellectual history sincethe beginning of modern science, in the seventeenth century. Of course, it ispossible that a final theory will never be found, that neither string theorynor any of the alternatives mentioned by Smolin and Woit will come to anything.Perhaps the most fundamental truth about nature is simply beyond the humanintellect, the way that quantum mechanics is beyond the intellect of a dog. Orperhaps, as Karl Popper believed, there will prove to be no end to thesuccession of deeper and deeper theories. And, even if a final theory is found,it will leave the questions about nature that most concern us—how the braingives rise to consciousness, how we are constituted by our genes—untouched.Theoretical physics will be finished, but the rest of science will hardlynotice.