Everything’s now tied to strings – superstring theory of universe
Gary Taubes
In August 1984 John Schwarz and Michael Green finally got everything tied together. For more than a decade they had been working on a theory of physics that required them to do some of the most difficult mathematics they had ever seen. Now they had just one absurdly simple problem left to solve. Schwarz was sitting behind a desk in an office in Aspen, Colo. Green was standing at the blackboard. All they had to do was multiply 31 by 16, and if the answer was 496, their long days of what they would soon consider splendid isolation would be over.
Schwarz scribbled the calculation on his note pad. Green worked it out on the blackboard. Green came up with 486. ”Oh dear,” he said in his soft London accent. ”It doesn’t work.”
Schwarz looked down at his pad. ”Try it again,” he said.
This time Green multiplied correctly, and — bingo! — he and Schwarz confirmed the mathematics, at least, of a theory called superstrings.
Superstrings is a theory of the universe, a ten-dimensional one, in which the fundamental building blocks of matter and energy aren’t infinitesimal points but infinitesimal strings. No theory in the past fifty years has elicited so much excitement and optimism.
Physicists, usually a reticent bunch, now unabashedly talk of a revolution. They compare the breakthrough in superstrings to the birth of quantum physics or Einstein’s creation of general relativity. They rave about the theory. They gush. They say it’s wholly natural to conceive of a ten-dimensional universe made of strings so small that if 1,000,000,000,000,000,000, 000,000,000,000,000 of them were laid end to end they would be all of a centimeter long. They say the mathematics behind superstrings is so compelling that you have to believe. ”It’s beautiful, wonderful, majestic — and strange, if you like,” says Edward Witten of Princeton, ”but it’s not weird.”
Superstring theory is the product of an unprecedented alliance between theoretical physics and mainline mathematics. Ever since general relativity, physics has had little influence on pure mathematics, and although mathematicians have influenced physicists, it has usually been with math developed quite a few years earlier ”kind of for its own sake,” as MIT mathematician Isadore Singer puts it.
”In string theory,” says Witten, ”physicists have stumbled into a very rich lode, like a vein of rare minerals, that leads to very interesting physics, and also very deep mathematics.”
And physicists are passionately mining this new field. Between 1976 and 1984, no more than two dozen papers were published on string theories. Most of those were written by the team of Green, now 40, of Queen Mary College of the University of London, and Schwarz, now 45, of Caltech. Within a year of their breakthrough, superstring papers were appearing at the rate of several dozen a month. As Schwarz puts it, ”If I had any thoughts that maybe I was a crackpot, they’ve been sort of laid to rest.”
The theory has turned physicists into mathematicians, and mathematicians into physicists, and the universe into an entity in which all matter and energy, all forces, all people, planets, stars, cats and dogs, quasars, atoms, automobiles, and everything else, from the instant of the Big Bang to the end of time, are the result of the actions and the interactions of these infinitesimal strings. The Theory of Everything, scientists call it — T.O.E. It just might be. It’s certainly the best bet yet.
Of course, there’s a catch — and it’s some catch. For the moment, at least, superstring the- ory describes a ten-dimensional universe — nine dimensions of space and one of time — and it describes that universe not at a microscopic scale or at an atomic scale but at what’s known as the Planck scale, which is roughly ten trillion trillion times smaller yet. Physicists surmise that at the instant of the Big Bang all nine spatial dimensions of the universe would have been, in some in- comprehensible manner, equal. But as the universe expanded, only three of the spatial dimensions expanded along with it. The other six remained curled up, like rosebuds that never bloomed, in tight geometries 10- 3 3 centimeters across.
It’s at this ultimate smallness that everything exists as the dance of one-dimensional strings in a ten- dimensional universe. A string vibrating and twitching in a specific fashion might manifest itself in the real world as a quark. Another string, shaking and rolling in a different fashion, might appear as an electron, or a photon, or one of the many other creatures of the subatomic bestiary. The strings are the same; only the modes of vibration change. When strings join or split apart, that interaction is the fundamental force from which all other forces of nature flow.
Somehwere, physicists . hope, wound within . the mathematics of . superstrings, there is a . path along which six of . the dimensions can be, . in effect, eliminated, leaving a . four-dimensional theory of the . real world. Unless that hap pens, the theory will remain . only a beautiful piece of mathe matics, with not a shred of ex perimental evidence to support . it. ”We keep banging away on . the theory,” says Schwarz. . ”The progress is rapid. The sub ject is blossoming. To get . a complete understanding of . superstrings may take decades. . To get a partial understanding, . sufficient to predict new phen. omona that are subsequently . confirmed, could happen with in the next five or ten years.”.
In getting as far as they’ve gotten in superstring theory, physicists have passed through three eras, which Witten calls the Incredibly Primitive, the Very Primitive, and the Probably Still Primitive. The Incredibly Primitive began in 1968, when Italian physicist Gabriele Veneziano came up with a theory to explain interactions between subatomic particles subject to the strong force, which is the force that binds protons and neutrons together in the nuclei of atoms. (There are four known forces in the universe. Every action, whether it’s a baseball flying off a bat or a star going supernova, can be attributed to one or a combination of those four: gravity, electromag- netism, the weak force, which is responsible for some radioactive decay of atomic nuclei, and the strong force.)
Veneziano’s theory did a remarkable job of describing what could happen when particles collided in an atom smasher, but it did little more. It said nothing about strings. It was simply a nice four-dimensional theory with a few problems that don’t have to be gone into here. It would be supplanted by something called quantum chromodynamics (QCD), which would do a more efficient job of describing the actions of the strong force.
In 1970 physicists Yoihiro Nambu of the University of Chicago, Leonard Susskind, now at Stanford, and Holger Nielsen of the Niels Bohr Institute in Copenhagen pointed out that the equations Veneziano had written describing the interactions between subatomic particles could be ap- plied with equal validity to string-like particles in which the ends looked like elementary particles. They concluded that subatomic particles were somehow strings, not points, as had been thought. This was a stunning idea, if for no other reason than that physicists still find it amazing that somebody could have intuitively made such a step. Thus began the Very Primitive era.
A year later Claud Lovelace, a theorist now at Rutgers, suggested that the string theory had some interesting possibilities if it was couched in the mathematical terms of a universe with 26 dimensions.
Still, string theory didn’t quite cut it. Aside from all those embarrassing dimensions, it ig- nored particles called fermions (quarks, electrons, etc.), which make up all matter. And it in- cluded one nonsensical particle known as a tachyon — which could exist only by perpetually moving faster than the speed of light — and other massless particles, the purpose of which nobody could really understand.
Schwarz took his first cut at string theory in 1969. The son of a research chemist, he majored in math at Harvard mainly because he was good at it in high school. He switched to physics when he went to grad school at Berkeley. ”I never could understand how a mathematician decides what he should be interested in,” he says. ”In physics there’s a definite problem you can work on — understanding nature.”
While a postdoc at Princeton in 1971, Schwarz, along with Andre Neveu of France, wrote a new string theory that built on the work of University of Florida physicist Pierre Ramond. This theory had only ten dimensions. And it did account for fermions. But it still included the tachyon, it was still a theory of the strong force, and it still had all those dimensions, as well as those massless particles that were no less a mystery than they had been in Veneziano’s theory.
By 1974, QCD was well established as the theory of choice for the strong force. Now, Schwarz, with another Frenchman, the late Joel Scherk, suggested that the string theory wasn’t merely a theory of the strong force, but perhaps a
Theory of Everything.
The T.O.E. is an obsession with physicists. The search for such a theory began more or less with Einstein, who, try as he would, failed to develop one. The idea is to write one theory, one set of equations, that will show the four known fundamental forces to be disparate manifestations of one even more fundamental force.
Physicists have pursued the T.O.E. for two main reasons. First, unification appeals to their sense of aesthetics. Why would nature bother with only three or four fundamental forces, and not five, or ten, or 207? A single supreme force somehow seems more sensible. Second, if in the Big Bang the universe burst from one unimaginably hot point, then at first all four forces would have had equal strength, and would have been, in fact, a single force. All particles would have been indistinguishable from one another in this inferno- to-beat-all-infernos, and may as well have been one and the same.
The various forces and particles we now know of could have branched off the family tree, so to speak, as the universe cooled down. A T.O.E. would describe the universe before the Big Bang as consisting of one fundamental force and one fundamental particle. It would describe the universe today as consisting of four forces and, depending on the method of counting, some 60 particles.
Physicists have concocted quantum theories to explain the strong, weak, and electromagnetic forces. In these theories, forces are transmitted by particle-like packets of energy — photons for electromagnetism, for example — that are tossed between the particles that make up matter. It’s a subatomic game of catch. In the esoteric lingo of physics, these energy packets are known as gauge fields, and the theories quantum or gauge field theories.
By focusing on the mathematical similarities among the theories explaining the three quantum forces, physicists have hoped to write one gauge field theory — known as the grand unified theory, or GUT — that accounts for all three. They already have an electroweak theory that unites electromagnetism and the weak force; now all they have to do is somehow tie in QCD, the theory of the strong force, and they have their GUT.
Gravity has been the odd force out. In the theory of general relativity first published in 1915, Einstein described gravity as the curvature of the universe. Matter, in Einstein’s universe, warps the fabric of space like a bowling ball sitting on a trampoline. Planets and moons, apples and the earth, perpetually fall toward each other along this warped surface. And general relativity works without benefit of any quantum esoterics.
To write a T.O.E., physicists have to interweave the mathematics of gravity with that of their other theories by explaining the force in the terms of quantum physics and gauge fields. Enter the graviton, the massless particle that would transmit gravity in the same way that the photon does electromagnetism — if indeed gravity works that way. But until superstrings, all attempts to de- vise a quantum theory of gravity have been sunk by fatal impediments known as infinities.
An infinity is what you get when you try to divide a number by zero. If you try it on a calculator, your machine will tell you that you’ve erred, that you’ve asked for the impossible. Physicists who tried to calculate anything with quantum gravity theories found that their hoped-for solutions turned up as infinities. Infinities can kill a seemingly good theory — quick.
Schwarz and Scherk’s 1974 interpretation of string theory offered the possibility of escap- ing the infinities by treating gravity both as a curvaceous piece of geometry in ten dimensions — the way Einstein described it in the geometry of four dimensions — and as the result of a gauge field in a quantum theory. With the advantage of hindsight, they could now think of one of the mass- less particles as a graviton, the requisite carrier of gravity in any quantum gravity theory. This seemed like exactly the kind of combination physicists would look for in a T.O.E., but the Schwarz-Scherk paper met with, as University of Texas Nobelist Steven Weinberg says, ”precious little attention.
”We couldn’t get over the idea of ten dimensions,” he says. ”It seemed to be in pretty bad disagreement with experiment. The general impression is that we live in three dimensions of space and one of time. This gave the theory a certain unacceptability.”
The world’s physicists also had more pressing matters to attend to. They had recently put together the electroweak theory, and the experimentalists had evidence that it worked. And they had QCD for the strong force, and were working with great optimism toward a grand unified theory.
On top of this, supersymmetry was emerging. It was an offshoot of the early string work, and was yet another unification concept touted as a potential T.O.E. Supersymmetry posited that he fundamental particles that transmit forces
— like photons — and the fundamental particles that make up matter — like quarks and electrons — were in some way mathematically equivalent. This theory attracted some avid fans because it used beautiful mathematics, but it turned off other theorists, who considered it nothing more than symmetrical sleight-of-hand. It pre dicted a whole spectrum of new particles, none of which has ever been found. In 1976 it too was extended to include gravity, in a theory called supergravity. Although physicists couldn’t quite figure out how to make supergravity work, they were hopeful.
Those who worked on grand unified theories didn’t think much of supersymmetrists, who, in turn, thought the classical route to a T.O.E. was hopelessly conservative. But together they de- fined what physics was worth pursuing and what wasn’t. And string theory wasn’t. All the stuff about strings and ten dimensions was just too much. ”It was considered by the people who really counted to be really bad physics,” says Green. He recalls writing a paper in 1976 with an American collaborator who hesitated to put his name on it, for fear that being linked to string theory would hurt his chances of getting tenure.
In 1976, Scherk, with Ferdinando Gliozzi of the University of Turin and David Olive of Imperial College of Science and Technology in London, wrote a paper that explained a critical step needed to make string theory work, but they and everybody else took it as a way to tackle supergravity and pursued that road. Scherk wrote no more papers on string theory before he died in 1980, and it was left to Schwarz and Green to consider the paper’s implications for strings. Between 1976 and 1980, Green says, there were almost no papers that had anything to do with strings.
Green, who did both his undergraduate and doctoral work at Cambridge, and wrote his thesis on the pre-string theory of Veneziano, says he was ”hooked on strings.” He kept working on them through the ’70s — even after 1976, when, he says, ”just about everybody else dropped the subject.” Even Schwarz was spending some of his time working on supergravity.
Their concentration on string theory wasn’t doing much for Green’s and Schwarz’s careers. In 1979, 13 years after getting his Ph.D., Schwarz was still only a research associate at Caltech, and Green had finally gotten a permanent job, albeit the lowest possible one, at Queen Mary after nine years of floating. In the summer of that year, they began their collaboration over a cup of coffee in the cafeteria of the European Laboratory for Particle Physics (CERN) outside Geneva. They were both visiting the lab for a month. Although they knew each other but vaguely, they were already aware that they had one thing in common: they were perhaps the only two people in physics who didn’t mind being considered borderline crackpots for working on something as unfashionable as strings. They both suspected that the theory might turn out to be wondrous.
Then and there, they decided they would take up where Gliozzi, Scherk, and Olive had left off, and try to make the link between strings and supersymmetry more concrete. By the end of the summer they had tried and failed. Green went back to London and Schwarz to Caltech.
In the summer of 1980 they met again at the Aspen Center for Physics and inaugurated the Probably Still Primitive Era of string theory. They showed that string theory included supersymmetry — which is what turned strings into superstrings — and that, at the relatively low energies (compared to those of the Big Bang) of the modern universe, string theory and supersymmetry appeared to be one and the same. They also suggested that this superstring theory might not have infinities, which should have brought them a lot of converts. They were ignored.
In 1982, Green and Schwarz proved that two of three versions of superstring theory had no infinities. Ignored again. ”Absolutely nobody started working on strings,” says Green. Although this was unnerving, it turned out to be to Green and Schwarz’s advantage. They could work together during the summer, then plan what they would do the next summer, and return to their regular jobs, Schwarz says, ”without having to worry about the fact that there are five thousand other people all working on exactly the same thing.” And when they were together, they really got on with it. ”I never worked with such intensity in my life,” says Green. ”Not so much physical effort as the concentration of thoughts in my head. I’ve never been so immersed in a subject.”
In the summer of 1984 the two again met in Aspen. Now eminent theorists were telling them that even if the super string theories had no infinities, which was doubtful, they absolutely must have something worse — anomalies. And that would be that. No question.
A theory with anomalies will fall apart fast. An anomaly is a kind of evil spirit that haunts the mathematics of quantum theories, making them perform strange and undesirable acts. For instance, one property of a quantum theory is that it won’t tell you where some fundamental particle, such as an electron, is; it will only give you the probability of its being in one spot or another. An anomaly-haunted theory, for bizarre reasons, may give negative probabilities: e.g., tell you that an electron might have a minus 30 per cent chance of being somewhere. This is like being told by your bookmaker that the Boston Red Sox have a minus 30 per cent chance of getting into the World Series. It’s a meaningless statistic, and probably bad news — although more so for your bookie than for the Red Sox.
Physicists tried to prevent these negative probabilities by incorporating what are called symmetries into quantum theories. But in the string theories, with their ten dimensions, symmetries had never helped. They might have got rid of the negative probabilities, but then the anomaly just surfaced somewhere else. Goodby theory.
Green and Schwarz would hear none of this criticism. They were working on blind faith. ”We just had the feeling that these string theories were so beautiful that they had to be correct,” says Green. They cranked through the mathematics of superstrings and found almost immediately that one type of anomaly was absent. It could have been luck. There could have been all sorts of anomalies that would kill the theory. But Schwarz and Green kept working — and the anomalies canceled, almost miraculously. And of all the infinite possible versions of the theory, they found that only two were wholly free of anomalies. It was as if the universe itself were picking its two favorite versions. (The details of one of these two possibilities were worked out by Schwarz and Green in Aspen. The other and more realistic one, in which the strings exist as closed loops, was pieced together three months later by a group now known as the Princeton String Quartet: David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm.)
This meant that, as far as superstrings was concerned, there seemed to be only two universes, and one of the two — the Princeton version — would be the universe we live in. All the other unifying theories, like supersymmetry and GUTs and even QCD and the electrowea theory, could be written in an infinite number of ways, as though there were an infinite number of possible universes. Physicists then had to pick a version of one of these theories, write in the numbers that describe features of this particular universe, and then use the theory’s equations to predict other experimental results. In superstrings, on the other hand, ”there’s nothing you can tinker with,” says Weinberg. ”They’re either right or wrong as they stand.”
The superstring theory had everything. It had gravitons and gauge fields for the quantum people and supersymmetry for the supersymmetrists, and one of the anomaly-free versions was such that, at the low energies of our latter-day universe, it appeared to have a lot in common with some grand unified theories that had already been suggested on the basis of observational experiment. ”From the point of view of public relations, we couldn’t have done better,” says Green.
What may be one of the greatest theoretical breakthroughs of the century was first announced to physicists during an amateur cabaret show at Aspen. Eight years earlier the Center for Physics had hosted another such show. It had ended with Murray Gell- Mann, the 1969 Nobelist in physics, jumping up from the audience on cue and babbling wildly what seemed like nonsense about how he’d just figured out the whole theory of the universe, of quarks and gravity and everything else. As he raved with increasing frenzy, two men in white coats came on and dragged him away. This time it was Schwarz who stood up as the performance ended. As he tells it, ”I started ranting and raving about how string theory was going to be the complete theory of nature and went on like that. And nobody knew anything about that yet, so they thought it was all a joke. Then the guys in the white coats came out and carried me off.”
It didn’t remain a joke for very long. Perhaps the first convert to superstrings was Witten. A few years earlier he had written papers setting forth exactly what might work and what definitely wouldn’t for an anomaly-free Theory of Everything. He’d also been one of the few physicists following Schwarz and Green’s work — and taking it seriously. In 1983 Witten and Luis Alvarez- Gaume of Harvard had shown how one string theory, although one that wasn’t overly relevant to the real world, could be anomaly-free.
Once Witten converted to the superstring theory, he brought it the rest of the credibility it needed. ”Ed Witten is a very brilliant man,” says Gell- Mann, ”so it was a splendid moment for string theory when he began to get interested.”
In fact, Witten, 35, is considered so bright that his colleagues are willing to take seriously virtually anything he suggests. He seems to have an equally awe-inspiring talent for both physics and mathematics. (There are brilliant young physicists who say they abandoned any hope of winning a Nobel when they met Witten and realized the caliber of their competition. And brilliant young mathematicians have been known to say they hoped Witten would stay in physics.)
Witten reacted immediately upon hearing of the Aspen breakthrough. ”Once we did the proof, it spread by word of mouth to Princeton, where Witten got a very garbled account of it,” says Green. ”But he instantly understood and, I’m told, within an hour reconstructed our arguments. He called us up and asked us to send the paper by Federal Express. He got it the next day, and he’d written a paper on it four days later. He was just astonishing. In fact, most people got his paper before ours, and he gave us a big advertisement.”
Another factor was now working in favor of acceptance of superstrings: the theorists were getting nowhere with their other theories and were beginning to realize it. By 1984 work on both GUTs and supergravity had stalled. ”The time was ripe,” says Weinberg. ”Partly because we’d tried a lot of other ideas that had already led us to think of space-time as having higher dimensions, that concept no longer seemed so frightening. More important, we’d gotten frustrated with everything else. We couldn’t make progress without a successful quantum theory of gravity, and string theories gave what seemed to be the only hope.”
Green and Schwarz found themselves dragged away from their work and onto the lecture circuit. In the spring of ’84 Green had given only one talk on superstrings — a ten-minute session at a conference in Trieste. Now the two were speaking weekly and at great length, even at East Coast institutions like Harvard and Princeton, where physicists previously wouldn’t have deigned to come to a talk on supergravity, let alone one on superstrings. ”These lectures were packed,” says Green. ”There were people in the corridors. At Princeton they had to transfer us to a larger lecture hall.”
(There was a down side to this. As the rest of the world came to believe in superstrings, the demand for information soon outstripped Schwarz and Green’s ability to provide it. In the summer of 1985, Green’s schedule included talks in Rome and Bari, Italy, followed by a superstrings workshop in Santa Barbara, a plenary talk in Kyoto, and two more workshops, one in Trieste and one in Cambridge, England. Schwarz’s schedule was equally exhausting. By the summer of ’86 he and Green were both promising to decline future lectures and get back to work on physics.)
From the lecture halls, the physicists who had heard Schwarz and Green went to their libraries for mathematics books that would give them the skills to deal with such a hot T.O.E. prospect. The books were often of little help. The mathematics of the theory was tough. Much of it hadn’t even been written down yet. To some extent, this mathematics was to blame for the previous lack of interest in superstrings. ”It’s not just that the mathematics is difficult,” Green says. ”It’s that the investment in effort needed to learn the subject required a faith that it was really leading somewhere. In this case, people thought it would lead nowhere.”
Now the physicists turned to the mathematicians for help. The game being played between the two groups is like a tennis match with the universe as the ball. The physicists write down the equations of super strings, which they believe will somehow describe the universe. The quantities in these equations can be interpreted as characteristics of the real world — the mass of an elec- tron, for instance — or, by the players on the other side of the net, as geometrical structures in the imaginary realms of mathematics.
The focus of the work now being done by physicists (with a lot of help from friendly mathematicians) is to bring superstring theory down from its ten-dimensional ivory tower to a four-dimensional form that can be used to make predictions that might be confirmed or refuted by earthly experiments. Without such an advance, no matter how beautiful its mathematics, the the- ory is worthless.
It’s this lack of experimental proofs that has brought super strings its few critics, the most vocal of whom has been Harvard Nobel laureate Sheldon Glashow. Glashow is a firm believer in what he calls the upward path of physics, as opposed to the downward path. The latter, as Glashow de- scribes it, starts from some brilliantidea and then attempts ”to go from a Theory of Everything to the mundane, silly little effects seen at accelerators or on the earth.” The upward path, he says, is a dirtier business. It starts at the bottom — with those mundane effects reported from experiments — and works up slowly to a T.O.E. The difference is that the upward path relies on ex- perimental results, and downwards physics doesn’t.
Superstrings is downward physics of the finest kind. In May, Glashow and Paul Gins parg of Harvard co-authored a column in Physics Today, entitled ”Desperately seeking superstrings?”, in which they compared the faith in super strings based solely on its mathematical beauty to faith in a supreme being, which comes with an equal lack of experimental evidence. ”Was it only in jest,” they wrote, ”that a leading string theorist suggested that ‘superstrings may prove as successful as God, Who has after all lasted for millennia and is still invoked in some quarters as a Theory of Nature’?”
To generate experimental predictions out of superstrings, someone must figure out how to perform compactification, the mathematical process of collapsing the ten dimensions of the theory into the four of reality. If that can be done, the physicists should find themselves sitting on a theory that will have a lot, if not Everything, to say about the mundane specifics of the real world, and they will then have to hope that these mundane specifics are considerate enough to agree with their theory. (Not surprisingly, Glashow and Ginsparg were pessimistic about ever generating any experimental predictions from the theory. 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.” Although Ginsparg has lost none of his pessimism about verifying the theory, he’s nonetheless working on super strings himself.)
Soon after the 1984 breakthrough, Witten, among others, realized that compactifying the six extra dimensions of the superstring universe would result in their curling into a geometrical object known as a Calabi-Yau manifold. It had been posited by mathematician Eugenio Calabi of the University of Pennsylvania in 1954, and its existence had been proved by Shing-Tung Yau of the University of California at San Diego in 1976. With the realization that Calabi-Yau manifolds were the key to compactification, theorists descended upon Yau to enlist his aid in finding the spe- cific manifold that would leave them with a single four-dimensional theory that described the real world.
Yau is the kind of mathematician who would have won a Nobel Prize in math if, as legend has it, Alfred Nobel’s mistress hadn’t precluded there ever being such an award by running off with a mathematician. Yau went to work on compactification and so far has found a few thousand possible manifolds that would satisfy the demands for compactification.
The physicists, of course, would have preferred one. (Being a mathematician, Yau doesn’t understand why physicists are so hot to discover the ultimate theory. ”Nature is probably much more profound than that,” he says.) Yau’s finding leaves them with two possibilities: one is to create tighter constraints on the mathematics so as to eliminate all possible manifolds except one. The other is considerably less elegant and more unworldly: assume that maybe there are thousands of possible universes after all, and that, for no particular reason, we’re living in only one of them.
So the work continues. ”We already see features of the theory that approximate the phenomona observed in the universe,” says Schwarz. ”There may be no fundamental obstacle to explaining nature with this theory; we just have to understand the mathematics better. We’re not yet in a situation where experimentalists can shoot us down, because we don’t yet know the predictions of the theory. However, we think it’s just a matter of time before we know them.”
The superstring theory has yet another very peculiar angle to it. Nobody knows what’s behind this T.O.E. The mathematics is beautiful, but nobody really knows why that is.
When Einstein formulated general relativity, he started with what’s now known as the equivalence principle: that the effect of gravity is indistinguishable from that of acceleration. As he put it, ”I was sitting in a chair in a patent office in Bern when all of a sudden a thought occurred to me: ‘If a person falls freely he will not feel his own weight.’ I was startled. This simple thought . . . impelled me toward a theory of gravity.” From there, Einstein went to the mathematics to create his theory.
Superstring theory probably has an underlying principle like equivalence, but nobody has an inkling of what it might be. What physicists have going for them is seeming mathematical miracles that have led to an anomaly-free theory that may describe the real world. This math gives them hope that the principle they seek is there to be uncovered. (Green ended a 1984 lecture at CERN with a tongue-in-cheek statement about these intriguing miracles. ”Is there some deep geometrical reason why in ten dimensions this theory is special?” he asked. ”I don’t think anybody knows. There are a few tantalizing coincidences, which are probably just coincidences. For example, the number 496* played a key role in the understanding of the cancelations in gravitational anomalies . . . The number 992 — twice 496 — comes up in an apparently completely different context . . . and if you double 992, you get the year in which the theory was formulated.”)
For Green, the serendipitousness of his and Schwarz’s discovery precludes any comparison between Einstein and Schwarz and himself. ”By chance we hit upon a theory that looks extremely plausible as a theory of nature,” he says. ”We don’t understand intuitively why that is. Einstein worked precisely the other way around. He thought very deeply about the physical world and realized by an amazing chain of reasoning that the world had to behave in a certain way. Then he worked for years on the equations. We have the equations, and we may eventually have the solutions, but the amazing thing is we don’t yet have the principle on which the theory must be based. There’s been this element of chance. I feel somewhat honored to be involved with it. Somewhat amused as well.”
Nobody knows how long it will take to wade through the mathematics of superstrings and fish out some hard answers. Witten compares the superstring progress to that in early quantum physics. It be- gan at the turn of the century and blossomed around 1913 with the development of the Bohr atom. In 1927, Heisenberg created the uncertainty principle, and quantum mechanics was really born. But not until the early 1950s did physicists have a working quantum theory of electromagnetism that allowed them to make concrete predictions about what they saw in their accelerators.
Although physicists have made considerable progress in understanding superstrings in just 15 years or so, Witten thinks they may have taken only one step on a long road to the ultimate Theory of Everything. ”To have the energy to face a difficult problem day after day, one needs theattitude that victory is just around the corner,” he says. ”But probably it isn’t.”
Superstrings is now as solidly entrenched in the dogma of science as any theory that had no experimental evidence to back it up. A few voices still warn that too many physicists are letting their dreams get the better of their common sense. (”Please heed our advice, that you too are not smitten,” rhymed Glashow shamelessly at a recent international conference, ”the book is not fin- ished, the last word is not Witten.”) But for the most part physicists have accepted strings and ten dimensions as the likely natural order of the universe, and are confident that they’ll eventually prove it.
Nevertheless, Green himself sounds a cautionary note: ”When I hear the phrase Theory of Everything, it sort of makes me think that the people who use it mean it’s the Theory of Everything they can think of explaining, rather than the Theory of Everything there really is. Even if we could really explain everything we can think of, which would truly be amazing, that would still leave a lot.”
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