The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next

by Lee Smolin

  Fig. 6. The propagation and interaction of strings are determined by the same law, which is to minimize the area of the surface in spacetime. On the right, we see the surface in spacetime traced out by two closed strings, which interact by exchanging a third closed string. On the left, we see the sequence of configurations in space, which come from taking slices through the picture in spacetime on the right. First we see two closed strings, then one splits off a third closed string, which travels and then joins the second string.

  This principle turns out to apply to strings as well. As a one-dimensional string moves through time, it makes a two-dimensional surface in spacetime (see Fig. 6). This surface has a certain area, defined roughly as the product of its length and its duration in time.

  The string moves so as to minimize this area. That is the whole law. It explains the motion of strings and, once strings are allowed to break and join, the existence of all the forces. It unifies all the forces we know with a description of the particles. And it is far simpler than the laws describing any of the things it unifies.

  String theory achieves yet another feat of unification. In the early nineteenth century, Michael Faraday had imagined the electrical and magnetic fields in terms of field lines—lines running between the poles of magnets, or between positive and negative electric charges. For Faraday, these lines were real; they were what conveyed the forces between magnets or charges.

  In Maxwell’s theory, the field lines became secondary to the fields, but it does not have to be this way. One can imagine that the field lines are what really exist and the forces between particles are field lines stretching between them. This cannot be achieved in classical theory, but it can in quantum theory.

  In a superconductor—that is, a material with little or no electrical resistance—the field lines of the magnetic field become discrete. Each line carries a certain minimal amount of magnetic flux. One can think of these field lines as a kind of atom of the magnetic field. In the early 1970s, three visionaries proposed that the same thing was true of the lines of force in QCD, which are analogous to the electric field lines of electromagnetism. This was how the Danish physicist Holger Nielsen came to be one of the inventors of string theory—he saw the strings as quantized lines of electric flux. That picture was further developed by Kenneth Wilson at Cornell, and ever since, the lines of a quantized electric field have been called Wilson lines. The third visionary was the Russian physicist Alexander Polyakov, who is perhaps our deepest thinker on the relationship between gauge theories and string theories. Polyakov gave the single most inspiring seminar I heard as a graduate student, in which he proclaimed his ambition to solve QCD exactly by re-expressing it as a theory of strings—the strings being the lines of quantized electric flux.

  According to these visionaries, the primary objects in a gauge theory are the field lines. They satisfy simple laws, which dictate how they stretch between charges. The fields themselves arise only as an alternative description. This way of thinking fits naturally into string theory, because the field lines can be taken to be strings.

  This suggests a kind of duality of descriptions: One can think of the field lines as the primary object and the basic laws as describing how they stretch and move, or one can think of the field as primary and the field lines just as a convenient way to describe the field. In quantum theory, either description works. This gives rise to a principle we call the duality of strings and fields. Either description works. Either can be taken to be fundamental.

  Pierre Ramond was denied tenure at Yale in 1976, a few years after having solved several of string theory’s central problems. It turns out that inventing a way to put fermions into string theory, discovering supersymmetry, and removing the tachyon—all in one blow—was not enough of an achievement to convince his colleagues that he deserved a professorship at an Ivy League institution.

  John Schwarz, meanwhile, had been denied tenure at Princeton, in 1972, in spite of his fundamental contributions to string theory. He then moved to Caltech, where he was a research associate for the next twelve years, supported by temporary funds that had to be renewed periodically. He didn’t have to teach if he didn’t want to—but neither did he have tenure. He discovered the first good idea about how gravity and the other forces could be unified, but apparently Caltech remained unconvinced that he belonged on their permanent faculty.

  There is no doubt that the original inventors of string theory paid heavily for their pioneering discoveries. To appreciate what kind of people these are, the reader must understand what this means in real terms. The friends you went to graduate school with are now full professors with tenure. They have good salaries, job security, they easily support families. They have high-status positions in elite universities. You have nothing. In your gut, you know that they have taken an easy road, while you have done something potentially much more significant, which has taken much more creativity and courage. They followed the herd and did what was fashionable; you discovered a whole new kind of theory. But you are still a postdoc or research associate or junior professor. You have no long-term job security and uncertain prospects. And yet you may be more active as a scientist—publishing more papers and supervising more students—than other people whose work in less risky directions has been rewarded with more security.

  Now, reader, ask yourself what you would do in that situation.

  John Schwarz kept working on string theory, and he continued to discover evidence that it could well be the unifying theory of physics. Although he couldn’t yet prove that the theory was mathematically consistent, he was sure he was on to something.* Even as the first string theorists faced formidable obstacles, they could inspire themselves by thinking about all the puzzles that would be solved if elementary particles were vibrations of strings. It is a pretty impressive list:

  String theory gave us an automatic unification of all the elementary particles, and it also unified the forces with one another. All come from vibrations of one fundamental kind of object.

  String theory automatically gave us gauge fields, which are responsible for electromagnetism and the nuclear forces. These naturally arise from the vibrations of open strings.

  String theory automatically gave us gravitons, which come from vibrations of closed strings, and any quantum theory of strings must involve closed strings. As a consequence, we got, for free, an automatic unification of gravity with the other forces.

  A supersymmetric string theory unified the bosons and fermions, which are both just oscillations of strings, thus unifying all the forces with all the particles.

  Furthermore, while supersymmetry may be true even if string theory is not, string theory provides a much more natural home for supersymmetry than do ordinary particle theories. While the supersymmetric versions of the standard model were ugly and complicated, supersymmetric string theories are deeply elegant objects.

  To top it all off, string theory achieved effortlessly a natural unification of the laws of motion with the laws that govern forces.

  Here then is the dream that string theory seemed to make possible. The whole standard model, with its twelve kinds of quarks and leptons and its three forces, plus gravity, could be unified, in the sense that all these phenomena arise from the vibrations of strings stretched in spacetime, following the simplest possible law: that the area is minimized. All the constants of the standard model can be reduced to a combination of Newton’s gravitational constant and one simple number, which is the probability for a string to break into two and join. And even the second number is not fundamental but a property of the environment.

  Given that string theory promised so much, it is not surprising that Schwarz and his few collaborators were convinced it must be true. As far as the problem of unification was concerned, no other theory offered so much on the basis of a single simple idea. In the face of such promise, only two questions remained: Does it work? And what is the cost?

  In 1983, while I was still a postdoc at the Institute for Advanced
Study in Princeton, John Schwarz was invited to give two lectures on string theory at Princeton University. I had not heard much about string theory before, and what I recall from his seminar is mostly the intense and edgy reaction of the audience, powered by equal parts interest and skepticism. Edward Witten, already a dominant figure in elementary-particle physics, interrupted often, asking a series of persistent, hard questions. I took this to be an indication of skepticism; only later would I come to see that it was an indication of his strong interest in the subject. Schwarz was confident, but there was a hint of stubbornness. I got the impression that he had spent many years trying to communicate his excitement about string theory. That talk convinced me that Schwarz was a courageous scientist, but it did not persuade me to work on string theory. For the time being, everyone I knew ignored the new theory and kept on with their various projects. Few of us realized that we were living in the last days of physics as we had always known it.

  8

  The First Superstring Revolution

  THE FIRST SUPERSTRING revolution took place in the fall of 1984. Calling it a revolution sounds a bit pretentious, but the term is apt. Six months before, only a handful of intrepid physicists were working on string theory. They were ignored by all but a few colleagues. As John Schwarz tells it, he and a new collaborator, the English physicist Michael Green, had “published quite a few papers and in each case I was quite excited about the results. . . . [I]n each case, we felt that people would now get interested, because they could see how exciting the subject was. But there was still just no reaction.”1 Six months later, several of string theory’s most vocal critics had begun working on it. In the new atmosphere, it took courage not to drop what you were doing and follow them.

  The tipping point was a calculation carried out by Schwarz and Green providing strong evidence that string theory was a finite and consistent theory. A bit more precisely, what they finally succeeded in showing was that a certain dangerous pathology afflicting many unified theories, called an anomaly, was absent in supersymmetric string theory, at least in ten spacetime dimensions.2 I recall that the response to that paper was both shock and jubilation: shock because some people had doubted that string theory could ever be made consistent with quantum mechanics at any level; jubilation because, by proving them wrong, Green and Schwarz had opened up the possibility that the final theory unifying physics was in our hands.

  No change could have taken place quicker. As Schwarz remembers it,

  [B]efore we even finished writing it up, we got a phone call from Ed Witten saying that he had heard . . . that we had a result on canceling anomalies. And he asked if we could show him our work. So we had a draft of our manuscript at that point, and we sent it to him by FedEx. There wasn’t e-mail then; it didn’t exist, but FedEx did exist. So we sent it to him, and he had it the next day. And we were told that the following day everyone in Princeton University and at the Institute for Advanced Study, all the theoretical physicists, and there were a large number of them, were working on this. . . . So overnight it became a major industry [laughter], at least in Princeton—and very soon in the rest of the world. It was kind of strange, because for so many years we were publishing our results and nobody cared. Then all of a sudden everyone was extremely interested. It went from one extreme to the other: the extreme of nobody taking it seriously, to the other extreme. . . . 3

  String theory promised what no other theory had before—a quantum theory of gravity that is also a genuine unification of forces and matter. It appeared to offer, in one bold and beautiful stroke, a solution to at least three of the five great problems of theoretical physics. Thus, all of a sudden, after so many failures, we had struck gold. (Schwarz, it is amusing to note, was promptly promoted from senior research associate to full professor at Caltech.)

  Thomas Kuhn, in his famous book The Structure of Scientific Revolutions, gave us a new way of thinking about events in the history of science that we think of as revolutions. According to Kuhn, a scientific revolution is preceded by the piling up of experimental anomalies. As a result, people begin to question the established theory. A few invent alternative theories. The revolution culminates in experimental results that favor one of the new alternatives over the old established theory.4 It is possible to take issue with Kuhn’s description of science, and I will do so in the closing section of the book. But since it describes what has happened in some cases, it serves as a useful point of comparison.

  The events of 1984 did not follow Kuhn’s structure. There never was an established theory addressing the problems that string theory addresses. There were no experimental anomalies; the standard model of particle physics and general relativity together sufficed to explain the results of all the experiments done until that time. Even so, how could one not call this a revolution? All of a sudden we had a good candidate for a final theory that could explain the universe and our place in it.

  For four or five years after the superstring revolution of 1984, there was a lot of progress, and interest in string theory grew rapidly. It was the hottest game in town. Those who went into it dived in with ambition and pride. There were a lot of new technical tools to learn, so to work in string theory required an investment of a few months to a year, which for a theoretical physicist is a long time. Those who did it looked down on those who wouldn’t, or (the suggestion was always there) couldn’t. Very quickly there developed an almost cultlike atmosphere. You were either a string theorist or you were not. A few of us tried to keep a commonsense approach: Here is an interesting idea; I’ll work on it some, but I’ll also pursue other directions. It was hard to make that stick, because those who jumped in weren’t much interested in talking with those of us who did not declare ourselves part of the new wave.

  As befits a new field, immediately there were academic conferences on string theory. These had an air of triumphant celebration. There was a sense that the one true theory had been discovered. Nothing else was important or worth thinking about. Seminars devoted to string theory sprang up at many of the major universities and research institutes. At Harvard, the string theory seminar was called the Postmodern Physics seminar.

  This appellation was not meant ironically. One thing that was seldom discussed in string theory seminars and conferences was how to test the theory experimentally. While a few people did worry about this, there were others who thought it wasn’t necessary. The feeling was that there could be only one consistent theory that unified all of physics, and since string theory appeared to do that, it had to be right. No more reliance on experiment to check our theories. That was the stuff of Galileo. Mathematics now sufficed to explore the laws of nature. We had entered the period of postmodern physics.

  Very quickly, physicists realized that string theory was not unique after all. Instead of a single consistent theory, we soon discovered that there were five consistent superstring theories in ten-dimensional spacetime. This gave rise to a puzzle that would not be solved for the next ten years or so. Still, it was not entirely bad news. Recall that Kaluza-Klein theory had a fatal problem: that the universes it describes are too symmetric, failing to agree with the fact that nature is not the same when viewed in a mirror. Some of the five superstring theories were able to avoid this fate and describe worlds as asymmetric as our own. And there were further developments confirming that string theory was finite (that is, that it would give only finite numbers as predictions for the result of any experiment). In the bosonic string, with no fermions, it is easy to show that there are no infinite expressions analogous to those of the theory of gravitons, but when you compute probabilities to a greater degree of precision, infinities can appear, which are related to the instability of tachyons. Since the superstring has no tachyons, this raises the possibility that the theory has no infinities.

  This was easy to verify, to a low order of approximation. Beyond that, there were intuitive arguments that the theory should be finite to every order of approximation. I recall a prominent string theorist saying th
at it was so obvious that string theory was finite that he wouldn’t study a proof even if there was one. But some people did endeavor to prove the finiteness of string theory past the lowest approximation. Finally, in 1992, Stanley Mandelstam, a highly respected mathematical physicist at Berkeley, published a paper that was believed to prove that superstring theories are finite to all orders of a certain approximation scheme.5

  No wonder people were so optimistic. The promise of string theory vastly exceeded that of any unified theory so far proposed. At the same time, we could see that it still had a long way to go to fulfill all this promise. For example, consider the problem of explaining the constants of the standard model. String theory, as noted in the last chapter, has only one constant that can be adjusted by hand. If string theory is right, the twenty constants of the standard model must be explained in terms of this one constant. It would be marvelous beyond words if all of those constants could be computed as functions of the single constant in string theory—a triumph greater than any in the history of science. But we weren’t there yet.

  Beyond this was a question that, as we discussed earlier, must always be asked of unified theories. How are the apparent differences between the unified particles and forces to be explained? String theory unifies all the particles and forces, which means it must also explain to us why they are different.