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

by Lee Smolin

  The first success was a prediction that when the gravitational field changed rapidly in time, elementary particles would be created. This idea could be applied to the early universe when it was rapidly expanding, and led to predictions that are used to this day in the study of the early universe.

  The success of these calculations inspired a few physicists to try something harder, which was to study the effect that a black hole can have on quantum particles and fields. The challenge here is that whereas black holes have a region where the geometry evolves very rapidly, this region is hidden behind a horizon. The horizon is a sheet of light that is standing still. It marks the boundary of a region within which all light is pulled inward, toward the center of the black hole. Thus no light can escape from behind the horizon. From the outside, a black hole seems static, but just inside its horizon is a region where everything is pulled toward stronger and stronger gravitational fields. These end in a singularity, where everything is infinite and time stops.

  The first crucial result connecting quantum theory to black holes was made in 1973 by Jacob Bekenstein, a young Israeli graduate student of John Archibald Wheeler’s at Princeton. He made the amazing discovery that black holes have entropy. Entropy is a measure of disorder, and there is a famous law, called the second law of thermodynamics, holding that the entropy of a closed system can never decrease. Bekenstein worried that if he took a box filled with a hot gas—which would have a lot of entropy, because the motion of the gas molecules was random and disordered—and threw it into a black hole, the entropy of the universe would seem to decrease, because the gas could never be recovered. To save the second law, Bekenstein proposed that the black hole must itself have an entropy, which would increase when the box of gas fell in, so that the total entropy of the universe would never decrease. Working out some simple examples, he was able to show that the entropy of a back hole must be proportional to the area of the horizon that surrounds it.

  This introduced a puzzle. Entropy is a measure of randomness, and random motion is heat. So shouldn’t a black hole also have a temperature? A year later, in 1974, Stephen Hawking was able to show that a black hole must indeed have a temperature. He was also able to fix the precise proportionality between the area of a black hole’s horizon and its entropy.

  There is another aspect of the temperature of black holes predicted by Hawking, which will be important to us later, and it’s that the temperature of a black hole is inversely proportional to its mass. This means that black holes behave differently from familiar objects. To get most things to heat up, you have to put energy into them. We fuel a fire. Black holes behave in the opposite way. If you put energy, or mass, in, you make the black hole more massive—and it cools off.5

  This mystery has since challenged every attempt to make a quantum theory of gravity: How can we explain the entropy and temperature of black holes from first principles? Bekenstein and Hawking treated the black hole as a classical fixed background within which quantum particles moved, and their arguments were based on consistency with known laws. They did not describe the black hole as a quantum-mechanical system, because that can be done only in a quantum theory of spacetime. So the challenge for any quantum theory of gravity is to give us a deeper understanding of Bekenstein’s entropy and Hawking’s temperature.

  The following year, Hawking found still another puzzle lurking in these results. Because a black hole has a temperature, it will radiate, like any hot body. But the radiation carries energy away from the black hole. Given enough time, all the mass in the black hole will turn into radiation. As it loses energy, the black hole gets lighter. And because of the property I just described, when it loses mass, it heats up, so it radiates faster and faster. At the end of this process, the black hole will have shrunk down to a Planck mass, and one needs a quantum theory of gravity to predict the final fate of the black hole.

  But whatever its final fate, there appears to be a puzzle concerning the fate of information. During the life of a black hole, it will pull in huge amounts of matter, carrying huge amounts of intrinsic information. At the end, all that’s left is a lot of hot radiation—which, being random, carries no information at all—and a tiny black hole. Did the information just disappear?

  This is a puzzle for quantum gravity, because there is a law in quantum mechanics that says that information can never be destroyed. The quantum description of the world is supposed to be exact, and there is a result implying that when all the details are taken into account, no information can be lost. Hawking made a strong argument that a black hole that evaporates away loses information. This appears to contradict quantum theory, so he called this argument the black-hole information paradox. Any putative quantum theory of gravity needs to resolve it.

  These discoveries of the 1970s were milestones on the way to a quantum theory of gravity. Since then, we have measured the success of an approach to quantum gravity partly by how well it answers the challenges posed by the entropy, temperature, and information loss in black holes.

  At about this time, an idea was finally proposed about quantum gravity that seemed to work, at least for a while. It involved applying the idea of supersymmetry to gravity. The result was supergravity.

  I was present at one of the first presentations ever given of this new theory. It was a conference in 1975 in Cincinnati on developments in general relativity. I was still an undergraduate at Hampshire College, but I went anyway, hoping to learn what people were thinking about. I remember some beautiful lectures by Robert Geroch, of the University of Chicago, who was then a star of the field, on the mathematics of infinite spaces. He got a standing ovation for one particularly elegant demonstration. Then, stuck in at the end of the conference was a talk by a young postdoc named Peter van Nieuwenhuizen. I recall that he was quite nervous. He began by saying that he was there to introduce a brand-new theory of gravity. He had my full attention.

  Van Nieuwenhuizen said that his new theory was based on supersymmetry, then a new idea unifying bosons and fermions. The particles you get from quantizing gravitational waves are called gravitons, and they are a type of boson. But for a system to have supersymmetry, it must have both bosons and fermions. General relativity has no fermions, so new fermions must be hypothesized to be the superpartners of the gravitons. “Sgraviton” is not an easy word to say, so they were called gravitinos.

  Since the gravitino had never been seen, he said, we were free to invent the laws it satisfies. For the theory to be symmetric under supersymmetry, the forces could not change when gravitinos were substituted for gravitons. This put a lot of constraints on the laws, and searching for solutions to those constraints required weeks of painstaking calculations. Two teams of researchers finished nearly simultaneously. Van Nieuwenhuizen was part of one of those teams; the other included my advisor-to-be at Harvard, Stanley Deser, who was working with one of the inventors of supersymmetry, Bruno Zumino.

  Van Nieuwenhuizen also spoke of a deeper way to think about the theory. You begin by thinking about the symmetries of space and time. The properties of ordinary space remain unchanged if we ourselves rotate, because there is no preferred direction. They also remain unchanged if we move from place to place, because the geometry of space is uniform. Thus, translations and rotations are symmetries of space. Recall that in chapter 4 I explained the gauge principle, which states that in some circumstances a symmetry can dictate the laws that the forces satisfy. You can apply this principle to the symmetries of space and time. The result is precisely Einstein’s general theory of relativity. This is not how Einstein found his theory, but had Einstein not lived, it is how general relativity might have been found.

  Van Nieuwenhuizen explained that supersymmetry can be seen as a deepening of the symmetries of space. This is because of a profound and beautiful property: If you change all the fermions into bosons and then change them back again, you get the same world you had before but with everything moved a little bit in space. I can’t here explain why this is true, but it
tells us that supersymmetry is in some way fundamentally connected to the geometry of space. As a consequence, if you apply the gauge principle to supersymmetry, the result is a theory of gravity—supergravity. Seen in this way, supergravity is a profound deepening of general relativity.

  I was a newcomer to the field, dropping in on a conference. I didn’t know anyone there, so I don’t know what van Nieuwenhuizen’s listeners thought about what he had to say, but I was deeply impressed. I went home thinking it was a good thing that the guy was so nervous, for if what he said was right, it would be really important.

  During my first year of graduate school, I took a course with Stanley Deser, who lectured about the new theory of supergravity. I got interested and started to think about it, but I was puzzled. What did it mean? What was it trying to tell us? I made a new friend there, a classmate named Martin Rocek, and he got excited as well. He quickly hooked up with Peter van Nieuwenhuizen, who was at Stony Brook, and began collaborating with him and his students. Stony Brook was not far away, and Martin brought me along on one of his visits there. Things were taking off in a big way, and he wanted to give me a chance to get in on the ground floor.

  It was like being offered one of the first jobs at Microsoft or Google. Rocek, van Nieuwenhuizen, and many of those I met through them have made brilliant careers out of supersymmetry and supergravity. I’m sure that from their point of view, I acted like a fool and blew a brilliant opportunity.

  For me (and for others, I’m sure), the merging of supersymmetry with a theory of space and time raised profound questions. I had learned general relativity from reading Einstein, and if I understood anything, it was how that theory merged gravity with the geometry of space and time. That idea was in my bones. Now I was being told that another deep aspect of nature was also unified with space and time—the fact that there are fermions and bosons. My friends told me this, and the equations said the same thing. But neither friends nor equations told me what it meant. I was missing the idea, the conception of the thing. Something in my understanding of space and time, of gravity and of what it meant to be a fermion or boson, should deepen as a result of this unification. It should not just be math—my very conception of nature should change.

  But it didn’t. What I found when I hung out with van Nieuwenhuizen’s students was a group of smart, technically minded kids frantically doing calculations, day and night. What they were doing was inventing versions of supergravity. Each version had a larger set of symmetries than the last, unifying a larger family of particles. They were working toward an ultimate theory that would unify all particles and forces with space and time. This theory had only a technical name, the N = 8 theory, N being the number of different ways to mix up fermions and bosons. The first theory—the one that van Nieuwenhuizen and Deser had introduced me to—was the simplest, N = 1. Some people in Europe had made N = 2. The week I was at Stony Brook, the people there were advancing toward N = 4, on their way to N = 8.

  They worked day and night, ordered food in, and put up with the tedium of the work with the giddy certainty that they were on to something new and world-changing. One of them told me that he was working as fast as he could because he was sure that when the word got out about how easy it was to make new theories, the field would be overrun. Indeed, if I recall right, that group did get N = 4, but they were scooped on N = 8.

  What they were doing didn’t seem easy to me. The calculations were mind-numbingly lengthy and tedious. They required complete precision: If one factor of 2 went missing somewhere, weeks of work might have to be thrown out. Each line of the calculation had dozens of terms. To make a line of a calculation fit on a page, they resorted to larger and larger pads of paper. Soon they were carrying around huge art pads, the biggest they could find. They covered each page in tiny, precise handwriting. Each pad represented months of work. The word “monastic” comes to mind. I was terrified. I stayed a week and fled.

  For decades afterward, I had rather uncomfortable relations with Peter, Martin, and the others. It may be that I was considered a loser for fleeing when they offered me the opportunity to join them in launching supergravity. Had I joined up, I might have been well placed to become one of the leaders of string theory. What I did instead was to go off in my own direction, eventually helping to found a different approach to the problem of quantum gravity. That made matters even worse: I was not only a loser who had abandoned the true faith, I was a loser in danger of becoming a rival.

  As I reflect on the scientific careers of the people I have known these last thirty years, it seems to me more and more that these career decisions hinge on character. Some people will happily jump on the next big thing, give it all they’ve got, and in this way make important contributions to fast-moving fields. Others just don’t have the temperament to do this. Some people need to think through everything very carefully, and this takes time, as they get easily confused. It’s not hard to feel superior to such people, until you remember that Einstein was one of them. In my experience, the truly shocking new ideas and innovations tend to come from such people. Still others—and I belong to this third group—just have to go their own way, and will flee fields for no better reason than that it offends them that some people are joining in because it feels good to be on the winning side. So I no longer get bothered when I disagree with what other people are doing, because I see that temperament pretty much determines what kind of science they will do. Luckily for science, the contributions of the whole range of types are needed. Those who do good science, I’ve come to think, do so because they choose problems that are suited to them.

  In any case, I fled the Stony Brook supergravity group but I didn’t lose interest in supergravity. On the contrary, I was more interested than ever. I was sure they were on to something, but the road they were taking was not one I could follow. I understood Einstein’s general theory of relativity, which meant that I knew how to demonstrate every essential property of it in a page or less of concise and transparent work. It seemed to me that if you understood a theory, it shouldn’t take weeks of calculations on an art pad to check its basic properties.

  I teamed up with another graduate student—a friend of mine from Hampshire College, John Dell, who was at the University of Maryland. We wanted to understand more deeply how it was that supersymmetry was part of the geometry of space and time. He found some papers by a mathematician named Bertram Kostant on a new kind of geometry that extended the math Einstein used by adding new properties that seemed to behave a bit like fermions. We wrote the equations of general relativity in this new context, and out popped some of the equations of supergravity. We had our first scientific paper.

  At about the same time, others developed an alternative approach to a geometry for supergravity called supergeometry. I felt then (and feel now) that their setup is clumsier than ours. It is much more complicated, but for certain things it works much better. It helped to simplify the calculations somewhat, and that was certainly appreciated. So supergeometry caught on, and our work was forgotten. John and I didn’t care, because neither approach gave us what we were looking for. Whereas the math worked, it didn’t lead to any conceptual leaps. To this day, I don’t think anyone really understands what supersymmetry means, what it says fundamentally about nature—if it’s true.

  Many years removed, I think I can finally fully articulate what drove me away from supergravity in those early days. Having learned physics by studying Einstein in the original, I had obtained a sense of the kind of thinking that went into a revolutionary new unification of physics. What I expected was that a new unification would start from a deep principle, like the principle of inertia or the equivalence principle. You would gain from this a deep and surprising insight that two things you had once seen as unrelated were actually at root the same thing. Energy is mass. Motion and rest are indistinguishable. Acceleration and gravity are the same.

  Supergravity was not doing this. Although it was indeed a proposal for a new unification, it was one
that could be expressed, and checked, only in the context of mind-crushingly boring calculations. I could do the math, but this was not the way I had been taught to do science by my readings of Einstein and the other masters.

  Another friend I made at that time was Kellogg Stelle, who was a few years older than I was and, like me, was a student of Stanley Deser. Together they were exploring the question of whether supergravity behaved better than general relativity when combined with quantum theory. Since there had still been no progress on the background-independent methods, they, like everyone else, used the background-dependent method that had failed so miserably when applied to general relativity. They were quickly able to see that it worked better when applied to supergravity. They checked the first place where an infinity had occurred in quantum general relativity and found instead a finite number.

  This was good news: Supersymmetry really did improve the situation! But the elation didn’t last long. It took Deser and Stelle only a few more months to convince themselves that infinities would abound in supergravity farther along. The actual calculations were too hard to do, even after months of work with art pads, but they found a way to test whether the results would ultimately be finite or infinite, and it turned out that all the answers more precise than the one they could check—which had turned out finite—would be infinite.

  They were not yet done, however, for there were all the other forms of supergravity to be tested. Perhaps one of those would finally yield a consistent quantum theory. One by one, each form was studied. Each one was a bit more finite, so that you had to go out farther in the sequence of approximations before the test failed. While the calculations were all too hard to do, there seemed no reason for any answer to be other than infinite past that point. There was a bit of hope that the final theory, the famous N = 8, would be different. It had finally been constructed by heroic work carried out in Paris. But it, too, failed the test—though there are some still holding out hope for it.