by Lee Smolin
Supergravity was and is a wonderful theory. But by itself it was not enough to solve the problem of quantum gravity.
Thus, by the early 1980s there had been no progress on making a theory of quantum gravity. Everything that had been tried, up to and including supergravity, had failed. As the gauge theories triumphed, the field of quantum gravity stagnated. Those few of us who insisted on worrying about quantum gravity felt like the high school dropout invited to watch his sister graduate from Harvard with simultaneous degrees in medicine, neurobiology, and the history of dance in ancient India.
If the failure of supergravity to lead to a good theory of quantum gravity depressed us, though, it was also liberating. All the easy things had been tried. For decades, we had attempted to make a theory by extending the methods of Feynman and his friends. There were now only two things to try: Give up methods based on a fixed background geometry, or give up on the idea that the things moving through the background geometry were particles. Both approaches were about to be explored, and both would yield—for the first time—dramatic successes on the road to quantum gravity.
II
A BRIEF HISTORY OF STRING THEORY
7
Preparing for a Revolution
SOMETIMES SCIENTIFIC PROGRESS stalls when we encounter a problem that just cannot be solved in the way we understand it. There is a missing element, a different sort of trick involved. No matter how hard we work, we won’t find the answer until someone somehow stumbles on this missing link.
Perhaps the first time this happened was with eclipses. Given the drama of a sudden darkening of the sky, the first order of business for early astronomers must have been to find a way to predict these scary events. Beginning several thousand years ago, people began to keep records of observations of eclipses, along with the motions of the sun, moon, and planets. It didn’t take them long to understand that the motion of the sun and moon is periodic; we have evidence that people knew that back in our cave-dwelling days. But eclipses were harder.
A few things would have been clear to early astronomers. Eclipses happen when the sun and the moon, which take different paths across the sky, meet each other. Their paths intersect at two places. For an eclipse to happen, the sun and moon must meet at one of these two points. So in order to predict eclipses, you have to keep track of the annual path of the sun and the monthly path of the moon. Simply follow the paths and note when the two bodies meet. The implication is that there must be a pattern that repeats in some multiple of the twenty-nine-and-a-half-day lunar period.
But this simple idea doesn’t work: Eclipses do not fall into a pattern governed exactly by the lunar month. We can easily imagine the generations of theorists who tried and failed to reconcile the motions of these two great bodies. It would have been as great a puzzle to them as reconciling general relativity and quantum theory is to us.
We do not know who realized that there was an element missing, but we owe whoever it was a great debt. We can imagine an astronomer, perhaps in Babylon or ancient Egypt, suddenly realizing that there were not just two periodic motions to consider but three. Perhaps it was a sage, who after decades of study knew the data by heart. Perhaps it was some young rebel, not yet brainwashed into thinking that you had to explain what was seen only in terms of observable objects. Whatever the case, this innovator uncovered a mysterious third oscillation in the data, occurring not once a month or once a year but approximately every eighteen and two-thirds years. It turns out that the points where the two paths cross on the sky are not fixed: They rotate as well, taking those eighteen-plus years to make a complete cycle.
The discovery of this third motion—the missing element—must have been one of the earliest triumphs of abstract thinking. We see two objects, the sun and the moon. Each has a period, known from earliest times. It took an act of imagination to see that something else was moving as well: the paths themselves. This was a profound step, because it required realizing that behind the motion you observe there are other motions whose existence can only be deduced. Just a few times since has science progressed by the discovery of such a missing element.
The idea that elementary particles are not pointlike particles but vibrations of strings may be another of these rare insights. It provides a plausible answer to several big problems of physics. If right, it is as profound a realization as the ancient discovery that the circles the planets travel on are themselves moving.
The invention of string theory has been called a scientific revolution, but it was a long time in the making. As in some political revolutions—but unlike scientific revolutions of the past—the string theory revolution was anticipated by a small vanguard, who toiled for years in relative isolation. They began in the late 1960s to explore what happened when the strongly interacting particles—that is, particles made from quarks, such as protons and neutrons, and thus governed by the strong nuclear force—scatter off one another. This is not one of the five problems, because it is now understood, at least in principle, in terms of the standard model. But before the standard model was invented, it was a central problem for elementary-particle theorists.
Besides protons and neutrons, there are a great many other particles made from quarks. These others are unstable; they are produced in accelerators by smashing a beam of protons at high energy into other protons. From the 1930s to the 1960s, we accumulated a lot of data about the various kinds of strongly interacting particles and what happened when two of them collided.
In 1968, a young Italian physicist named Gabriele Veneziano saw an interesting pattern in the data. He described the pattern by writing down a formula that described the probabilities for two particles to scatter from each other at different angles. Veneziano’s formula fit some of the data remarkably.1
It caught the interest of some of his colleagues, in Europe and in the United States, who puzzled over it. By 1970 a few were able to interpret it in terms of a physical picture. According to this picture, particles could not be seen as points, which is how they had always been seen before. Instead, they were “stringlike,” existing only in a single dimension, and they could be stretched, like rubber bands. When they gained energy, they stretched; when they gave up energy, they contracted—also just like rubber bands. And like rubber bands, they vibrated.
Veneziano’s formula thus was a doorway to a world in which the strongly interacting particles were all rubber bands, vibrating as they traveled, colliding with one another and exchanging energy. The various states of vibration would correspond to the various kinds of particles produced in the proton-smashing experiments.
This interpretation of Veneziano’s formula was developed independently by Yoichiro Nambu at the University of Chicago, Holger Nielsen at the Niels Bohr Institute, and Leonard Susskind, now at Stanford University. Each thought he had done something fascinating, but they found there was little interest in their work. Susskind received a rejection from Physical Review Letters indicating that his insight was not significant enough to publish. As he later put it in an interview, “Boom! I felt like I had gotten hit over the head with a trashcan, and I was very, very deeply upset.”2
But a few people did get it and began to work on the same interpretation. It would perhaps have been more accurate to call the ensuing set of ideas rubber-band theory. But as that lacked a certain dignity, it was string theory that was born.
As a theory of the strongly interacting particles, string theory was after a time supplanted by the standard model. But this does not mean that string theorists were wrong; in fact, the strongly interacting particles do behave a lot like strings. As discussed in chapter 4, the force between the quarks is now described most fundamentally by a gauge field, and the basic law seems to be given by quantum chromodynamics, or QCD, which is part of the standard model. But in some circumstances the result can be described as if there were rubber bands between the quarks. This is because the strong nuclear force is very unlike the electromagnetic force. While that force becomes weaker with distan
ce, the force between two quarks approaches a constant strength as we pull the two quarks apart and then remains constant no matter how far apart they are after that. This is why we don’t ever see free quarks in accelerator experiments, only particles made of bound quarks. However, when quarks are very close together, the force between them weakens. This is important. The string (or rubber-band) picture works only when the quarks are at a sufficient distance from one another.
The original string theorists lacked this essential insight. They imagined a world in which quarks were tied together by rubber bands, period—that is, they tried to make string theory a fundamental theory, not an approximation to anything deeper. When they tried to understand the strings qua strings, trouble emerged. The problems stemmed from two reasonable requirements they imposed on their theory: First, string theory should be consistent with Einstein’s special theory of relativity—that is, it should respect the relativity of motion and the constancy of the speed of light. Second, it should be consistent with quantum theory.
After a few years’ work, it was found that string theory, as a fundamental theory, could be consistent with special relativity and quantum theory only if several conditions were satisfied. First, the world had to have twenty-five dimensions of space. Second, there had to be a tachyon—a particle that goes faster than light. Third, there had to be particles that could not be brought to rest. We refer to these as massless particles, because mass is the measure of a particle’s energy when it is motionless.
The world does not appear to have twenty-five dimensions of space. Why it is that the theory was not just abandoned then and there is one of the great mysteries of science. What is certain is that this reliance on extra dimensions deterred many people from taking string theory seriously before 1984. A lot rests on who was right—the people who rejected the idea of extra dimensions before 1984 or those who became convinced of their existence afterward.
The tachyons also posed a problem. They had never been seen; even worse, their presence signaled that the theory was unstable and, quite possibly, inconsistent. It was also the case that there are no strongly interacting particles with no mass, so the theory failed as a theory of the strongly interacting particles.
There was a fourth problem. String theory contained particles, but not all the particles in nature. There were no fermions—and thus no quarks. This was a huge problem for an alleged theory of the strong interactions!
Three of the four problems were addressed in a single move. In 1970, the theorist Pierre Ramond found a way to alter the equations describing a string, so that it would have fermions.3 He found that the theory would be consistent only if it had a new symmetry. This symmetry would mix the old particles with the new ones—that is, it would mix bosons with fermions. This was how Pierre Ramond discovered supersymmetry; thus, whatever the fate of string theory, it proved to be one route to the discovery of supersymmetry, so as an incubator of new ideas, it was already fruitful.
The new supersymmetric string theory also addressed two other problems. It had no tachyons, so that major obstacle to taking strings seriously was eliminated. And there were no longer twenty-five dimensions of space, just nine. Nine is not three, but it is closer. With time added, the new supersymmetric string (or superstring, for short) lives in a world of ten dimensions. This is one less than eleven, which, strangely, is the maximum number of dimensions for which one can write a theory of supergravity.
At about the same time, a second way to put fermions into the string was invented by Andrei Neveu and John Schwarz. Like Ramond’s, their version of the theory had no tachyons and lived in a world with nine spatial dimensions. Neveu and Schwarz also found that they could get the superstrings to interact with one another, and they got formulas that were consistent with the principles of quantum mechanics and special relativity.
So there was just one puzzle left. How could the new supersymmetric theory be a theory of the strong interactions if it contained massless particles? But in fact there do exist bosons with no mass. One is the photon. A photon never sits still and it can go only at the speed of light. So it has energy but no mass. The same is true of the graviton, the hypothetical particle associated with gravitational waves. In 1972, Neveu and another French physicist, Joël Scherk, found that the superstring had states of vibrations corresponding to gauge bosons, including the photon. This was a step in the right direction.4
But an even bigger step was taken two years later, by Scherk and Schwarz. They found that some of the massless particles predicted by the theory could actually be gravitons.5 (The same idea occurred independently to a young Japanese physicist, Tamiaki Yoneya.6)
The fact that string theory contained gauge bosons and gravitons changed everything. Scherk and Schwarz proposed immediately that string theory, rather than being a theory of the strong interactions, was instead the fundamental theory—the theory that unifies gravity with the other forces. To see how beautiful and simple this is, note how these photon-like and graviton-like particles arise from strings. Strings can be both closed and open. A closed string is a loop. An open string is a line; it has ends. The massless particles that might be photons come from vibrations of either open or closed strings. The gravitons come only from vibrations of closed strings, or loops.
The ends of an open string can be seen as charged particles. For example, one end could be a negatively charged particle, such as an electron; the other would then be its antiparticle, the positron, which is positively charged. The massless vibration of the string between them describes the photon that carries the electrical force between the particle and the antiparticle. Thus, you get particles and forces alike from the open strings, and if the theory is designed cleverly enough, it can produce all the forces and all the particles of the standard model.
If there are only open strings, there is no graviton, so it seems as though gravity is left out. But it turns out that you must include the closed strings. The reason is that nature produces collisions between particles and antiparticles. They annihilate, creating a photon. From the string point of view, this is described by the two ends of the string coming together and joining. The ends go away and you’re left with a closed loop.
In fact, the particle-antiparticle annihilation and the closing of the string is necessary, if the theory is to be consistent with relativity, meaning the theory is required to have both open and closed strings. But this means it must include gravity. And the difference between gravity and the other forces is naturally explained, in terms of the difference between open and closed strings. For the first time, gravity plays a central role in the unification of the forces.
Isn’t this beautiful? The inclusion of gravity is so compelling that a reasonable and intelligent person might easily come to believe in the theory based on this alone, whether or not there was any detailed experimental evidence for it. Especially if that person has been searching for years for a way to unify the forces, and everything else has failed.
But what gives rise to it? Is there a law that requires the ends of strings to meet and join? Herein lies one of the most beautiful features of the theory, a kind of unification of motion and forces.
In most theories, particle motion and the fundamental forces are two separate things. The law of motion tells how the particle moves in the absence of external forces. Logically there is no connection between that law and the laws that govern the forces.
In string theory, the situation is very different. The law of motion dictates the laws of the forces. This is because all forces in string theory have the same simple origin—they come from the breaking and joining of strings. Once you describe how strings move freely, all you have to do to add forces is add the possibility that a string can break into two strings. By reversing the process in time, you can rejoin two strings into a single string (see Fig. 5). The law for breaking and joining turns out to be strongly prescribed, to be consistent with special relativity and quantum theory. Force and motion are unified in a way that would have been im
possible in a theory of particles as points.
Fig 5. Top: Two open strings join at their ends. Middle: The two ends of an open string join to make a closed string. Bottom: Two closed strings join to make a single closed string.
This unification of forces and motion has a simple consequence. In a particle theory, you can freely add all kinds of forces, so there is nothing to prevent a proliferation of constants describing the workings of each force. But in string theory, there can be only two fundamental constants. One, called the string tension, describes how much energy is contained per unit-length of string. The other, called the string coupling constant, is a number denoting the probability of a string breaking into two strings, thus giving rise to a force; as it is a probability, it is a simple number, without units. All the other constants in physics must be related to these two numbers. For example, Newton’s gravitational constant turns out to be related to the product of their values.
Actually, the string coupling constant is not a free constant but a physical degree of freedom. Its value depends on the solution of the theory, so rather than being a parameter of the laws, it is a parameter that labels solutions. One can say that the probability for a string to break and join is fixed not by the theory but by the string’s environment—that is, by the particular multidimensional world it lives in. (This habit of constants migrating from properties of the theory to properties of the environment is an important aspect of string theory, which we will run into again in the next chapter.) On top of all of this, the law that strings satisfy is beautiful and simple. Imagine blowing a bubble. It makes a perfectly spherical shape as it expands. Or look at the bubbles next time you take a bubble bath. Their shapes are a manifestation of a simple law, which we will call the law of bubbles. The law states that the surface of a bubble takes up the minimal area it can, given the constraints and forces on it.
