Feynman's Rainbow Read online

  Considering how different the four forces are, a single theory describing all of them may seem to be a farfetched goal. For instance, the electromagnetic force can attract or repel, but the gravitational force always attracts. The strong force grows weaker at short distances, whereas the gravitational and electromagnetic forces grow stronger. And the forces also have an almost unimaginable range of strengths: The strong force is about a hundred times stronger than the electromagnetic force, which is a thousand times stronger than the weak force, which is billions of billions of billions times stronger than the gravitational force. The four forces also play different roles in our lives, and in the functioning of the universe. Gravity is, of course, what holds us to the earth, and is responsible for the ebb and flow of tides. But its most important effects in nature are on the cosmic scale. Gravity causes planets to form and to orbit their stars, and enables the nuclear furnace in a star’s core that gives the light and warmth that lead to life. And long before their planets existed it was gravity’s squeeze that caused these stars themselves to coalesce. The electromagnetic force is important to us mainly on the atomic scale. The electromagnetic forces amongst atoms and molecules, for instance, make objects visible, allow oxygen to bind to red blood cells, and stop your hand from going through the wall when you lean on it. It is the force that lends to materials most of the properties they possess. And it is the harnessing of this force, mostly in the twentieth century, that accounts for most of the conveniences of modern times: from lights to telephones to radio and television to computers. The other two forces, the strong and weak forces, govern a world that exists on scales far smaller than even the atomic world of electromagnetism: the inside of the nucleus. The weak force governs the radioactive decay of the nucleus called beta decay. The strong force is responsible for atomic energy. It is the power of this force, unleashed from the nuclei that correspond to less than a third of an ounce of uranium, that destroyed the city of Hiroshima.

  How could these four forces be described by a single theory? History provides a lesson here: In a way there are really five forces, but we speak of only four because the first unification of forces happened so long ago. It was the unification of the theories of electricity and magnetism, a kind of “prequel” to the present quest. The story goes something like this: Long, long ago (the sixth century B.C.), in a faraway land (ancient Greece), the simplest electromagnetic phenomena, magnetism and static electricity, were studied by a wise philosopher named Thales. From his time until the nineteenth century, human beings learned more and more about electricity and magnetism, but nothing indicated to them that these were anything other than two separate classes of phenomena. Together with gravity, electricity and magnetism constituted the three known forces of nature. Then, around the year 1820, several scientists in different parts of Europe discovered that wires carrying electric currents had mysterious magnetic properties. This was a strong hint that the forces of electricity and magnetism were related, but no one quite knew how. In the next few decades all these mortals could conjure up to describe the effects they had seen was a hodgepodge of empirical laws. Then in 1865 a Scottish physicist, barely five foot four, named James Clerk Maxwell used this hodgepodge of laws to lead him to a wondrous set of equations. In just a few lines, they showed the world how electric and magnetic forces arose from electric charges and currents—and, most important, from each other. Maxwell had thus produced a unified theory of two of the three ancient forces, electricity and magnetism, or, as we now call it, electromagnetism.

  History also shows that Maxwell’s unification was more than a thing of theoretical beauty: A study of its implications revealed revolutionary new effects. For instance, his equations indicated that accelerating charges could produce waves of electromagnetic fields. These waves always moved at the same speed—which his calculations showed to be the speed of light. This provided to Einstein the inspiration for his theory of special relativity. And once Maxwell discovered that light is an electromagnetic phenomenon, it became clear that there could also exist other kinds of electromagnetic waves. This paved the way for German experimentalist Heinrich Rudolf Hertz to create the first radio waves, and eventually for the invention of such technologies as radio, television, radar, satellite communications, X-ray machines, and microwave ovens. In his Lectures on Physics, Feynman wrote, “. . . there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics.”

  Physicists call a single theory that explains all the forces of nature a “unified field theory.” It is worth taking a moment to think about what this means. For a theory to be a unified theory it has to go beyond the description of the individual forces to describe the relationship of the forces to each other, as Maxwell did when he showed how electric forces could create magnetic forces and vice versa.

  Most physicists seeking a unified field theory demand even more: They seek to show how all the forces of nature arise from a single more fundamental force, or underlying principle. Though there is little experimental evidence that this is actually true of nature (or that it isn’t), they seek such a theory anyway, out of an aesthetic sense, or out of faith that somewhere there is a single key to all of nature’s laws. Such a unified theory would be the ultimate triumph of Greek-style physics. It is in the search for such a theory that Einstein spent most of his life, his post-relativity years, gradually drifting from the mainstream of physicists, who were more focused on more practical issues.

  Beyond mathematical beauty and the potential discovery of new physical phenomena, a unified field theory also promises to answer fundamental questions about why we exist at all. It is the balance of the four forces of nature, their relative strengths and varied properties, that allows the universe to exist as we know it. For instance, suppose that the gravitational force were not so feeble compared to the strong force. Then stars would compress further and their nuclear fuel would burn out much more quickly, preventing the evolution of life. On the other hand, if gravity were much weaker, electromagnetic repulsion would prevent matter from coalescing into stars at all. If the strong force were not so much stronger than electromagnetic forces, most atomic nuclei would disintegrate. And if the numbers of electrons and protons in matter were even one percent out of balance, the electromagnetic force between you and someone a yard away would be greater than the weight of the earth. The forces of nature are disparate, but in fine balance. Why? Though separate theories can describe the individual forces, only a theory encompassing all the forces can answer this fundamental question of existence.

  When Einstein started seeking a unified field theory, he was at a huge disadvantage: The strong and weak forces had not yet been discovered. But by 1981, electromagnetism and the weak force had been united in a single theory, and physicists had ideas about how to include the strong force. Progress toward a unified theory was tantalizing. Thirty years after Einstein’s death, his quest gained a new popularity. The term “a theory of everything” entered physicists’ vocabulary. The biggest obstacle to success, everyone agreed, was gravity. Not only didn’t physicists know how to include gravity in a unified theory, but there still existed no quantum theory of gravity, even as an isolated force. Unless you believed John Schwarz. Schwartz claimed that his theory could unite all the forces, even gravity, in a single quantum theory.

  The theory that was Schwarz’s obsession was called string theory. The strings in string theory have little relation to ordinary strings, thin lines of fiber you might tie around your finger to remind you to buy milk on your way home. The physicist’s strings were first proposed by Japanese physicist Yoichiro Nambu and American physicist Leonard Susskind in 1970. The idea was that what appeared to be a point particle might really be a tiny, undulating string. What could be the use of such a strange idea? At first, its use seemed to be that it might solve the old problem caused by the experimentalists, who kept discovering new particles. Even the number of quarks, with which Murray was
able to explain the existence of a large number of particles in terms of far fewer, had had to be greatly increased in the years since he had first proposed them. So the early allure of string theory was closely related to an idea that Murray helped originate in the 1950s, even before he came up with quarks—that all these particles may simply be alternative forms of the same thing.

  In string theory there is one and only one theory that encompasses all forces, and one and only one fundamental particle—the string. Its properties would depend on the state of vibration it is in, just as the mode of vibration determines the sound created by a violin string, but in this case different states of vibration would manifest themselves as different particles, instead of different sounds. This one entity, the string, would thus account for the wide variety of particles in nature and explain the forces they react to.

  From the mathematical form string theory took, there were strong indications that it held the promise of being a unified field theory of all forces, even gravity. To some, like Schwarz, this seemed to be a miracle. But these were only general properties of the theory, not predictions you could test in the lab. So the most important question remained open: Was string theory correct?

  You might think that this would be an easy thing to check. You look closely at a particle. Is there a little string dancing around in there, or isn’t there? But elementary particles are so small we cannot see them with enough precision to make out such finer structure. It is analogous to the reason that, from a great distance, that violin-shaped mole on your nose might look like the tiny beauty spot your mother always said it was. Still, the fact that we cannot check directly whether particles are actually made of strings doesn’t mean that a theory built around this assumption has no consequences. Suppose you looked at my life from a distance, say from the limited interactions you have with me as a colleague, but not as a friend. You might think, he speaks intelligently, has good credentials, landed this plum job at Caltech—he appears to be a successful, confident guy. But what am I on a deeper level? This is something that, given our relationship, you might not be able to check directly. So you might theorize. At home, do I read Jane Austen novels, tend quietly to my garden, and play the violin? Or do I guzzle martinis and try to keep my neighbor the garbage man from blowing his brains out? There are certainly certain circumstances in which the behavior of the Leonards of the two theories would diverge, and by observing me in such a circumstance, you could infer which is closer to the truth. And so it is with strings. Even if we are not so intimate with nature as to be able to check directly whether particles are made of strings, the question is, can we manufacture a situation in which the observable consequences predicted by string theories and nonstring theories conflict? To be able to propose such an experiment was the string theorists’ greatest hope. Unfortunately, no one could figure out how to do it. The theory was just too mathematically complex.

  Since string theorists didn’t know how to make any testable predictions, they invented another goal for their theory, at least in the short term. It has been dubbed “postdiction.” In this approach, rather than making the prediction of some new phenomenon, string theory would provide the explanation of something that was already known, but not understood. For instance, we know the values of many fundamental physical quantities, such as the mass of the quarks, or the charge of the electron, but have no idea why they have those values. String theory had the potential to change that: It promises to produce these numbers from scratch. But no one could figure out how to do that, either.

  During the 1970s little of the promise of string theory had been realized. Then, certain inconsistencies were discovered. Everyone, including John Schwarz, figured it would take another mathematical miracle to eliminate these inconsistencies. Schwarz and a tiny group of collaborators believed so strongly that string theory was correct that they began searching for the miracle. To them, the mathematical structure they had already uncovered—for instance, the promise of including gravity—was already a mathematical miracle, and they were ready to allow the theory to lead them forward to the next one. Everyone else simply dropped the theory.

  One of the problems with string theory Schwarz did not try to dispel was the problem of dimensions: String theory is not mathematically consistent in just three spatial dimensions. The strings of string theory had length, breadth, and height, but they also required extension into six additional dimensions that don’t seem to exist in the real world. Not as bad as my method of infinite dimensions, but these extra dimensions were not an artifact of a mathematical approximation method. According to string theory, the extra dimensions had to be real. String theorists “solved” this problem by adjusting the theory mathematically so that the extra six dimensions were, like the strings, so tiny in extent that they would have naturally gone unnoticed, and, in fact, be virtually impossible to detect.

  It was as if we lived in a two-dimensional world, say confined to the surface of the earth, and suddenly a physicist said, hey, look, there exists this extra dimension, up and down, that we have never before noticed. People might ask, how could we not have noticed something so obvious as a new direction? If this “up and down” really exists, I should be able to jump, or toss a ball upward. You can jump, the physicist says, but the dimension is tiny, so your jump can take you only the tiniest fraction of a millimeter upward. So meager is your jump that you’d never even notice getting off the ground.

  To a few, string theory’s requirement that extra dimensions exist represented a great discovery—like Planck’s discovery of the quantum principle, or Einstein’s discovery that space and time are intertwined. To those few string theory presented an exciting challenge: Find an indirect but measurable consequence of the extra dimensions (while, in the meanwhile, still working to eliminate the theory’s other inconsistencies). But, even at Caltech, most physicists reacted to Schwarz as if he had proposed that everyone move to Nevada to join the secret team studying aliens at Area 51.

  Constantine was one of them. I found him sitting at his desk. He had an inside office—no window. The fluorescent light overhead buzzed. It would have depressed me to have to listen to the buzzing all day. It would have depressed me to have no natural light. Too many things depressed me then, except when I was working. But nothing seemed to ever depress Constantine. He looked tired, though.

  “Got to bed at four. Hey—life is tough,” he said. He made some gesture with his hands and face that I understood to mean that life is not tough at all. He had been out partying with his American girlfriend, a stunning blond actress named Meg.

  I was jealous of him and Meg. Constantine was very handsome, in a Mediterranean sort of way—of slight build, but perfectly sculpted, with alluring eyes and a great smile. He was always tanned, and though he was in his twenties, his hair had just enough gray to lend him an air of sophistication. When he smoked cigarettes it reminded you of one of those ads meant to make it look sexy. At times I had the secret fantasy of running into him in twenty years to find him all white-haired and wrinkled, maybe even a little hunched over. In my fantasy I would be completely unchanged, except for an intangible maturation that greatly enhanced my sex appeal.

  I told Constantine I was going to have a talk with John Schwarz.

  “Why would you do that?” he asked.

  I said, “I thought he might be a good mentor.”

  Constantine laughed. “Mentor? He can’t even mentor himself.”

  “He seems to take on students.”

  “Come on. The guy’s been here nine years and he still doesn’t have tenure. He’s not even a professor. He’s a research fellow just like you and me.” He made another of his Greek—or maybe Italian—gestures, a dismissive motion with his hands of the sort you might make to a busboy to indicate you are done and he can take your plate.

  “Well, if he’s been here nine years he must have faculty support somewhere. Some kind of pull,” I said.

  Constantine took his own pull—on his cigarette. He blew the smok
e toward the ceiling, then he looked at me with a smile. “He’s a mule. He teaches, he takes on a lot of students. Does the work so guys like Feynman can get a free ride.”

  “Well, with that big load maybe he’ll appreciate having another person to work with,” I said.

  “I’m sure he’ll be happy to teach you all about his work. After all, no one else really cares.”

  “Thanks for your support, Constantine.” I walked out of his office.

  “What? Did I say something bad?” he asked as I was leaving.

  Schwarz’s office was around the corner. His door was open. He looked fortyish, and was very clean-cut. He sat at his desk, reading a preprint, which is what physicists call the manuscript for a research paper. Since the journals take so long to actually publish a paper, most current work is circulated and read in preprint form (and these days can be downloaded from the Web). He looked up at me.

  “Yes?”

  I introduced myself. He smiled, “Yes, I had heard you were a new arrival.”

  “I was interested in getting to know everyone, and what they worked on.”

  “I work on string theory,” he said, as if it were a household word.

  “I thought maybe you could explain a little about your research.”

  “I don’t really have the time,” he said.

  “Another time, then . . .” I said. “When might be good?”

  He got up and walked to the bookshelf. He gathered a half-dozen preprints and reprints of articles.

  “Here,” he said, “just read these.”

  He handed me the material and got back to work as if I wasn’t there. He had doled out all the words he was willing to spare, and seemed even to be hoarding his supply of eye contact.