Feynman's Rainbow Read online

  I imagined you could chart this cultural landscape along the lines of Saul Steinberg’s classic New Yorker magazine cover looking westward from Manhattan. I pictured, in the foreground, at the center of the world, the different aspects of elementary particle theory—like the buildings of Manhattan. This is what Feynman and Murray and most of those on the floor worked on. The surrounding areas—off in New Jersey somewhere—represented mathematics and other areas of theoretical physics. In the vast and distant middle of the country were the marginalized great plains of experimental physics. Finally, on the far coast, were some tiny structures—applied physics, the life sciences, and other professions hardly worthy of attention. As long as I stayed near the world’s center, I was free to move about. But the farther my research might stray from it, the stronger the force I would feel pulling me back.

  Feynman always made a point of ignoring such forces. He was interested in all of physics, in other sciences, and in many other creative endeavors. Even socially, he would not conform. Expected to behave with a certain professorial decorum, he would go to a strip club to work on his physics. At the strip club, he’d be expected to drink alcohol, or maybe cavort with the strippers. But he didn’t drink, and was faithful to his wife. What I didn’t realize at the time was that I, too, had the power to ignore the force of other people’s expectations.

  I didn’t have the insight back then to apply this analysis of the strong force to myself, yet this young professor’s idea appealed to me. I also figured that since he had had early success, like me, and he had succeeded in making it to the next step—as a tenured professor at Caltech—he would be a promising mentor.

  I stepped into his office. Several houseplants and a poster of the Huntington Gardens—a famous nearby botanical garden—adorned the room. It was only the second time I had ever seen plants in a physicist’s office. The other was a mathematical physicist I once knew but he doesn’t really count because his plants were all dead from lack of water.

  The young professor was a large, rotund fellow. He looked cheerful. After a bit of small talk, I asked what he was working on these days, trying to be as nonchalant as possible. Most researchers are happy to find collaborators, but no one wants a desperate collaborator. My nonchalance must have been exaggerated though, because he gave me a funny look.

  “I’m just going around,” I said, “getting acquainted with what everyone on the floor is doing.”

  “I get it.” He smiled. But he still didn’t answer.

  “So . . . what are you working on?” I asked once more.

  “Oh, you won’t want to work on that.”

  “You never know,” I said.

  He kept smiling, but he didn’t speak. I stared at him as a driver might stare at a streetlight, waiting for it to turn green. But the light didn’t change.

  I read once about a study that concluded that the trait most correlated with success in graduate school is persistence. I felt that in sociology researchers often had an excess of this trait themselves—they persisted in drawing conclusions beyond the point of statistical validity. Still, being a persistent fellow, I often took comfort from that study.

  “So what do you work on?” I persisted.

  He shrugged. “Oh, these days . . . mostly gardening.” His smile remained undiminished through his answer.

  Out in the corridor I supposed he earned his keep teaching, but I looked down upon him. To teach science was not to be a scientist, and to me, back then, not worthy of his position. From then on, I always thought of him as Professor Gardening.

  I ran into my friend Constantine. He was a postdoctoral fellow from Athens. His father was Greek, but his mother was Italian, and he seemed to have inherited from her an impeccable sense of style, both in the way he dressed and in his approach to physics.

  “Don’t you know about him?” he whispered. “He’s burned out. They gave him tenure right after graduate school because everyone was fighting to get him. Turns out he’s just a one-trick pony.” Constantine smirked.

  A one-trick pony. I smirked back out of obligation, but I was thinking, just like me. Except that nobody made the awful mistake of giving me tenure. In a few years I would be completely lost, I imagined, and have to take a depressing job like my neighbor in the defense industry. I couldn’t see myself designing missiles, though, at least not without final say on against whom they were used.

  My head still ached, so I went to Helen, the department secretary, looking for more aspirin. She had the office on the other side of Murray’s from mine—the one between Murray and Feynman—and had been in the department about as long as they had. As I approached her office I heard her saying to someone inside, “You sure gave that bank teller a hard time.”

  And then Murray’s voice, “Oh, you heard that?”

  And Helen: “How could I not?”

  Murray emerged from her office. He nodded. I nodded. I went in to see Helen.

  “You have a headache?” she said when I asked for the pills. “I’m not surprised.”

  I gave her a look: What did that mean?

  “If you don’t mind my saying so, you haven’t looked very happy lately.”

  “Oh, I’m just . . . struggling with what I’m going to work on next.”

  “Well I don’t know anything about physics, but it seems to me that everyone does that. At least the ones who haven’t given up.”

  I said, “I bet Feynman doesn’t.”

  “Professor Feynman? Why, he’s had long dry spells. Everyone knows that—at least everyone here. But he always bounces back. I’m sure you will, too.”

  She gave me the pills. Then she said, “Or if not, you’ll find something else to do with your life. You’re still young.”

  VIII

  IN HIS YEARS OF practicing physics, Feynman had solved several of the toughest problems of the postwar era. In between, I confirmed, there were some prolonged periods of inactivity. And indeed, he always bounced back. And whereas Murray worked almost exclusively in the field of elementary particle physics, Feynman had made important contributions in many areas—low-temperature physics, optics, electrodynamics. He seemed to have a knack for finding the right problem to work on, and at the right time. I wondered, what was his approach? What took more talent, choosing the right problem, the issue I was now struggling with, or finding the solution? And once he settled on a problem, what did it take to solve it?

  When you first came here and asked to discuss how I approached a problem, I panicked. Because I really don’t know. I think it’s like asking a centipede which leg comes after which. I have to think a while, try to look back and quote some problems.

  In some cases finding the problem you work on could be a result of a very good creative imagination. And solving it may not take nearly the same skill. But there are problems in math and physics where there is the reverse situation. The problems become sort of obvious and the solution is hard. It’s hard not to notice the problem and yet the techniques and methods known at the time and the amount of information known to people is a small amount. In that case the solution is the ingenious thing.

  A very good example is Einstein’s theory of relativity and gravity—the general theory of relativity. With relativity it was clear that they had to combine somehow this theory of special relativity, that light travels at a certain speed, c, with the phenomenon of gravitation. You can’t have that—you can’t have the old, Newtonian gravity with infinite speeds, and the relativity theory that limits speeds. So you have to modify the theory of gravity somehow.

  Gravity had to be modified to fit the theory of relativity, that light undergoes motion at a certain speed. Well, that’s not much to start with. How to do it?! That was the challenge!

  That this had to be done was obvious to Einstein. It wasn’t obvious to everyone, because to them the special theory of relativity wasn’t yet obvious. But Einstein had gotten past that. So he saw this other problem. It was obvious, but the way of solving it, that took the utmost imagination. Th
e principles that he had to develop! He used the fact that things were weightless when they fell. It took a very, very lot of imagination.

  Or let’s take the problem I’m working on now. It’s perfectly obvious to everybody. We have this mathematical theory called quantum chromodynamics that is supposed to explain the properties of protons and neutrons and so on.

  In the past if you had a theory and wanted to find out if it was right you just took it out, looked at what happened in the theory, and compared it to experiment. Here, the experiments are already really done. We know lots of properties of the protons. And we have the theory. The difficulty is that it’s new, and we don’t know how to calculate the consequences of this theory, because we haven’t got the mathematical power.

  To invent a way of doing it. Now how do you do that? You have to create or invent a way to do it. I don’t know how to do it. Here the problem is obvious, and the solution is hard.

  It took many pieces of imagination to find this theory, people noticing patterns and gradually discovering things, ultimately the quarks, and then trying to find the simplest theory. So there was a long history that produced this particular problem. It took us a long time to get here, but now our noses have been kind of rubbed in it.

  Rubbing our noses in it. It was an interesting expression for him to use. I found it comforting when Feynman revealed that he, too, got frustrated.

  I am working on this very hard problem now, and have been for the last few years. The first thing I tried to do with this problem is try to find some sort of mathematical way of doing it, solving some equations. How did I do that? How did I get started on figuring it out? It’s probably kind of determined by the difficulty of the problem. In this case, I just tried everything. It’s taken two years, and I’ve struggled with this method and that method. Maybe that’s what I do—I try as much as I can different kinds of things that don’t work, and if it doesn’t work I move on to some other way of trying it. But here I realized after trying everything that I couldn’t do that. That none of my tricks worked.

  So then I thought, well, if I understood how the thing behaved, roughly, that would tell me more or less what kind of mathematical forms I might try. So then I spent a lot of time thinking about how it worked, roughly.

  There are also some psychological things there. First of all, in my later years I take only the most difficult problems. I like the most difficult problems. The problems that nobody has solved, and therefore the chances that I’m going to solve it are not too high. But I feel now that I’ve got a position now, the tenure, I don’t worry about wasting the time it takes to work on a long project. I don’t have to say I’ve got to get my degree in a year. It’s true that I may not last so long physically, but I don’t worry about that.

  His illness was always there in the room with us, an angel of death patiently waiting for his time to run out.

  The next psychological aspect is, I have to think that I have some kind of inside track on this problem. That is, I have some sort of talent that the other guys aren’t using, or some way of looking, and they are being foolish not to notice this wonderful way to look at it. I have to think I have a little bit better chance than the other guys, for some reason. I know in my heart that it is likely that the reason is false, and likely the particular attitude I’m taking with it was thought of by others. I don’t care; I fool myself into thinking I have an extra chance. That I have something to contribute. Otherwise I may as well wait for him to do it, whoever it is.

  But my approach is that I’m never the exact same as someone else. I always think I have an inside track, I always try another way. And I think that because I’m trying another way that’s it. They haven’t got a chance. It’s exaggerated. And I have to work myself up to this exaggeration. I always consider it something like Africans when they were going out to battle, to beat drums and get themselves excited. I talk to myself and convince myself that this problem is tractable by my methods and the other guys are not doing it right. The reason they haven’t gotten it is that they aren’t doing it right. And I’m going to do it a different way. I talk myself into this, and I get myself enthusiastic.

  The reason is, when there is a hard problem, one has to work a long time and has to be persistent. In order to be persistent, you have got to be convinced that it’s worthwhile working so hard, that you’re going to get somewhere. And that takes a certain kind of fooling yourself.

  This last problem, I really did fool myself. I haven’t gotten anywhere. I couldn’t say my approach is very good. My imagination is failing me. I’ve figured out qualitatively how it works, but I can’t figure out quantitatively how it works. When the problem is finally solved, it will all be by imagination. Then there will be some big thing about the great way it was done. But it’s simple—it will all be by imagination, and persistence.

  People who have never worked in physics tend to describe it with words like dry, exact, and precise. Real-life physics is as far from that as is the practice of law from the theoretical debate in law school, or the practice of medicine from the theory of physiology and disease. The law might consist of definite rules, but its application is subject to interpretation, incomplete knowledge, practical considerations, and the psychology of those in judgment. Medical science might detail the symptoms of a disease, but few patients step into their doctor’s office quoting textbook presentations of their malady. With experience doctors learn how to make judgments. Physics is also an art. Few real physics problems can be what you would, strictly speaking, call “solved.” To a physicist solving a problem involves judging which aspects of a phenomenon are its essence, and which can be ignored, what part of the mathematics to be faithful to, and what to alter. For instance, a hydrogen atom consists of an electron orbiting a single proton. It is the only one of the hundred-plus types of atoms whose quantum equations can be solved exactly. And if you do something as simple as placing the hydrogen atom in a magnetic field, then the equations, altered to include the magnetic field, cannot be solved.

  Take the problem of finding the light emitted by a hydrogen atom in a magnetic field. You have to simplify. You might begin by assuming the magnetic field is what’s essential, and drop the mathematical terms that involve the proton, or you might begin by assuming the effect of the proton is dominant, and drop the terms that represent the magnetic field. Or, as I did in my Ph.D. dissertation, you might rewrite the equations as if the world had infinite dimensions. To solve a physics research problem involves assumption after assumption, approximation upon approximation, and those great leaps of imagination people call thinking outside the box. It involves the ability to move forward, follow your intuition, and accept that you don’t fully understand what you are doing. And most of all, it entails believing in yourself.

  Feynman’s approach to solving quantum chromodynamics was to write down a simplified form of the theory—and see what the properties of the theory were under that assumption. Feynman’s work on the problem was reminiscent of one of his most famous earlier works—his theory of liquid helium. The problem was to explain theoretically some pretty bizarre properties of that fluid. For instance, it did not boil, and if you put it in a beaker, it would creep up the sides and spill out until the beaker was empty. After seeing physicists frustrated trying to solve this problem directly, in his usual Babylonian style, Feynman decided the best approach is to “wave our hands, use analogies with simpler systems, draw pictures, and make plausible guesses.” This was Feynman’s trademark: not powerful mathematics, but powerful imagination, combined with physical understanding. He solved the helium problem in a series of famous papers in the mid-1950s. He was obviously hoping to repeat that success here.

  Feynman did not live to solve the problem of quantum chromodynamics. And in the twenty-plus years since our discussion, no one else has solved it, either. Today the only new results calculated from the theory do not come from a deeper understanding or a mathematical solution of the theory, but from the continued application to i
t of ever more powerful computers.

  IX

  AS I CONTINUED my search for a problem, I thought about what Feynman had said about an inside track. What are my strengths? I was always more mathematically inclined than most of my fellow students. I was also a rebellious type—drawn by my nature to anything that went against the grain of accepted wisdom. Most of the other faculty on the floor were working, like Feynman, on discovering better ways of solving problems in quantum chromodynamics. This quest involved mostly ordinary mathematics, and was considered one of the most important problems of the day.

  But there was also one professor, John Schwarz, whose research involved quite exotic mathematics, and was completely outside the mainstream.

  There are four known forces in nature—electromagnetism, gravity, the strong force, and its subnuclear partner, the weak force. Physicists have a theory describing the interactions caused by each of these forces—quantum electroweak theory, a generalization of quantum electrodynamics, describes both electromagnetism and the weak force; general relativity, which is not a quantum theory, describes gravity; and quantum chromodynamics describes the strong force. The belief that all natural phenomena can be explained by fundamental physical law is called reductionism. The belief in reductionism is widespread in physics, and cuts across “party lines,” from the Greeks like Murray to the Babylonians like Feynman. That means that most physicists believe that nothing happens in the universe that is not the result of one or more of the four fundamental forces—from the birth of a child to the birth of a galaxy. Given that most physicists hold this view, developing theories of the four forces is about the most important pursuit a theoretical physicist can undertake. Schwarz worked on a single theory that, if true, would subsume (and alter) all these theories. His new theory would rewrite them in one fell swoop, replacing them all with just one, all-encompassing theory.