Feynman's Rainbow Read online

  Though Feynman scorned the study of philosophy, it was such differences in philosophy that underlay the friction between the two men. Feynman used to say there were two kinds of physicists, the Babylonians and the Greeks. He was referring to the opposing philosophies of those ancient civilizations. The Babylonians made western civilization’s first great strides in understanding numbers and equations, and in geometry. Yet it was the later Greeks—in particular, Thales, Pythagoras, and Euclid—whom we credit with inventing mathematics. This is because Babylonians cared only whether or not a method of calculation worked—that is, adequately described a real physical situation—and not whether it was exact, or fit into any greater logical system. Thales and his Greek followers, on the other hand, invented the idea of theorem and proof—and required that for a statement to be considered true, it had to be an exact logical consequence of a system of explicitly stated axioms or assumptions. To put it simply, the Babylonians focused on the phenomena, the Greeks on the underlying order.

  Both approaches can be powerful. The Greek approach brings with it the full force of the logical machinery of mathematics. Physicists of this ilk are often guided by the mathematical beauty of their developing theories. And it has led to many beautiful applications of mathematics—such as Murray’s classification of particles. The Babylonian approach allows a certain freedom of imagination, and allows you to follow your instinct or intuition, your “gut feeling” about nature, without worrying about rigor and justification. This aesthetic has also led to great triumphs—triumphs of intuition and “physical reasoning,” that is, reasoning based principally on the observation and interpretation of physical processes, and not driven by mathematics. In fact, physicists employing this kind of thinking sometimes violate the formal rules of mathematics, or even invent strange new (and unproved) math of their own based on their understanding of experimental data. In some cases this has left mathematicians bringing up the rear—either justifying the physicists’ novel use of their ideas, or investigating why their “unwarranted” use gives pretty accurate answers anyway.

  Feynman considered himself a Babylonian. He relied on his understanding of nature to guide him wherever it might lead. Murray was more the Greek type—wanting to categorize nature, to impose an efficient mathematical order on the underlying data.

  Though it angered Murray for Feynman to refuse to identify the internal elements of protons as quarks, this is exactly what you would expect from a Babylonian-style thinker. Feynman had explained some data by pointing out that it seemed as if an internal structure were present. He didn’t see in that data any compelling reason to take the further step of identifying the internal structure as the one proposed by Murray. To a Greek-style thinker, the fact that this identification would tie in to a beautiful mathematical classification scheme was a compelling reason to make it.

  Despite Feynman’s characterization of these approaches as Babylonian and Greek, a similar philosophical tension has played out with many other characters and movements throughout history, for instance, among the Greeks themselves: Plato and Aristotle. Plato believed that, underlying the varied phenomena of the material world, there are eternal and immutable patterns. It is the description of these, in mathematical terms, that physicists such as Murray seek. Aristotle felt that Plato got it backward. To him, the ideal—that is, abstract—description of nature was a myth, or perhaps a convenience, and what we really ought to be concerned with were the phenomena we perceive with our senses. Like Feynman, he worshiped nature itself, not the (possible) underlying abstraction.

  Feynman’s distinction seemed to me to also mirror Sperry’s theory about the two hemispheres of the brain. The left, seeking order and organization, is Murray, the Greek, the Platonic, and the right, perceiving patterns and emphasizing intuition, is Feynman, the Babylonian, the Aristotelian. In light of its physical root within the brain, it is no wonder that their difference in approach extended beyond physics, to the way they lived their lives. It was a life choice with which I, too, without realizing it, would soon be confronted.

  In many ways Feynman was Murray’s intellectual nemesis. Though in 1981 Feynman had not yet been discovered by the popular media, in the physics world his persona had already outshone Murray for decades. The Feynman legend began when, in 1949, at age thirty, he wrote that series of papers for the Physical Review. Ever since Isaac Newton, you created a theory in physics by writing down an equation, or set of equations, called differential equations. Then you calculated the consequences of the theory by solving the differential equations. Quantum theories were no different. For instance, to discover what quantum electrodynamics—the quantum theory of electrically charged particles—predicted for the future behavior of an electron, a physicist in the 1940s would first describe its current, or “initial,” state. This mathematical function contains information describing quantities such as the electron’s momentum and energy at the beginning of a process or experiment. The goal of the theorist would be to describe these same quantities at the end of the process or experiment (that is, to calculate what is called its “final state”) or at least to calculate the probability that it reaches a particular final state of interest. To accomplish this, the physicist would solve a differential equation. Feynman’s formulation of quantum theory did away with the need to solve the differential equation.

  In Feynman’s approach, to find the probability that an electron that started in a given initial state would end up in some particular final state you add, using certain rules, contributions from all the possible paths, or histories, of the electron that could take it from the initial state to the final one. To Feynman, this was what distinguished the quantum world from the everyday, or classical, world. In classical theories a particle followed a definite path, just as objects seem to in our everyday world. The strange quantum world arises because you have to take into account extra paths. For large objects, the way you add up the paths makes only one of these important, the familiar classical path, so you don’t notice any quantum effects. But for subatomic particles, such as the electron, you cannot ignore paths in which the electron travels to the far reaches of the universe, or zigzags back and forth in time. The quantum electron shoots around the universe in a cosmic dance, from present to future to past, from here to everywhere in the universe, and back. In following these paths, it ignores the orthodox rules of motion and acts as if nature had let go of the controls. As Feynman put it, even “the temporal order of events . . . is irrelevant.” Yet somehow, like the music of instruments in harmony, all these paths, added together, add up to the final quantum state that the experimenter observes.

  Feynman’s method was radical, and at first glance, absurd. In our science-oriented culture, we expect order. We have developed a strong idea of time and space, and that time progresses from past to present to future. But underlying this order, according to Feynman, are processes that are free from following such rules. Feynman as usual would never discuss such metaphysical aspects of his theory. Later, when I got to know him, I felt I understood how he could conjure up such a theory: He himself behaved much like the electron.

  Feynman’s approach was hard for physicists at the time to grasp and accept. The so-called “path integrals” he had invented to sum the paths were mathematically unproven, and, at times, ill-defined. And his pictorial technique for generating answers from his theory—today called Feynman diagrams—was unlike anything physicists had seen before. Physicists demanded proof. They wanted a mathematical derivation of his formulae starting from the usual formulation of quantum theory. But he had developed his method employing intuition and physical reasoning—plus plenty of trial and error. He couldn’t prove it. When he presented his method at a conference in 1948, he was roundly attacked by star physicists like Niels Bohr, Edward Teller, and Paul Dirac. They demanded the Greek approach, and here he was, a Babylonian. Yet in the end they could not ignore him: He could do theoretical calculations in a half hour that took them months.

  Ev
entually another young physicist, Freeman Dyson, showed how Feynman’s approach was related to the usual one, and it slowly caught on. Some, such as Murray himself, speculate whether Feynman’s method, his path integrals and Feynman diagrams, rather than Newton’s approach employing differential equations, isn’t the true foundation of all physical theory.

  Though to physicists Feynman was legendary, and Murray all too human, in some ways Murray had been more influential in guiding the direction of the field. This is because Murray, ever seeking order and control, had always sought the leadership role. Feynman avoided it, preferring to let his work speak for itself.

  How did I fit in?

  The source of my own success was my Ph.D. dissertation and several papers I wrote with a Berkeley postdoctoral fellow from Greece named Nikos Papanicolaou. Like Feynman, Nick and I explored a way of connecting the quantum and classical worlds: We discovered that the quantum world would look similar to our classical world if only we lived in a universe with many more than the three dimensions of space we are familiar with. Then we showed how certain problems in atomic physics would be easily solvable if the world had an infinite number of dimensions. And finally, we showed how to compensate for the false assumption of infinite dimensions, and find answers that are accurate and relevant to our 3-D world. When the smoke cleared, I had been stunned at the accuracy of our approach. But most of all, I was proud of our originality.

  Our work had been cited a year or so earlier in an article in the semitechnical professional journal Physics Today by a young Princeton professor named Edward Witten, who, in the coming decade, would take the late Professor Feynman’s place as the number one Yoda of the physics world (and eventually occupy Murray’s old office). After that article, others began to cite our work. The number of citations grew to dozens. I lost track when it reached one hundred. I also found myself being treated with a new respect. My Ph.D. advisor was suddenly interested in the minute details of my work. Out of the blue, an old professor from my undergraduate days sent his regards. Professors started treating me as if what I said about things might be worth listening to. As the time came to think about what I would do next, the bad thoughts started coming. The doubts. Could I ever repeat my success? And then came the job offer from Caltech.

  Whether Greek, Babylonian, or just native Chicagoan, I knew I had to discover my own style and approach to physics—and to life. Yet first I had to get over my feelings that my discovery was a fluke, and my success some kind of hoax, or a lucky break that would never happen again. I spent weeks in that state of mind, staring for long stretches at one journal or another, hardly turning the pages, nothing sinking in. I would go to seminars unable to focus on the topic. I would have conversations with fellow postdocs in the corridors, but barely be able to follow the simplest lines of thought.

  At home I started spending evenings with a couple of neighbors who had found their niche in the world smoking joints. Edward, a thin, short Caltech physics grad, smoked away his boredom and moral qualms with a job doing weapons research, and Ramon—whom everyone called Ray—a garbage man, smoked to forget the smells he had been subjected to earlier in the day. I sat beside them, a twenty-seven-year-old has-been nervous about keeping the secret that he was, in reality, a never-was. Together, we’d watch reruns of Columbo, or The Rockford Files, secure in the knowledge that whether we paid attention or not, the bumbling detectives would always get their man.

  Meanwhile, winter came, and with it the new semester and the new year. By now I would see Feynman, back from his surgery, coming and going from his office down the hall. I figured if anyone could help me emerge from my creative drought, it would be my idol Feynman. His writings had first excited me about physics, and now fate had dropped me into the department just a few doors down from him. All I had to do was walk a few steps and knock on his door. Fortunately, with all my naïveté and self-doubt, I did have pluck, or chutzpah as my parents would say. Not even living legends were unapproachable. So Feynman, who despised psychology even more than philosophy, would soon become my leading advisor on both the philosophy and the mind of the scientist.

  V

  WHEN I FIRST SET eyes upon him, the image did not match the legend. Feynman was sixty-three—about ten years older than Murray—but he looked gaunt and aged. His long gray hair was thinning; his step lacking in energy. With my state of mind at the time I might have looked a bit like him, but Feynman’s malaise was unlike my own. It was common knowledge by then that Feynman was terminally ill. In his recent surgery he had had a widespread tumor entangling his intestines removed in a marathon fourteen-hour procedure. It had been his second cancer surgery.

  I stepped over to his office, knocked, and introduced myself. He was polite, and welcomed me. I had had no direct experience with death. It was hard for me not to feel pity, as I might for a deformed person I saw on the street. The thought of actually talking to a dying person made me uncomfortable. Strangely, I would find that being one did not seem to have the same effect on him. I could see right away that there was still an energy about him, a gleam in his eye. He may have had terminal cancer, but his spirit still zigzagged around the universe.

  Though my heart was pounding, I was surprised at the impression he made. He didn’t have that distancing sheen of brilliance that Murray had; in fact, there was nothing about him that indicated greatness. If I had run into him on the street, and hadn’t seen pictures, I might have thought he was a retired cab driver from Brooklyn. I had the impression that in his younger days he must have possessed a certain earthy sexuality. After we had exchanged a few words, he mumbled a “see-you-around” and looked back down at his work. I left.

  A few days later I bumped into Feynman outside the Lauritsen Lab.

  “Mlodinow, right?” I was flattered that he remembered, and happy he didn’t pronounce my name in some weird Russian way. I asked where he was going.

  “To the cafeteria.”

  “The cafeteria or the Athenaeum?” I asked. Unlike the elegant Athenaeum, a place favored by Murray—and most faculty—where the men often wore suits and the servers were students, the cafeteria back then was an unremarkable joint with food I imagined you might find in an army mess hall. It was usually referred to by its more descriptive nickname, “the Greasy.” Feynman gave me a look. Apparently, the Athenaeum wasn’t his style. He invited me to join him at the Greasy.

  The Caltech cafeteria in those days had a novel way of cooking their hamburgers. They would partially cook dozens of them around ten in the morning and leave them stacked at the back of the grill. When you ordered a burger, they would flip it off one of the stacks and more or less finish cooking it. As it turned out, this culinary technique meant that the kitchen had much in common with the microbiology lab, except that their hamburger was probably cheaper than the sterile agar used in the labs. We came in around two, near closing, by which time the burgers had been kept half-cooked and tepid for several hours. Still naïve in the ways of Caltech, I ordered two burgers, one with fries, the other with onion rings. For me, it was breakfast.

  We sat down. Feynman usually drew a crowd at the Greasy, but this late there wasn’t anyone else around. We sat in silence for a moment. I tried to think of something intelligent to say to break the ice. My mind was a blank. The feeling was a lot like one I’d have again many years later, accepting a computer game award in Cannes. Then, I was onstage, in a spotlight in front of thousands. I had uttered a few lines that I had prepared, and then made ready to walk offstage. But the beautiful French TV celebrity who acted as host surprised me with a question. I couldn’t think of anything to say to her, not even my name. It was as if the spotlight had saturated my neural circuits, making intelligent thought impossible. I wished I were pretty enough to charm everyone with my smile, then wave and walk off like a star. Instead, I just stood there embarrassed as she finally answered her own question.

  With Feynman I got off easy. He looked at my tray. Then he looked at me and smiled.

  “I u
sed to overeat,” he said. “If I really liked the food I’d eat so much I would feel uncomfortable. That was dumb. I don’t do it anymore.”

  “I think I can learn a lot from you,” I said, then realized how stupid it must have sounded.