by James Gleick
There Was Also Presented (by Feynman) …
Wheeler had arranged as rapid a news service as the available technology permitted. On his first day back in Princeton he pressed his graduate students into service as scribes. They reproduced his notes page by page onto mimeograph blanks and printed dozens of copies, turning their forearms magenta. For months this samizdat document served as the only available introduction to the new Schwingerian covariant quantum electrodynamics. Only a few pages were devoted to Feynman, with his “alternative formulation” and curious diagrams. Dyson read the Wheeler notes avidly. Bethe had tried to get him an invitation to Pocono (“you can imagine that I was highly pleased and flattered,” Dyson wrote his parents), but Oppenheimer refused to consider someone whose current caste was student.
Feynman himself was assigned the task of writing a nontechnical account of the Pocono meeting for a new trade journal for physicists, Physics Today—anonymously, he hoped. He explained renormalization à la Schwinger, concluding:
A major portion of the conference was spent in hearing and discussing these results of Schwinger. (((One conferee put it: “We did not have time to discuss a great deal, for we had to take time out to learn some physics.” He was referring to this work of Schwinger.)))
There was also presented (by Feynman) a theory in which the equations of electrodynamics are artificially altered so that all quantities including the inertia of the electron turn out finite. The results of this theory are in essential agreement with those of Schwinger, but they are not as complete.
In the same runner-up vein Feynman was asked to help select a winner for a new prize the National Academy of Sciences was awarding for “an outstanding contribution to our knowledge of the nature of light.” When Schwinger saw Feynman’s name on the list of judges, he inferred correctly that the prize was meant for him. What was quantum electrodynamics about, if not light, in all its many dresses?
No one had been more definitively impressed by Schwinger, and unimpressed by Feynman, than Oppenheimer. Awaiting him back in Princeton was a startling confirmation of Schwinger’s theory, in the form of a letter from a Japanese theorist, Shin’ichirō Tomonaga, whose claim to glory began with the words: “I have taken the liberty of sending you copies of several papers and notes …”
Japan’s physicists had just begun making significant contributions to the international community in the 1930s—it had been Hideki Yukawa at Kyōto University who first proposed that a massive, short-lived, undiscovered particle might act as a “carrier” of the nuclear force, binding protons together in the atom’s core—when the war isolated them utterly. Even with the war’s end, channels to occupied Japan opened slowly. News of the Lamb shift reached Kyōto and Tokyo not through American physicists and not through journals, but from a squib in a newsmagazine.
Tomonaga, a native of Tokyo and a graduate of Kyōto University, a classmate and friend of Yukawa, had been deeply influenced by Dirac; he belonged to a small group that translated Dirac’s famous textbook into Japanese. In 1937 he traveled to Germany to study with Heisenberg; returning at the war’s onset in 1939, he stopped briefly in New York to visit the World’s Fair. He worked out what he called a “super many time” theory, in which every point in the field had its own clock—a workable notion, he found, despite the seeming absurdity of trying to manipulate infinitely many time variables. In his thoughts on physics he traversed much of the ground covered by his European and American counterparts, but with a far greater sense of solitude, hardly diminished by his time in Germany. He recorded a dark mood in his diary from time to time:
After supper I took up my physics again, but at last I gave up. Ill-starred work indeed! … Recently I have felt very sad without any reason, so I went to a film… . Returning home I read a book on physics. I don’t understand it very well… . Why isn’t nature clearer and more directly comprehensible? … As I went on with the calculation, I found the integral diverged—was infinite. After lunch I went for a walk. The air was astringently cold… . All of us stand on the dividing line from which the future is invisible. We need not be too anxious about the results, even though they may turn out quite different from what you expect… .
His occasional emotional desolation paled in light of what faced him in the months after the surrender, when shortages of food and housing overshadowed all else in Japan. He made a home and an office in a battered Quonset hut on the Tokyo University grounds. He furnished it with mats.
Although Oppenheimer knew nothing of Tomonaga’s personal circumstances, he knew what he and his Los Alamos compatriots had wrought on Japan, and he also wished to preserve the internationalism of physics in the face of what suddenly seemed an American hegemony. He could hardly have been better placed to appreciate Tomonaga’s letter—clear evidence that a Japanese physicist had not just matched the essentials of Schwinger’s work but had anticipated it. Tomonaga had not published, and he had not created the entire Schwingerian tapestry, but he had been first. Oppenheimer immediately gave Tomonaga his imprimatur in a letter to each of the Pocono participants. “Just because we were able to hear Schwinger’s beautiful report,” he wrote, “we may better be able to appreciate this independent development.” For Dyson, working in Pocono’s aftermath to understand the new theories, the revelation of Tomonaga’s papers lay in what seemed a simple beauty. He thought that he now understood Schwinger and that not all Schwinger’s complications were necessary. Graduate students poring over the Pocono notes already suspected this, despite the acclaim their elders were awarding. Later Dyson quoted “an unkind critic” as having said, “Other people publish to show how to do it, but Julian Schwinger publishes to show you that only he can do it.” He seemed to strive for an exceptional ratio of equations to text, and the prose posed serious challenges to the Physical Review’s typesetters.
Schwinger occasionally heard what sounded like carping amid the applause: comments to the effect that he was a soulless Paganini, all flash and technique instead of music; that he was more mathematician than physicist; that he too carefully smoothed the rough edges. “I gather I stand accused,” Schwinger said later, “of presenting a finished elaborate mathematical formalism from which had been excised all the physical insights that provide signposts to its construction.”
He had removed the signposts. He never liked to show the rough pathways of his thinking, any more than he liked to let his audiences see notes when he lectured. Yet all his mathematical power could not have produced his joining of relativity and quantum electrodynamics if he had lacked the intuition of a physicist. Beneath the formalism lay a profound—and historically minded—conviction about the nature of particles and fields. To Schwinger renormalization was not just a mathematical trick. Rather it marked a mutation in physicists’ understanding of what a particle was. His central physical insight, had he expressed it in the compromised language of everyday speech, might have sounded like this:
Are we talking about particles or are we talking about waves? Until now, everyone has thought that their equations—the Dirac equation, for example, which is supposed to describe the hydrogen atom—referred directly to the physical particles. Now, in a field theory, we recognize that the equations refer to a sublevel. Experimentally we are concerned with particles, yet the old equations describe fields. When you talk about fields, you presume that you can describe, and somehow experience, exactly what goes on at every point in space at every time; when you talk about particles, you merely sample the field with measurements at occasional instants.
A particle is a cohesive thing. We know we have a particle only when the same thing stays there as time goes on. The very language of particles implies phenomena with continuity over space and time. Yet if you make measurements at only disconnected instants, how do you know there is a particle? Experiments probe the field only crudely—they look at large spaces over long times.
The essence of renormalization is to make the transition from one level of description to the next. When you begin
with field equations, you operate at a level when particles are not there from the start. It is when you solve the field equations that you see the emergence of particles. But the properties—the mass and the charge—that you ascribe to a particle are not those inherent in the original equations.
Other people say, “Oh, the equations have divergences, you have to cancel them out.” That is only the form, not the essence of renormalization. The essence lies in recognizing that the theories of Maxwell and Dirac are not about electrons, positrons, and photons but about a deeper level.
Cross-Country with Freeman Dyson
Feynman had a tendency to vanish with the end of the school year, leaving behind a vacuum populated by uncorrected papers, ungraded tests, unwritten letters of recommendation. Often Bethe covered for his lapses in the paperwork of teaching. Still, June might bring a tirade from Lloyd Smith, the department chairman:
Your sudden departure from Ithaca without completing the grades in your courses, especially those involving seniors who may thus be prevented from graduating, has caused the Department considerable embarrassment. I have begun to be somewhat apprehensive over what would appear to be a feeling of indifference concerning the obligations and responsibilities to the University …
Feynman would jot some grades—round numbers, none higher than 85—and then start doodling equations.
This June found him at the wheel of his secondhand Oldsmobile, rushing across the country at a constant 65 miles per hour. In the passenger seat Freeman Dyson eyed the scenery and occasionally wished Feynman would slow down. Feynman thought Dyson was a bit dignified. Dyson liked the role of foreign observer of the American scene: here was his chance to play Tocqueville peering at the wild West from the vantage point of Route 66. Missouri, the Mississippi River (thick and reddish-brown, just as he had imagined it), Kansas, Oklahoma—none of this struck him as very Western, actually. In fact it looked not unlike his rural corner of New York. He had decided that modern America resembled Victorian England, particularly in the attention devoted to furnishing middle-class homes and women. His destination was Ann Arbor, Michigan, where he intended to pursue Schwinger, who was presenting his work in a series of summer-school lectures. Feynman, meanwhile, was heading for Albuquerque to resolve an entanglement with a woman he had known at Los Alamos. (She was Rose McSherry, a secretary whom he dated after Arline’s death. Another of Feynman’s current attachments was needling him by calling McSherry his “movie queen.” Dyson’s guess was that he would marry her.)
Dyson realized that he was not taking the direct route to Ann Arbor, but he relished the chance to spend time with Feynman. No one interested him as much. In the months since Pocono, he had begun to think that his mission might be to find a synthesis of the difficult new theories of quantum electrodynamics—rival theories, as he saw it, though to most of the community the rivalry seemed lopsided. He had heard Feynman’s theory in informal blackboard sessions, and it still troubled him that Feynman was, as it seemed, merely writing down answers instead of solving equations in the normal manner. He wanted to understand more.
They drove, sometimes stopping for hitchhikers, more often maintaining a determined pace, and Feynman confided more in Dyson than he had done with any friend in his adult life. He startled Dyson with a grim outlook on the future. He felt certain that the world had seen only the beginning of nuclear war. The memory of Trinity, sheer ebullient joy at the time, haunted him now. Philip Morrison, his Cornell colleague, had published an admonitory description of an atomic blast on East 20th Street in Manhattan—Morrison had witnessed the Hiroshima aftermath and wrote this account in a horrifyingly vivid past tense—and Feynman could not meet his mother at a midtown restaurant without thinking about the radius of destruction. He could not shake a feeling that normal people, without the burden of his accursed knowledge, were living a pitiful illusion, like ants tunneling and building before the giant’s boot comes down. This was a classic danger sign—the feeling of being the only sane man, the only man who truly sees—but Dyson suddenly felt that Feynman was as sane as anyone he knew. This was not the jester he had first described to his parents. Dyson wrote later: “As we drove through Cleveland and St. Louis, he was measuring in his mind’s eye distances from ground zero, ranges of lethal radiation and blast and fire damage… . I felt as if I were taking a ride with Lot through Sodom and Gomorrah.”
As they drew closer to Albuquerque, Feynman was also thinking about Arline. Sometimes it occurred to him that her death might have left him with a feeling of impermanence. Spring flooding in the Oklahoma prairie closed the highway. Dyson had never seen rain fall in such dense curtains—nature as raw as these plainspoken Americans, he thought. The car radio reported people trapped in cars, drowned or rescued by boats. They pulled off the road in a town called Vinita and found lodging in a hotel of the kind Feynman knew all too well from his weekend trips to visit Arline: an “office” on the second floor, a sign reading, “This hotel is under new management, so if you’re drunk you came to the wrong place,” a hanging cloth covering the doorway to the room he shared with Dyson for fifty cents apiece. That night he told Dyson more about Arline than ever before. Neither of them forgot it.
They talked about their aspirations for science. Feynman cared far less than Dyson about his still-patchwork scheme for renormalizing quantum electrodynamics. It was his sum-over-histories theory of physics that claimed his passion. As Dyson saw, it was a grand vision and a unifying vision—too ambitious, he thought. Too many physicists had already stumbled in pursuit of this grail, including Einstein, notoriously. Dyson—more than anyone who heard Feynman at Pocono or attended his occasional seminars at Cornell, more even than Bethe—was beginning to see just how far Feynman sought to reach. He was not ready to concede that his friend could out-Einstein Einstein. He admired Feynman’s gall, the largeness of his dream, the implicit attempt to unify realms of physics that were more distant from one another than anything in human experience. On the largest scale, the scale of solar systems and galactic clusters, gravity reigned. On the smallest scale, particles still awaiting discovery bound the atom’s nucleus with unimaginably strong forces. Dyson considered it enough to walk the “middle ground,” the realm that after all encompassed everything in between: the furniture of everyday life, the foundations underlying chemistry and biology. The middle ground, where quantum theory ruled, extended to all phenomena that could be seen and studied without the help of either a mammoth telescope or a behemoth particle accelerator. Yet Feynman wanted more.
It was essential to his view of things that it must be universal. It must describe everything that happens in nature. You could not imagine the sum-over-histories picture being true for a part of nature and untrue for another part. You could not imagine it being true for electrons and untrue for gravity. It was a unifying principle that would either explain everything or explain nothing.
Many years later each man recalled their night in Vinita, Dyson showing how unshakably he revered his friend still, Feynman showing how he could use storytelling as a strategy—a dagger and a cloak. Dyson wrote:
In that little room, with the rain drumming on the dirty window panes, we talked the night through. Dick talked of his dead wife, of the joy he had had in nursing her and making her last days tolerable, of the tricks they had played together on the Los Alamos security people, of her jokes and her courage. He talked of death with an easy familiarity which can come only to one who has lived with spirit unbroken through the worst that death can do. Ingmar Bergman in his film The Seventh Seal created the character of the juggler Jof, always joking and playing the fool, seeing visions and dreams that nobody else believes in, surviving at the end when death carries the rest away. Dick and Jof have a great deal in common.
And Feynman:
The room was fairly clean, it had a sink; it wasn’t so bad. We get ready for bed.
He says, “I’ve got to pee.”
“The bathroom is down the hall.”
We hear girl
s giggling and walking back and forth in the hall outside, and he’s nervous. He doesn’t want to go out there.
“That’s all right; just pee in the sink,” I say.
“But that’s unsanitary.”
“Naw, it’s okay; you just turn the water on.”
“I can’t pee in the sink,” he says.
We’re both tired, so we lie down. It’s so hot that we don’t use any covers, and my friend can’t get to sleep because of the noises in the place. I kind of fall asleep a little bit.
A little later I hear a creaking of the floor nearby, and I open one eye slightly. There he is, in the dark, quietly stepping over to the sink.
And Dyson:
That stormy night in our little room in Vinita, Dick and I were not looking thirty years ahead. I knew only that somewhere hidden in Dick’s ideas was the key to a theory of quantum electrodynamics simpler and more physical than Julian Schwinger’s elaborate construction. Dick knew only that he had larger aims in view than tidying up Schwinger’s equations. So the argument did not come to an end, but left us each going his own way.
