Джеймс Глик - Genius - The Life and Science of Richard Feynman

In the end Bethe turned Oppenheimer around. He cast his vote explicitly with the Feynman theory and let the

audience know that he felt Dyson had more to say. He took Oppenheimer aside privately, and the mood shifted. By January, the war had been won. At the American Physical Society meeting Dyson found himself almost as much a hero as Schwinger had been the year before. Sitting in the audience with Feynman beside him, he listened as a speaker talked admiringly of “the beautiful theory of Feynman-Dyson.” Feynman said loudly, “Wel , Doc, you’re in.” Dyson had not even got a doctoral degree. He went on an excited lecture tour and told his parents that he was a certified big shot. The reward that lasted, however, was a handwritten note that had appeared in his mailbox in the dying days of the fal , saying simply, “ Nolo contendere. R.

O. ”

Dyson Graphs, Feynman Diagrams

It was the affair of Case and Slotnick at the same January meeting that brought home to Feynman the ful power of his machinery. He heard a buzz in the corridor after an early session. Apparently Oppenheimer had devastated a physicist named Murray Slotnick, who had presented a paper on meson dynamics. A new set of particles, a new set of fields: would the new renormalization methods apply?

With physicists looking inward to the higher-energy particles implicated in the forces binding the nucleus, meson theories were now rising to the fore. The flora and fauna of meson theories did seem to resemble quantum

electrodynamics, but there were important differences—

chief among them: the counterpart of the photon was the meson, but mesons had mass. Feynman had not learned any of the language or the special techniques of this fast-growing field. Experiments were delivering data on the scattering of electrons by neutrons. Infinities again seemed to plague many plausible theories. Slotnick investigated two species of theory, one with “pseudoscalar coupling”

and one with “pseudovector coupling.” The first gave finite answers; the second diverged to infinity.

So Slotnick reported. When he finished Oppenheimer rose and asked, “What about Case’s theorem?”

Slotnick had never heard of Case’s theorem—and could not have, since Kenneth Case, a postdoctoral fel ow at Oppenheimer’s institute, had not yet publicized it. As Oppenheimer now revealed, Case’s theorem proved that the two types of coupling would have to give the same result. Case was going to demonstrate this the next day.

For Slotnick, the assault was unanswerable.

Feynman had not studied meson theories, but he scrambled for a briefing and went back to his hotel room to begin calculating. No, the two couplings were not the same.

The next morning he buttonholed Slotnick to check his answer. Slotnick was nonplussed. He had just spent six intensive months on this calculation; what was Feynman talking about? Feynman took out a piece of paper with a formula written on it.

“What’s that Q in there?” Slotnick asked.

Feynman said that was the momentum transfer, a

quantity that varied according to how widely the electron was deflected.

Another shock for Slotnick: here was a complication that he had not dared to confront in a half-year of work. The special case of no deflection had been chal enge enough.

This was no problem, Feynman said. He set Q equal to zero, simplified his equation, and found that indeed his night’s work agreed with Slotnick. He tried not to gloat, but he was afire. He had completed in hours a superior version of a calculation on which another physicist had staked a major piece of his career. He knew he now had to publish.

He possessed a crossbow in a world of sticks and clubs.

He went off to Case’s lecture. At the end he leapt up with the question he had ready: “What about Slotnick’s calculation?”

Schwinger, meanwhile, found the spotlight sliding away.

Dyson’s paper carried a sting—Dyson, who had seemed such an eager student the summer before. Now this strange wave of Dyson-Feynman publicity. As Schwinger said later with his incomparably sardonic obliqueness,

“There were visions at large, being proclaimed in a manner somewhat akin to that of the Apostles, who used Greek logic to bring the Hebrew god to the Gentiles.”

Feynman now presented his own logic in his own voice.

He and Dyson appeared at a third and last smal gathering of physicists, this time at Oldstone-on-the-Hudson, New York, the final panel of the triptych that had begun at Shelter Island two years earlier. He published an extended set of papers—they would stretch over three years and one

hundred thousand words—that defined the start of the modern era for the next generation of physicists. After his path-integrals paper came, in the Physical Review , “A Relativistic Cut-Off for Classical Electrodynamics,”

“Relativistic Cut-Off for Quantum Electrodynamics,” “The Theory of Positrons,” “Space-Time Approach to Quantum Electrodynamics,” “Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction,” and “An Operator Calculus Having Applications in Quantum Electrodynamics.” As they appeared, the younger theorists who devoured them realized that Dyson had given only a bare summary of Feynman’s vision. They felt invigorated by his images—beginning with the unforgettable bombardier metaphor in the positron paper—and by his way of insisting on the plainest statements of physical principles in physical language:

The rest mass particles have is simply the work done in separating them against their mutual attraction after they are created… .

How would such a path appear to someone whose future gradually became past through a moving present?

He would first see …

No aspiring physicist could read these papers without thinking about what space was, what time was, what energy was. Feynman was helping physics live up to the special promise it made to its devotees: that this most fundamental of disciplines would bring them face to face with the primeval questions. Above al , however, to young physicists

the diagrams spoke loudest.

Feynman had told Dyson, with a slight edge, that he had not bothered to read his papers. “Feynman and I real y understand each other,” Dyson wrote home cheerily. “I know that he is the one person in the world who has nothing to learn from what I have written; and he doesn’t mind tel ing me so.” Feynman’s students, however, sometimes noticed what seemed to them an undercurrent of anger in the pointed comments he would make about Dyson. He had started hearing about Dyson’s graphs—irritating. Why graphs ? he asked Dyson. Was that the mathematician in him, putting on airs?

Feynman’s space-time method had other antecedents besides Dyson’s graphs, as it happened. A 1943 German textbook by Gregor Wentzel contained a paral el depiction of a particle exchange process in beta decay. A Swiss student of Wentzel’s, Ernst Stückelberg, had developed a diagrammatic approach that even embraced the conception of time-reversed positrons; parts of this he published, in French, and parts were returned as unpublishable. (Wentzel himself was the unimpressed referee.) Their diagrams showed glimmerings of the style of visualization that Feynman now brought to fruition. His own ful -dress version final y appeared in a paper he sent off in late spring 1949. “The fundamental interaction”—an image that would burn itself into the brains of the next generation of field theorists—showed two electrons interacting by exchanging a single photon.

A diagram from a little-known 1941 paper of Ernst Stuckelberg, showing aversion of time reversal in particle trajectories.