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Genius_ The Life and Science of Richard Feynman - James Gleick [77]

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a Hamiltonian” for a system: if they could find one, then they could go ahead and calculate; if not, they were helpless. In Wheeler and Feynman’s view of direct action at a distance, the Hamiltonian method had no place. That was because of the introduction of time delays. It was not enough merely to write down a complete description of the present: the positions, momentums, and other quantities. One never knew when some delayed effect would hurtle into the picture out of the past (or in the case of Wheeler and Feynman, out of the future). Because past and future interacted, the customary differential-equation point of view broke down. The alternative least-action or Lagrangian approach was no luxury. It was a necessity.

With all this on his mind, Feynman went to a beer party at the Nassau Tavern. He sat with a physicist lately arrived from Europe, Herbert Jehle, a former student of Schrödinger in Berlin, a Quaker, and a survivor of prison camps in both Germany and France. The American scientific world was absorbing such refugees rapidly now, and the turmoil of Europe seemed more palpable and near. Jehle asked Feynman what he was working on. Feynman explained and asked in turn whether Jehle knew of any application of the least-action principle in quantum mechanics.

Jehle certainly did. He pointed out that Feynman’s own hero, Dirac, had published a paper on just that subject eight years before. The next day Jehle and Feynman looked at it together in the library. It was short. They found it, “The Lagrangian in Quantum Mechanics,” in the bound volumes of Physikalische Zeitschrift der Sowjetunion, not the best-read of journals. Dirac had worked out the beginnings of a least-action approach in just the style Feynman was seeking, a way of treating the probability of a particle’s entire path over time. Dirac considered only one detail, a piece of mathematics for carrying the wave function—the packet of quantum-mechanical knowledge—forward in time by an infinitesimal amount, a mere instant.

Infinitesimal time did not amount to much, but it was the starting point of the calculus. That limitation was not what troubled Feynman. As he looked over the few bound pages, he kept stopping at a single word: analogue. “A very simple quantum analogue,” Dirac had written. “… They have their classical analogues… . It is now easy to see what the quantum analogue of all this must be.” What kind of word was that, Feynman wondered, in a paper on physics? If two expressions were analogous, did it mean they were equal?

No, Jehle, said—surely Dirac had not meant that they were equal. Feynman found a blackboard and started working through the formulas. Jehle was right: they were not equal. So he tried adding a multiplication constant. Calculating more rapidly than Jehle could follow, he substituted terms, jumped from one equation to the next, and suddenly produced something extremely familiar: the Schrödinger equation. There was the link between Feynman’s Lagrangian-style formulation and the standard wave function of quantum mechanics. A surprise—by analogous Dirac had simply meant proportional.

But now Jehle had produced a small notebook. He was rapidly copying from Feynman’s blackboard work. He told Feynman that Dirac had meant no such thing. In his view Dirac’s idea had been strictly metaphorical; the Englishman had not meant to suggest that the approach was useful. Jehle told Feynman he had made an important discovery. He was struck by the unabashed pragmatism in Feynman’s handling of the mathematics, so different from Dirac’s more detached, more aesthetic tone. “You Americans!” he said. “Always trying to find a use for something.”

The Aura


This was Richard Feynman nearing the crest of his powers. At twenty-three he was a few years shy of the time when his vision would sweep hawklike across the breadth of physics, but there may now have been no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear to the senior physicists

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