Genius_ The Life and Science of Richard Feynman - James Gleick [149]
Dyson gleefully retorted that he was crazy. Still, Feynman had caught the intuitive essence of the two-slit experiment, where an electron seems aware of every possibility.
Feynman’s path-integral view of nature, his vision of a “sum over histories,” was also the principle of least action, the principle of least time, reborn. Feynman felt that he had uncovered the deep laws that gave rise to the centuries-old principles of mechanics and optics discovered by Christiaan Huygens, Pierre de Fermat, and Joseph-Louis Lagrange. How does a thrown ball know to find the particular arc whose path minimizes action? How does a ray of light know to find the path that minimizes time? Feynman answered these questions with images that served not only for the novel mysteries of quantum mechanics but for the treacherously innocent exercises posed for any beginning physics student. Light seems to angle neatly as it passes from air to water. It seems to bounce like a billiard ball off the surface of a mirror. It seems to travel in straight lines. These paths—the paths of least time—are special because they tend to be where the contributions of nearby paths are most closely in phase and most reinforce one another. Far from the path of least time—at the distant edge of a mirror, for example—paths tend to cancel one another out. Yet light does take every possible path, Feynman showed. The seemingly irrelevant paths are always lurking in the background, making their contributions, ready to make their presence felt in such phenomena as mirages and diffraction gratings.
Optics students learned alternative explanations for such phenomena in terms of waves like those undulating through water and air. Feynman was—with finality—eliminating the wave viewpoint altogether. Waviness was built into the phases carried by amplitudes, like little clocks. Once, with Wheeler, he had dreamed of eliminating the field itself. That idea had proved fanciful. The field had lodged itself deeply in the consciousness of physicists. It was indispensable and it was multiplying—a new particle, such as the meson, meant a new field, like a new plastic overlay, of which the particle was a quantized manifestation. Still, Feynman’s theory retained the mark of its original scaffolding, though the scaffolding was long discarded. The actors were, more clearly than ever, particles. That became an attractive feature for physicists seeking help in visualization, in an experimental world dominated more and more by the cloud trails, the nomenclature, the behaviorism of particles.
Schwinger’s Glory
Feynman’s path integrals belonged to a loose kit of ideas and methods, a private physics that he had assembled but not organized. Much relied on guesswork or, as he said, “semi-empirical shenanigans.” It was all hodgepodge and purpose-driven, and he could barely communicate it, let alone prove it, even to his most sympathetic listeners, Bethe and Dyson. In the fall of 1947 he attended a formal lecture by Bethe on his approach to the Lamb shift. When Bethe concluded by stressing the need for a more reliable way of making the theory finite, a way that would observe the requirements of relativity, Feynman realized that he could compute the necessary correction. He promised Bethe an answer by the next morning.
By morning he realized that he did not know enough about Bethe’s calculation of the electron’s self-energy to translate his correction into the normal language of physics. They stood together at the blackboard for a while, Bethe explaining his calculation, Feynman trying to translate his technique, and the best answer they could reach diverged not modestly, like Bethe’s, but horrendously. Feynman, thinking about the problem physically, was sure it should not diverge at all.
In the days that followed, he taught himself about self-energy all over again. When he reexpressed his equations in terms of the observed, “dressed” mass of the electron instead of the theoretical, “bare” mass, the correction