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By Root 2182 0

point the central new tenet of field theory: “that two particles do not interact directly but, rather the interaction is explained as being caused by one of the particles influencing the field in its vicinity, which influence spreads until it reaches the second particle.” Electrons do not simply bounce off one another, that is. They plow through that magnificent ether substitute, the field; the waves they make then swish up against other electrons. Schwinger did not pretend to break ground in this paper. He showed his erudition by adopting “the quantum electrodynamics of Dirac, Fock, and Podolsky,” the “Heisenberg representation” of potentials in empty space, the “Lorentz-Heaviside units” for expressing such potentials in relatively compact equations. This was heavy machinery in soft terrain. The field of Maxwell, which brought electricity and magnetism together so effectively, now had to be quantized, built up from finite-size packets that could be reduced no further. Its waves were simultaneously smooth and choppy. Schwinger, in his first effort at professional physics, looked beyond even this difficult electromagnetic field to a more abstract field still, a field twice removed from tangible substance, buoying not particles but mathematical operators. He pursued this conception through a sequence of twenty-eight equations. Once, at equation 20, he was forced to pause. A fragment of the equation had grown unmanageable—infinite, in fact. To the extent that this fragment corresponded to something physical, it was the tendency of an electron to act on itself. Having shaken its field, the electron is shaken back, with (so the mathematics insisted) infinite energy. Dirac and the others had grudgingly settled on a response to this difficulty, and Schwinger handled it in the prescribed manner: he simply discarded the offending term and moved on to equation 21.

Julian Schwinger and Richard Feynman, exact contemporaries, obsessed as sixteen-year-olds with the abstract mental world of a scientist, had already set out on different paths. Schwinger studying the newest of the new physics, Feynman filling schoolboy notebooks with standard mathematical formulas, Schwinger entering the arena of his elders, Feynman still trying to impress his peers with practical jokes, Schwinger striving inward toward the city’s intellectual center, Feynman haunting the beaches and sidewalks of its periphery—they would hardly have known what to say to each other. They would not meet for another decade; not until Los Alamos. Long afterward, when they were old men, after they had shared a Nobel Prize for work done as rivals, they amazed a dinner party by competing to see who could most quickly recite from memory the alphabetical headings on the spines of their half-century-old edition of the Encyclopaedia Britannica.

As his childhood ended, Richard worked at odd jobs, for a neighborhood printer or for his aunt, who managed one of the smaller Far Rockaway resort hotels. He applied to colleges. His grades were perfect or near perfect in mathematics and science but less than perfect in other subjects, and colleges in the thirties enforced quotas in the admission of Jews. Richard spent fifteen dollars on a special entrance examination for Columbia University, and after he was turned down he long resented the loss of the fifteen dollars. MIT accepted him.

MIT

A seventeen-year-old freshman, Theodore Welton, helped some of the older students operate the wind-tunnel display at the Massachusetts Institute of Technology’s Spring Open House in 1936. Like so many of his classmates he had arrived at the Tech knowing all about airplanes, electricity, and chemicals and revering Albert Einstein. He was from a small town, Saratoga Springs, New York. With most of his first year behind him, he had lost none of his confidence. When his duties ended, he walked around and looked at the other exhibits. A miniature science fair of current projects made the open house a showcase for parents and visitors from Boston. He wandered over to the mathematics exhibit, and there,