The following is an exerpt from David Kaiser's Drawing Theories Apart, in which we find this section on Freeman Dyson's realization of the mathematical equivalence between two physical theories put forth by Richard Feynman and Julian Schinger while recovering from a stupor of exhaustion. It quotes a letter written by Dyson to his parents, which apparently is not digitized and is sitting in storage at Princeton University.

Soon it was not only Henry Bethe who delighted in Feynman’s company. Dyson began to spend more and more time talking with Feynman, and they became fast friends. Describing Feynman as “half genius and half buffoon, who keeps all physicists and their children amused with his effervescent vitality,” Dyson wrote home about his frequent chat sessions with Feynman chat sessions that roamed from quantum electrodynamics to Feynman’s love life and beyond. Feynman’s new diagrammatic techniques initially struck Dyson as they struck so many others as inscrutable: “Feynman is a man whose ideas are as difficult to make contact with as Bethe’s are easy,” Dyson explained to his parents; he found Feynman’s diagrams “completely baffling.” Yet Dyson had ample opportunity to learn more about Feynman’s difficult ideas during the spring semester, around the time that Feynman presented his new diagrammatic methods at the Pocono meeting. A few months later, Dyson received an even more intense dose of Feynmaniana when they drove from Cleveland to Albuquerque together, Feynman to visit a girlfriend and Dyson to do some sightseeing. The car trip gave Dyson the opportunity to see parts of the American Midwest and Southwest for the first time; he also got to share many intense hours deep in conversation with his new friend. Not all the talk focused narrowly on physics: in the midst of their “Odyssey,” as Dyson called it, flooding closed parts of Route 66 in Oklahoma and they had to scramble for lodging in “what Feynman called a ‘dive,’ viz. a hotel of the cheapest and most disreputable character.” (In Feynman’s less sanitized version, it was a brothel.) After their cross-country road trip, Feynman spent several weeks in New Mexico, where he continued to work on his new diagrammatic calculations, while Dyson made his way by bus to Ann Arbor, Michigan, for the annual summer school in theoretical physics, held during July and August.

The main attraction in Ann Arbor that summer was Julian Schwinger. Following his triumphant daylong presentation at the Pocono meeting on his own approach to rendering QED’s infinities harmless, Schwinger strode into town with an entourage of eager acolytes in tow. “Yesterday the great Schwinger arrived, and for the first time I spoke to him,” Dyson wrote home that summer. “His talks have been from the first minute excellent; there is no doubt that he has taken a lot of trouble to polish up his theory for presentation at this meeting. I think in a few months we shall have forgotten what preSchwinger physics was like.” Dyson listened to the lectures in the mornings and worked on his own research during the afternoons. His thoughts turned to ways of “tidying up” some details within Schwinger’s new formalism, which paid immediate dividends: “I was very glad of this, as it enabled me to speak to Schwinger and the other ‘big shots’ and get some ideas out of them.”

Thus, by early August 1948, Dyson and Dyson alone had spent intense time working face-to-face with both Feynman and Schwinger, talking in detail about their rival methods. After the summer school ended, Dyson took a bus trip to Berkeley to spend a few weeks relaxing and then began his journey back across the country, again making his way by bus. “On the third day of the journey a remarkable thing happened,” Dyson excitedly told his parents: “going into a sort of semi-stupor as one does after 48 hours of bus-riding, I began to think very hard about physics, and particularly about the rival radiation theories of Schwinger and Feynman.”

Gradually my thoughts grew more coherent, and before I knew where I was I had solved the problem that had been in the back of my mind all this year, which was to prove the equivalence of the two theories. Moreover, since each of the two theories is superior in certain features, the proof of the equivalence furnished incidentally a new form of the Schwinger theory which combines the advantages of both. This piece of work is neither difficult nor particularly clever, but it is undeniably important if nobody has done it in the meantime. So you can imagine that I became quite excited over it when I reached Chicago, and sent off a letter to Bethe announcing the triumph. I have not had time yet to write it down properly, but I am intending as soon as possible to write a formal paper and get it published.

As soon as he arrived at the Institute for Advanced Study that September, he set about writing his “magnum opus.”

“After a very brief visit to Cornell, to collect my various belongings, I settled down to work at writing up the physical theories I mentioned in the last letter,” Dyson reported to his parents near the end of September 1948, having just arrived in Princeton. “I found, as one often does when one comes to write, that the job was even bigger than I had imagined, and I was for about five days stuck in my rooms, writing and thinking with a concentration which nearly killed me. On the seventh day the paper was complete, and with immense satisfaction I wrote the number at the bottom of the last page.” He was clearly exhausted: “Having emerged from that, I feel I shall not do any more thinking for the rest of the year.” Through his toil, he had managed to demonstrate the mathematical though by no means conceptual equivalence between Schwinger’s and Feynman’s formalisms; this was no mean feat, he explained to his parents, since “Feynman and Schwinger talk such completely different languages, that neither of them is able to understand properly what the other is doing.” Worse still, no one else could understand what either of them was doing: neither had “published any moderately intelligible account of his work.” Feynman had published nothing at all on his new diagrams, and Schwinger had published only a two-page letter to the editor; the first of Schwinger’s long articles had only just been submitted from the Ann Arbor summer school, and would not appear in print until the middle of November. Thus, Dyson had to do more than simply demonstrate the equivalence of the two approaches in his own paper; he had to present the rudiments of both formalisms more or less from scratch “in itself a valuable service to humanity,” he mused to his parents. Dyson submitted his paper to the Physical Review in October 1948.