In any case, the miserable economy did not allow the luxury of experimental research. Tomonaga was living with his family in a laboratory, half of which had been bombed to bits. Nambu arrived at the University of Tokyo as a research assistant and lived for three years in a laboratory, sleeping on a straw mattress spread over his desk (and always dressed in military uniform for lack of other clothes). Neighboring offices were similarly occupied, one by a professor and his family.
A Hungry Peace
Getting food was everyone’s preoccupation. Nambu would sometimes find sardines at Tokyo’s fish market, which rapidly produced a stench because he had no refrigerator. On weekends he would venture to the countryside, asking farmers for whatever they could offer.
Several other physicists also used the room. One, Ziro Koba, was working with Tomonaga’s group at Bunrika on the self-energy problem. Some of the officemates specialized in the study of solids and liquids (now called condensedmatter physics) under the guidance of Kotani and his assistant Ryogo Kubo, who was later to attain fame for his theorems in statistical mechanics. The young men taught each other what they knew of physics and regularly visited a library set up by MacArthur, perusing whatever journals had arrived.
At a meeting in 1946 Sakata, then at Nagoya University—whose physics department had moved to a suburban primary school—proposed a means of dealing with the infinite self-energy of the electron by balancing the electromagnetic force against an unknown force. At the end of the calculation, the latter could be induced to vanish. (At about the same time, Abraham Pais of the Institute for Advanced Study in Princeton, N.J., proposed a similar solution.) Although the method had its flaws, it eventually led Tomonaga’s group to figure out how to dispose of the infinities, by a method now known as renormalization.
This time the results were published in Progress of Theoretical Physics, an English-language journal founded by Yukawa in 1946. In September 1947 Tomonaga read in Newsweek about a striking experimental result obtained by Willis E. Lamb and Robert C. Retherford of Columbia University. The electron in a hydrogen atom can occupy one of several quantum states; two of these states, previously thought to have identical energies, actually turned out to have slightly different energies.
Right after the finding was reported, Hans Bethe of Cornell University had offered a quick, nonrelativistic calculation of the “Lamb shift,” as the energy difference came to be known. The effect is a finite change in the infinite selfenergy of the electron as it moves inside an atom. With his students, Tomonaga soon obtained a relativistic result by correctly accounting for the infinities.
Their work strongly resembled that being done, almost at the same time, by Julian S. Schwinger of Harvard University. Years later Tomonaga and Schwinger were to note astonishing parallels in their careers: both had worked on radar, wave propagation and magnetrons as part of their respective war efforts, and both used Heisenberg’s theory to solve the same problem. The two shared a Nobel Prize with Richard Feynman in 1965 for the development of quantum electrodynamics. (Feynman had his own idiosyncratic take—involving electrons that moved backward in time—which Freeman Dyson of the Institute for Advanced Study later showed was equivalent to the approach of Tomonaga and Schwinger.) And both Tomonaga’s and Schwinger’s names mean “oscillator,” a system fundamental to much of physics.