Sin-Itiro Tomonaga

Shin’ichirō Tomonaga, usually cited in English as Sin-Itiro Tomonaga, was born in Tokyo on March 31, 1906, the eldest son of the philosopher Tomonaga Sanjūrō. The household ran on books. His father translated Kant into Japanese, edited a journal of philosophy, and eventually held a chair at Kyoto Imperial University. The boy who grew up listening to dinner-table arguments about ethics and metaphysics turned, in the end, toward physics, but the habit of patient definitional work, of asking what a concept actually means before computing anything with it, would mark his theoretical style for the rest of his life. He entered Kyoto Imperial University in 1926 and found himself sitting next to a quiet, intense classmate named Hideki Yukawa. The two of them, almost the same age and almost the same temperament, would become the cornerstones of Japanese theoretical physics.

After graduating in 1929 Tomonaga stayed on at Kyoto as an unpaid assistant for three years, then in 1931 left for Tokyo to join the spectroscopy group that Yoshio Nishina had set up at the new Riken institute. Nishina had studied under Niels Bohr in Copenhagen, had co-discovered the Klein-Nishina formula for Compton scattering, and was determined to import the new quantum mechanics wholesale into Japan. The Riken group became, in effect, Japan’s Copenhagen. Tomonaga read Heisenberg, Dirac, and Pauli alongside Nishina and translated the latest German papers for the rest of the lab. In 1937 a Riken fellowship sent him to Leipzig, where he spent two years inside Werner Heisenberg’s research group, working on the quantum theory of nuclear matter. He had crossed half the world to study with the man whose 1925 paper had founded the entire subject.

Tomonaga was born in Tokyo in 1906. He was the second child and eldest son of a Japanese philosopher, Tomonaga Sanjūrō. He entered the Kyoto Imperial University in 1926. Hideki Yukawa, also a Nobel laureate, was one of his classmates during undergraduate school. During graduate school at the same university, he worked as an assistant in the university for three years. In 1931, after graduate school, he joined Nishina's group in RIKEN. In 1937,…

The Leipzig years ended in 1939 when the outbreak of war in Europe forced Tomonaga home. He defended a doctoral thesis at the University of Tokyo on the work he had begun in Germany, took up a professorship at the Tokyo University of Education, and then watched as the Pacific war closed Japan off almost completely from the rest of the international physics community. Letters stopped arriving. Journals stopped arriving. The cyclotron at Riken was eventually destroyed by occupation forces and thrown into Tokyo Bay. Tomonaga and his small group of students worked through the entire war in a kind of intellectual quarantine, sustained by what they had brought home from Europe and by their own ingenuity.

In that quarantine, between 1941 and 1943, Tomonaga did the work that would eventually win the Nobel Prize. He was thinking about a deep problem in quantum electrodynamics. The original 1929 formulation by Heisenberg and Pauli treated time as a single global variable, the same instant for every point in space, which was natural in non-relativistic physics but awkward in a relativistic theory where simultaneity itself depends on the observer. Tomonaga rebuilt the theory using what he called the super-many-time formalism: instead of a single time coordinate, every point in space was given its own local time, and the state of the field was specified along an arbitrary spacelike surface. The equations now treated space and time symmetrically. The covariance of the theory, the property that all observers see the same physics, became manifest rather than something one had to check by hand. He published the paper in 1943, in Japanese, in Bulletin of I.P.C.R. Research. Almost no one outside Japan saw it.

When the war ended in 1945, Tokyo was rubble. Tomonaga’s group reassembled in shells of buildings, sharing chalk and writing on scraps of paper. Through the late 1940s he and his students pushed the super-many-time formalism into a tool for computation. In 1948 they reopened a 1939 paper by Sidney Dancoff that had attempted, and failed, to show that the divergent integrals in quantum electrodynamics could be made finite by absorbing them into renormalized charges and masses. Dancoff had made an arithmetic mistake; he had dropped one term in the perturbation series, and his cancellation had not quite worked. Tomonaga, applying his manifestly covariant machinery, redid the calculation, found the missing term, and showed that the cancellation went through cleanly. The infinities of QED were not signs that the theory was wrong, they were signs that one was asking the wrong questions about it. Reorganize the questions in terms of the masses and charges actually measured in the laboratory, and finite answers emerged. He used the method to compute the Lamb shift in hydrogen, a tiny splitting in the spectrum that Willis Lamb had measured experimentally only the year before.

Tomonaga did not know it, but in Cambridge, Massachusetts, Julian Schwinger had reached the same conclusion by a different route, and in Ithaca, Richard Feynman had reached it by a third. The three of them, working independently on three continents, with almost no contact during the war years, had each found a way to extract finite predictions from QED. Tomonaga’s paper, mailed to Robert Oppenheimer at the Institute for Advanced Study in 1948 as a courteous summary of what the Japanese group had been doing, was the announcement to the rest of the world. Oppenheimer read it, recognized immediately what it was, and pressed the editors of Physical Review to publish a translation. In a now-famous gesture, Oppenheimer also wrote to the Pocono Conference of 1948 (where Schwinger and Feynman had presented their own approaches to a sometimes-baffled American audience) and told them that a Japanese physicist had been ahead of all of them for years.

Tomonaga came to Princeton in 1949 at Oppenheimer’s invitation, met Schwinger and Feynman in person, and gave a series of lectures at the Institute for Advanced Study that left no doubt his super-many-time method was equivalent to the American approaches. Freeman Dyson, then a young Englishman at the Institute, was meanwhile doing the work that would unify all three formalisms into a single computational machinery (the Feynman diagram), but in those first months it was Tomonaga’s clarity that gave the field a vocabulary. He returned to Japan the following year, having declined a permanent position in America, because his students needed him and Japanese physics needed to be rebuilt.

The next two decades he spent doing exactly that. He took the leadership in founding the Institute for Nuclear Study at the University of Tokyo in 1955. He served as president of the Tokyo University of Education. He sat on government committees, fought for research funding, and oversaw the training of a generation of Japanese physicists who would build the institutions that today host KEK and Kamiokande and the experiments that detected neutrino oscillations. Along the way he also did notable physics of his own. The Tomonaga-Luttinger liquid, a model of one-dimensional interacting electrons that he proposed in 1950, became the foundational example of non-Fermi-liquid behavior and is still taught in every graduate condensed-matter course. He wrote a textbook, Quantum Mechanics, in two volumes, in Japanese, that an entire generation of Japanese physics students learned from.

The Nobel Prize was announced on October 21, 1965. Tomonaga was sixty years old. The award was shared with Schwinger and Feynman for what the citation called fundamental work in quantum electrodynamics with deep-ploughing consequences for the physics of elementary particles. Tomonaga was in hospital when the call came, recovering from a fall, and the official photograph from the press conference shows him sitting up in a hospital bed with a polite, slightly embarrassed smile. He delivered his Nobel lecture by recording, having his student deliver it for him in Stockholm.

In 1976 the Japanese government awarded him the Grand Cordon of the Order of the Rising Sun. He had by then become quietly central to Japanese public life as the elder statesman of science, a man who would write essays for newspapers on the dangers of nuclear weapons and on the cultural meaning of theoretical research. He spent his last years writing a popular book about the spin of the electron, working from his hospital bed, dictating to his wife when he was too weak to hold a pen. He died of throat cancer in Tokyo on July 8, 1979.

What Tomonaga gave the quantum story was a particular kind of patience. Where Schwinger’s papers were dense thickets of formalism and Feynman’s were brilliant flashes of pictorial insight, Tomonaga’s were patient, definitional, almost philosophical in their care about what concepts meant before they were used. He took the time, alone in a country cut off from the world, to ask what it would mean for a quantum theory to look the same to every observer, and he answered the question well enough that when the war ended and the borders reopened, what he had built fit exactly into what the rest of the world had been groping toward. The renormalization of QED is the joint property of three men, but the manifest covariance of the resulting theory, the way every equation now visibly respects relativity, is in a deep sense Tomonaga’s gift. He is the lecturer who built the same building as Schwinger and Feynman, working in solitude with smaller materials, and who arrived at the door at exactly the right time.

Sin-Itiro Tomonaga taught quantum field theory to think relativistically without pretending to.