Toichiro Kinoshita: the theorist whose calculations of g-2 shed light on our understanding of nature

In both his personal and his professional life, the pioneering theoretical physicist Toichiro “Tom” Kinoshita forged the steadiest of paths through the most tumultuous of times. Born on 23 January 1925 in Tokyo, Japan, he spent the bulk of his career in the US where he played a trailblazing role in the development of quantum electrodynamics (QED). Most notably, his calculations of one of its key constants – g-2 – helped make QED the most precise theory in the history of physics.

Kinoshita, who died on 23 March 2023 aged 98, was no stranger to me. He was the father-in-law of a close friend and I had known him for almost three decades. In fact, I was fortunate to be able to talk with Kinoshita in depth about his long and fruitful career during an eight-hour oral-history interview that I carried out in 2016 for the Niels Bohr Library and Archives of the American Institute of Physics.

Japanese roots

As I discovered during our conversation, Kinoshita was the heir to a family of rice-farm owners who expected their male child to take over the family business. Their plans were disrupted by Japan’s role in the Second World War, which had already begun by the time Kinoshita was a teenager. Most of his peers were drafted to serve in the military, many never to return.

But Kinoshita was lucky. The Japanese military wanted those who had a talent for physics to calculate bomb trajectories for artillery barrages at the battle front. The authorities therefore pushed Kinoshita through a tightly compressed version of his high school and college curriculum at the University of Tokyo. Along the way, he learned advanced physics from mentors who taught articles, smuggled into Japan by submarine, that had been written by Werner Heisenberg and other German physicists.

Kinoshita learned advanced physics from mentors who taught articles, smuggled into Japan by submarine, that had been written by Werner Heisenberg and other German physicists

In August 1945, while on his university summer break, Kinoshita was at home with his parents in the city of Yonago when he heard on the radio that Hiroshima, which lay about 125 km to the south, had been flattened. As he told me in our interview, Kinoshita knew – from the magnitude of the explosion – that this was no ordinary bomb, but one that had to be tapping atomic energy.  “I knew what atomic energy can do, so I thought immediately this must be an A-bomb,” he said.

A few days later he was at Shinjuku train station in Tokyo when everyone was unexpectedly instructed to stay put for important news. In what was a highly unusual move, the Japanese emperor came on the public address system to announce that Japan had surrendered. Kinoshita was relieved, as others around him were too; like so many Japanese people he was afraid of and appalled by the war begun by his country’s military leaders. “Wow, that’s good. I don’t have to die,” he recalled thinking.

Hundreds of thousands of American troops arrived a few weeks later and occupied the country. The new US-installed government pushed through a nationwide land-reform programme. The Kinoshita family’s land was seized and distributed among its sharecroppers, leaving Kinoshita with no inheritance. Strange as it may seem, he was thrilled because his sudden poverty freed him of his family’s expectations that he would become a landlord of rice farms. Instead, he would be able to pursue physics.

Surviving on grants from the University of Tokyo and from teaching physics classes at another nearby university, Kinoshita graduated in 1947 before going on to do a PhD. His mentor was Sin-Itiro Tomonaga, who later shared the 1965 Nobel Prize for Physics with Richard Feynman and Julian Schwinger. Tomonaga brought Kinoshita to the attention of Robert Oppenheimer, the US physicist who had headed up the Manhattan atomic-bomb project.

Oppenheimer in turn arranged for Kinoshita and his colleague Yoichiro Nambu – another future Nobel laureate – to be postdocs at the Institute for Advanced Study (IAS) in Princeton, New Jersey. Kinoshita could, however, barely scrape together the money for the passage and he was forced to take a cargo boat from Tokyo to Seattle. He also had to leave behind his wife Masako or “Masa” Kinoshita (née Matsuoka) – a former student in one of his classes whom he had married in 1951. Her wealthy parents, members of Japan’s small Marxist community, had been jailed during the war, then lost everything when Allied bombs destroyed their family business.

From Seattle, Kinoshita visited labs on the US west coast, including the Lawrence Berkeley Laboratory and the California Institute of Technology. Travelling by bus and train, he headed east across the Rockies, visiting first Denver and then Enrico Fermi’s lab in Chicago. Eventually he arrived in Princeton, with his wife joining him in 1953. Later that year he stayed with a landlady who couldn’t pronounce “Toichiro” and so dubbed him “Tom” – a name that was to stick for the rest of his life.

Wobbly foundations

In 1956 – after two years at the IAS and another at Columbia University in New York – Tom and Masa ended up at Cornell University, where he stayed for the rest of his career. There, Masa practised a traditional Japanese textile artform known as kumihimo, or “gathered threads”, giving workshops in the US and Japan, and publishing a monumental, 360-page book on the subject in 1994. She rediscovered and developed an archaic and nearly forgotten form of kumihimo that involved complex loops, redeploying it using her background in mathematics.

In 1962 Kinoshita visited CERN on a Ford Foundation fellowship. On the second day of his visit to Geneva, he joined a lab tour, and – while on the very first stop – found himself mesmerized by a graph that experimentalists at the Proton Synchrotron had tacked to the wall. Having measured the way muons wobble in a magnetic field, they wanted to know how their findings tallied with the theoretical value and were seeking someone who could calculate it.

Kinoshita was stunned by the graph, which reminded him of aspects of the research into QED he had carried out with Tomonaga during the war.  He dropped out of the tour, went to the library, and worked the rest of the night. The next morning he returned to the Proton Synchrotron and told the experimentalists, “I know how!”

It was exciting work, for the number was intimately woven into the foundations of QED. That theory conceives of particles as spinning magnets, with the ratio of their magnetic moments to their spin known as g. In the simplest form of quantum mechanics, g has a value of exactly 2. But reality had to be different, for muons are tugged by traces of all other particles – known and unknown, leptons and hadrons – each of which slightly affects the wobble.

Given that QED was a blueprint incorporating everything that theorists knew about, the difference between the experimentally determined value of g and 2 therefore measured the comprehensiveness and accuracy of the entire theoretical architecture of QED. In other words, measuring g-2 could reveal if that architecture was sound, even if it couldn’t tell you the exact location of any defect.

In fact, g-2 was so fundamental to QED that if nature contained new physics – particles or forces not yet discovered, and thus not in the theory – they would show up as the difference between the theoretically predicted amount and the value measured in experiments. Rarely does it make sense to go all out in pursuing calculations of a number; nobody measures recipe ingredients to thousandths of a gram or petrol to billionths of a litre. But g-2 is different. From a muon’s wobble, you can get precision.

The calculations, though, were incredibly hard, because they were unsolvable and thus had to proceed in a series of successive, ever more precise approximations. What’s more, each newly discovered particle and force had to be incorporated. Physicists commonly expresses this complexity in terms of the “Feynman diagrams” of each possible interaction, with each diagram corresponding to a series of long equations, and Kinoshita had to evaluate hundreds and even thousands of them.

When physicists say that QED is the most precisely calculated theory in the history of science, they can thank Kinoshita

Back then, Kinoshita worked alone and by hand in calculating g-2. As the years went by, he took on more helpers and used more powerful computers. Kinoshita eventually spent over half a century as a pioneer in the physics use of supercomputers and became one of their biggest users as he summed six, eight and then 10 orders of Feynman diagrams to calculate g-2 ever more precisely. When physicists say that QED is the most precisely calculated theory in the history of science, they can thank Kinoshita.

Meanwhile, a series of ever larger and more precise experiments were built to compare the experimental value with his: a sequence of three at CERN, one at Brookhaven National Laboratory and another at Fermilab. Sometimes the results were close to Kinoshita’s number, spreading fear among physicists that there was no new physics, while at other times the results were so far off from the predicted value that experimentalists and theorists alike were thrilled.

Kinoshita became an increasingly high-profile physicist as the go-to person for understanding the foundations of the Standard Model of particle physics. In fact, g-2 became an ever more high-profile number, as the world’s most powerful accelerator, the Large Hadron Collider, was eking out fewer and fewer surprises.

Despite officially retiring from Cornell in 1995, Kinoshita remained active in physics. In 2018, aged 93, he published a paper in Physical Review D (97 036001) refining his calculation of g-2 to the 10th order. His final paper – on the general theory of g-2 calculations to all orders –appeared the following year in Atoms (7 28). His student and close collaborator Makiko Nio, from RIKEN research lab in Japan, is one of the physicists now continuing the work.

The critical point

Quiet, methodical and meticulous, Kinoshita always appreciated or would contribute to the humour in every situation. Late in his life, friends learned to look for the sign that he was about to make a witty remark: an almost imperceptible uptick at both corners of his mouth, and a slight deepening of the wrinkles that fringed them. Eventually, Kinoshita moved away from Cornell, reluctantly, to a house in Amherst, Massachusetts, built by the architect Ray Kinoshita, one of his three daughters.

She had designed a house for herself with a separate living area for her parents, with shoji screens, open shelving and a wooden deck looking out into the woods, similar to the living quarters they had been accustomed to. The University of Massachusetts made Kinoshita an adjunct and gave him an office, where he showed up almost every day until COVID hit.

Admiring colleagues periodically put Kinoshita forward for a Nobel prize. He never received it, surely because his contributions, though indispensable to contemporary physics, are difficult to label. Physicists, however, benefit hugely from people like Kinoshita, who are intimately familiar with the resources, methods and techniques that underpin their field. Such physicists propel the discipline forward, yet cannot be easily pigeon-holed as discoverers or theory-creators. Kinoshita was like a reliable and trustworthy engineer who gives you the confidence that the house you and your entire community are living in won’t collapse.

Masa sadly died last year, and Tom soon after. The two will be buried together in Ithaca, near Cornell. Their headstone has been designed by their daughter Ray and by Ray’s own daughter Emilia Kinoshita, a designer and materials researcher. It will feature a blend of Feynman diagrams and kumihimo patterns, embodying the deepest shapes and rhythms of the unruly world that Masa and Tom lived through and explored.