# Stueckelberg

We could not count ourselves among the old baron’s friends; we met him only once, at his apartment in the old town of Geneva, on a frigid gray day in February, 1984. A discreet brass plate outside the door bore the words: E. C. G. Stueckelberg, 20 rue Henri Mussard. Stueckelberg’s wife ushered us into a close, dark, oppressively hot office, and left to tell her husband, whom she referred to as the “professor,” of our arrival. Lighted only by a window facing the sleet-gray foothills of the Jura Mountains, the small room was jammed with the impedimenta of Victorian life: grand piano, rolltop desk, oversized sofa piled with wooden boxes. Portraits of Stueckelberg’s titled ancestors marched across the walls, their frames done in faded gilt and black. Scattered everywhere were hundreds of books: philosophy, physics, biology, theology, and genealogy; Goethe, Swinburne, and Pauli; English, French, German, and Danish; a life’s accumulation of learning, heaped in voluptuous and dusty confusion.

Stueckelberg appeared in the doorway, supporting himself on two canes. His sport coat hung on him slackly; plastic bags of tobacco and pipe cleaners were taped to his canes and on the armrest of his chair, his hair was mostly gone. The window light played across his long, angular face, the features thinned by his long fight with gravity. His fumbled in the bags and, after a few moments, extracted a fat, solid meerschaum pipe. “I’m living entirely on medicaments,” he said suddenly. “I have terrible athrosis, arthritis, whatever you call it.” He had spoken English rarely since he taught at Princeton a half-century before. From his shirt he withdrew a thick pair of glasses. A match flared; he sucked the pipe into smoky life with evident satisfaction.

Ernst Carl Gerlach Stueckelberg, Baron Souverain of the Holy Roman Empire of the Teutonic Nations of Breidenbach at Breidenstein and Melsbach, professor of particle physics at the universities of Geneva and Lausanne, and the man who just may have first renormalized quantum electrodynamics, was born in Basel on February 1, 1905. His father’s family had been citizens of the canton since the fourteenth century; his mother was the baroness of a minute, forgotten fiefdom in central Germany. Stueckelberg acquired his Ph. D. in Munich at the age of twenty-two, under the aegis of Arnold Sommerfeld. Sommerfeld’s name was sufficient to win him a post at Princeton University, in Princeton, New Jersey, where he taught until the Depression forced the school to let him go.

Once back in Switzerland, Stueckelberg had the first bit of what was to be a long run of misfortune. He discovered that even though he had been an associate professor at Princeton, he did not have the academic qualifications to teach in Switzerland, and thus was obliged to write another thesis. For many years after, he could find a job only as a Privatdozent, a poorly paid teaching assistant, at the University of Zürich. To make the matters worse, he foolishly invested and lost the considerable wealth that belonged to his first wife, whom he married in 1931. Facing bankruptcy, he was forced to go into the military service to earn his keep, further delaying his academic career and making it difficult to leave Switzerland, something of a backwater, to meet his colleagues. Under considerable financial and personal pressure, Stueckelberg began to exhibit symptoms of what would today be called manic-depressive behavior. Most of the time he was rational, even brilliant, but occasionally he would feel a fit coming on and pack himself off to the asylum for a few weeks. Over the years, he had a score of different treatments, including electroshock therapy. Nothing helped.

Personal troubles notwithstanding, he gradually managed to acquire a small reputation for the originality and difficulty of his work. Unfortunately, the reputation has to be spread by word of mouth, because many of Stueckelberg’s most important thoughts were dismissed out of hand by his colleague in Zürich, Wolfgang Pauli. He predicted the first of the hundreds of subatomic particles discovered shortly before and after the war, but did not publish the idea after Pauli told him it was ridiculous. (Later, the Japanese physicist Hideki Yukawa received a Nobel Prize for this idea.)

When Stueckelberg did publish, his papers were written in a convoluted style that not even Pauli could understand; they were further complicated by his habit, not uncommon among the most mathematically inclined theorists, of invented a special notation to replace the helter-skelter of mathematical symbols that is the common language of physics. Stueckelberg switched the ordinarily used terms for variables with those for parameters, put the indices on the opposite side of the symbols, and filled his equations with an incomprehensible forest of curved arrows and colored letters. Moreover, his papers were usually in French and published in the venerable but not widely read Swiss journal Helvetica Physica Acta. “I practically always published there,” he told us in the course of a long conversation. “It was easy—also, my secretary knew only French. This was one reason that my papers were never read. At that time, German and English were common languages for physics, but French was not. I also must admit that when I reread my papers later on, I saw that they were very complicated. I don’t know why, but I had a very complicated style. By the way, my friend—he has since died—Professor [Jean] Wiegle always put on the introduction and the summary, and these are understandable.”

Sometimes, too, he courted obscurity by his enthusiasm for questionable research programs. Convinced that all reality should be described by real numbers such as one, three-sevenths, and the square root of two, Stueckelberg devoted years to a quixotic attempt to eliminate imaginary numbers, such as the square root of minus one, from the equations of quantum theory. Unfortunately, imaginary numbers, whatever the difficulty one has in picturing them, are a central feature of contemporary physics, as firmly embedded in modern theory as pi in geometry. In the midst of such dubious schemes, he would sometimes toss out another, almost unrelated idea of fundamental import. As an aside to a paper on the atomic nucleus, for example, he postulated that the number of “heavy particles,” by which he meant the protons and neutrons, in the Universe never changed. If they could decay into other, lighter particles, matter itself would be unstable, even so slightly radioactive, and the world as we know it would eventually disintegrate. Testing the validity of the old man’s postulate is, in a sense, the purpose of the experiment in the salt mine beneath the shore of Lake Erie.

In the mid-1930s, he began to consider the divergences in electrodynamics. The infinities became a focal point of Stueckelberg’s career; he lavished years after their removal. Even decades later, when we met him, he face came alight when he discussed his theoretical strategems, the shortcuts he he had devised, the cutoffs and approximations he had brewed. Reciting equations from memory, he traced their symbols in the air with small movements of his long, tobacco-stained fingers. Profligate with his ideas, he followed two separate tracks, a quantum and a classical approach. Each was idiosyncratic: nether was understood; both were ignored. He explained his ideas to Pauli and Weisskopf; neither understood the presentation. They left Switzerland, and Stueckelberg, who was still in the army, was almost totally isolated from physics. Nonetheless, he apparently wrote up a lengthy paper—in English, for once—that outlined a complete and correct description of the renormalization procedure for quantum electrodynamics. Sometime in 1942 or 1943, he apparently mailed it to the Physical Review. It was rejected. “They said it was not a paper, it was a program, an outline, a proposal,” Stueckelberg remembered. “Afterward, I was told that our friend and teacher, Gregor Wentzel—he was the expert [referee]—he got my paper.” He rejected it? “Oh, it was done in an extremely obscure style,” he said. Stueckelberg was not a bitter man. “Later, he took the manuscript and wanted to have it published to show that I got it before.” We asked if he had the manuscript, which would help him establish priority. “I never cared much about that question,” he replied. “I don’t know what happened to the original copy. I lost it, it completely disappeared.”

War swept over Europe. Even in neutral Switzerland, Stueckelberg was mobilized, although he obtained special dispensation from the army to teach his seminar every other week. It was his only contact with science. Nonetheless, he struggled to carry out the program rejected by the Physical Review. By the end of the war, in 1945, he seems to have done it.

The triumph, if there was one, was short-lived. He wife divorced him a year later. Long before, he had agreed to her family’s demand for a marriage contract; now he courted ruin when he was forced to restore the fortune he had lost. When there was time between his need to scare up money and his sessions in the hospital, he wrote up bits and pieces of his ideas. Eventually they were presented in a complete form in a chapter of the thesis of one of his students, Dominique Rivier. But by then Schwinger had come out with his program, and Stueckelberg, who had the ideas first, published afterward.

He continued to do important work. In 1951, for example, he and his student, André Petermann, invented something called the renormalization group, which is now essential to the construction of grand unified theories. Stueckelberg brought a dog, Carlo III, to seminars at CERN, the new particle accelerator laboratory outside Geneva. When Carlo barked, people would turn expectantly to Stueckelberg. He would survey the blackboard—“There’s always a mistake on them,” he said—and point out the error. The rumor grew that somehow Carlo spotted the problems. As Stueckelberg grew older, he appeared less often at seminars. By the mid-1960s, years of experimental medication had slurred his speech, interfering with his thinking. Crippled by arthritis, he was carried to colloquia in the arms of his former students—a painful procedure that Stueckelberg described to us in detached, ironic detail, chuckling every now and then at his own frailty. He married again. He turned to the embrace of the Roman Catholic Church.

After we had talked for a couple of hours, he abruptly extended a hand as light and dry as a dead leaf. He was tired; the interview was over. The array of barons on the wall glowered in the deepening twilight. The old man gathered up his two canes and painfully lifted himself out of his chair. “I look forward every day to my eventual journey to Heaven.” A heavy gold cross dangled from his thin neck. He as trembling slightly from the effort of standing. “We live too long,” he said.

$~$

Seven months later, on September 4, 1984, Ernst Stueckelberg was buried in Geneva at Plain Palais, the cemetery where Calvin had been laid to rest three centuries before.

(from The Second Creation by Robert P. Crease and Charles C. Mann, Macmillan, New York, 1986, pp. 140-144).

Advertisement