by James Gleick
The diagram is an aid to visualization. But it serves physicists mainly as a bookkeeping device. Each diagram is associated with a complex number, an amplitude that is squared to produce a probability for the process shown.
In fact each diagram represented not a particular path, with specified times and places, but a sum of all such paths. There were other simple diagrams. He represented the self-energy of an electron—its interaction with itself—by showing a photon line returning to the same electron that spawned it. There was a grammar of permissible diagrams, corresponding, as Dyson had emphasized, to the permissible mathematical operations. Still, the diagrams could grow arbitrarily complicated, virtual particles appearing and disappearing in an intricate, recursive mesh. Feynman’s first H-shaped diagram for interacting electrons was the only such diagram with one virtual photon. Drawing all the possible diagrams with two virtual photons showed how quickly the permutations grew. Each made a contribution to the final computation, and more complicated diagrams became enormously difficult to calculate. Fortunately the greater the complication the less the probability and the smaller, therefore, the effect on the answer. Even so, physicists would shortly find themselves agonizing over pages of diagrams resembling catalogs of knots. They found it was worth the effort; each diagram could replace an effective lifetime of Schwingerian algebra.
Self-interaction. It is necessary to sum the amplitudes corresponding tomany Feynman diagrams to add the contributions for every way an event can occur. The continual possibility of virtual particles materializing and vanishing causes increasing complexity. Here an electron interacts with itself, in effect- the self-energy problem that first troubled Feynman in his work with Wheeler. It emits and absorbs its own virtual photon.
Feynman diagrams seemed to depict particles, and they had sprung from a mind focused on a particle-centered style of visualization, but the theory they anchored—quantum field theory—gave center stage to the field. In a sense the paths of the diagrams, and the paths summed in the path integrals, were the paths of the field itself. Feynman read the Physical Review more avidly than ever in the past, watching for citations. For a while it was all Schwinger—a paper would be pages of glyphs and would culminate in a neat expression that Feynman felt he could simply have written down as a starting point. He was sure this could not last. It did not. Feynman’s method, Feynman’s rules, began to take over. In the summer of 1950 a paper appeared with small “Feynman diagrams” on the first page—“following the simplified methods introduced by Feynman.” A month later came another: “a technique due to Feynman… . The calculation of matrix elements can be simplified greatly by use of the Feynman-Dyson methods.” The unreasonable power of the diagrams in the hands of students frustrated some of the elders, who felt that physicists were waving a sword that they did not understand. As the flood of papers began to cite Feynman, Schwinger went into what he described as his retreat. “Like the silicon chip of more recent years, the Feynman diagram was bringing computation to the masses,” he said. Later, people who overlooked the note of hoi polloi quoted this remark as though Schwinger had intended a tribute. He had not. This was “pedagogy, not physics.”
Yes, one can analyze experience into individual pieces of topology. But eventually one has to put it all together again. And then the piecemeal approach loses some of its attraction.
Making the increasingly precise calculations for which quantum electrodynamics became famous requi red formidable exercises in combinatorics.
Schwinger’s students at Harvard were put at a competitive disadvantage, or so it seemed to their fellows elsewhere, who suspected them of surreptitiously using the diagrams anyway. This was sometimes true. (They revered him, though—his night-owl ways, his Cadillac, his theatrically impeccable lecture performances. They emulated his way of saying, “We can effectively regard …” and they tried to construct the perfect Schwinger sentence: one graduate student, Jeremy Bernstein, liked a prototype that began, “Although ‘one’ is not perfectly ‘zero,’ we can effectively regard …” They also worried about Schwinger’s ability to materialize silently beside them at the lunch table; a group of his graduate students protected themselves with a conversational convention in which Schwinger meant Feynman and Feynman meant Schwinger.)
Murray Gell-Mann later spent a semester staying in Schwinger’s house in Cambridge and loved to say afterward that he had searched everywhere for the Feynman diagrams. He had not found any, but one room had been locked …
Away to a Fabulous Land
Bethe worried that Feynman was growing restless after four years at Cornell. There were entanglements with women: Feynman pursued them and dropped them, or tried to, with increasingly public frustration—so it seemed even to undergraduates, who knew him as the least professorial of professors, likely to be found beating a rhythm on a dormitory bench or lying supine and greasy beneath his Oldsmobile. He had never settled into any house or apartment. One year he lived as faculty guest in a student residence. Often he would stay nights or weeks with married friends until these arrangements became sexually volatile. He seemed to think that Cornell was alternately too large and too small—an isolated village with only a diffuse interest in science outside the confines of its physics department. Furthermore, Hans Bethe would always be the great man of physics at Cornell.
An old Los Alamos acquaintance, Robert Bacher, after serving on the new Atomic Energy Commission, was moving to Caltech, where he was charged with rebuilding an obsolete-looking physics program. He was swimming in a lake during a summer vacation in northern Michigan when Feynman’s name came into his head. He rushed back to shore, tracked Feynman down by telephone, and within a few days had him there visiting.
Feynman agreed to consider Pasadena, but he was also thinking about possibilities even more faraway, exotic, and warm. South America was on his mind. He had gone so far as to study Spanish. Pan American Airways had opened the continent to American tourists on a large scale, jumping from New York to Rio de Janeiro in thirty-four hours for roughly the price of the fortnight-long ocean voyage, and the popular magazines were filling with sensual images: palms and plantations, hot beaches and gaudy nights. Carmen Miranda and bananas still dominated the travel writing. There was a new note, too, of the apocalyptic fear that had dogged Feynman: the Soviet Union had demonstrated its first working atomic bomb in September 1949, and worries about nuclear war were entering the national consciousness and spurring a panicky civil defense movement. Emigrations to South America became an odd symptom. One of Feynman’s girlfriends told him seriously that he might be safer there. John Wheeler said—by way of imploring Feynman to join work on a thermonuclear bomb—that he was estimating “at least a 40 percent chance of war by September.”
When a Brazilian physicist visiting Princeton, Jayme Tiomno, heard that Feynman was flirting with Spanish, he had suggested a switch to Portuguese and invited him to visit the new Centro Brasiliero de Pesquisas Físicas in Rio for several weeks in the summer of 1949. Feynman accepted, applied for a passport, and left the continental United States for the first time. He did learn enough Portuguese to teach physicists and beseech women in their native language. (By the end of the summer he had persuaded one of them, a Copacabana resident named Clotilde, who called him meu Ricardinho in her mellifluous Portuguese, to come live with him in Ithaca—briefly.) Late the next winter he impulsively asked the centro to hire him permanently. Meanwhile he was negotiating seriously with Bacher. He had endured one too many days kneeling in cold slush as he tried to wrap chains around his tires. Caltech appealed to him. It reminded him of the other Tech, such a pure haven for the technically minded. Four years at a liberal-arts university had not softened his outlook. He was tired of “all the ins and outs of the small town and the bad weather,” he wrote Bacher, and added, “The theoretical broadening which comes from having many humanities subjects on the campus is offset by the general dopiness of the people who study these things and by the Department of Home Economics.” He warne
d Bacher about one of his weaknesses: he did not like having graduate students. At Cornell “poor Bethe” had ended up covering for him again and again.
I do not like to suggest a problem and suggest a method for its solution and feel responsible after the student is unable to work out the problem by the suggested method by the time his wife is going to have a baby so that he cannot get a job. What happens is that I find that I do not suggest any method that I do not know will work and the only way I know it works is by having tried it out at home previously, so I find the old saying that “A Ph.D. thesis is research done by a professor under particularly trying circumstances” is for me the dead truth.
He had a sabbatical year coming. He was going to make his escape, one way or another.
Once (and it was not yesterday), a diligent student of field theory wrote later at Niels Bohr’s institute in Copenhagen, there lived a very young mole and a very young crow who, having heard of the fabulous land called Quefithe, decided to visit it. Before starting out, they went to the wise owl and asked what Quefithe was like.
Owl’s description of Quefithe was quite confusing. He said that in Quefithe everything was both up and down. Physicists need more than ideas and methods. They need a version of history, too, a narrative cabinet for ordering their bits of knowledge. So they create a legend of search and discovery on the fly; they turn hearsay and supposition into instant lore. They discover that it is hard to teach a pure concept without clothing it in at least a fragment of narrative: who discovered it; what problem needed solving; what path led from not knowing to knowing. Some physicists learn that there is such a thing as physicists’ history, necessary and convenient but often different from real history. The fable of Quefithe—“quantum field theory”—with a Schwinger mole and a Feynman crow, an owl resembling Bohr, and a fox like Dyson, lovingly satirized a story that had entered the community’s store of self-knowledge as rapidly as the path integrals and Feynman diagrams: If you knew where you were, there was no way of knowing where you were going and conversely, if you knew where you were going, there was no way of knowing where you were… .
Clearly, if they were ever going to learn anything about Quefithe, they had to see it for themselves. And that is what they did.
After a few years had passed, the mole came back. He said that Quefithe consisted of lots of tunnels. One entered a hole and wandered through a maze, tunnels splitting and rejoining, until one found the next hole and got out. Quefithe sounded like a place only a mole would like, and nobody wanted to hear more about it.
Not much later the crow landed, flapping its wings and crowing excitedly. Quefithe was amazing, it said. The most beautiful landscape with high mountains, perilous passes and deep valleys. The valley floors were teeming with little moles who were scurrying down rutted paths. The crow sounded like he had taken too many bubble baths, and many who heard him shook their heads. The frogs kept on croaking “It is not rigorous, it is not rigorous!” … But there was something about crow’s enthusiasm that was infectious.
The most puzzling thing about it all was that the mole’s description of Quefithe sounded nothing like the crow’s description. Some even doubted that the mole and the crow had ever gotten to the mythical land. Only the fox, who was by nature very curious, kept running back and forth between the mole and the crow and asking questions, until he was sure that he understood them both. Nowadays, anybody can get to Quefithe—even snails.
CALTECH
The California Institute of Technology had entered the 1920s with an engineering building, a physics building, a chemistry laboratory, an auditorium, and an orange grove on a dusty, underirrigated thirty acres a few minutes east of the thriving civic center of Pasadena, a town of new money in search of monuments. The scent of orange and rose floated from the gardens of porticoed homes often described as mansions, built in a relaxed Spanish and Italianate style that was coming to be thought of as Californian. Walls were a pale stucco, roofs a red tile. “Pasadena is ten miles from Los Angeles as the Rolls-Royces fly,” one commentator said in 1932. “It is one of the prettiest towns in America, and probably the richest.” Albert Einstein wintered there for three years, posing for pictures on a bicycle to the delight of the institute administrators, attending, as Will Rogers said, “every luncheon, every dinner, every movie opening, every marriage and two-thirds of the divorces,” before he finally decided Princeton suited him better. Even as the Depression began to reverse Pasadena’s fortunes, Caltech’s rose on every new tide in science. A new Caltech laboratory polished the giant lens for the great telescope under way at Palomar Mountain. Caltech made itself the American center of systematic earthquake science; one of its young graduates, Charles Richter, devised the ubiquitous measurement scale that carries his name. The school moved quickly into aeronautic science, and a group of enthusiastic amateurs firing off rockets in the hills about the Rose Bowl became, by 1944, the Jet Propulsion Laboratory. Foundations and industrialists were eager to look beyond their usual East Coast funding targets. A cornflakes manufacturer paid for a building that became the Kellogg Radiation Laboratory, and its reigning expert, Charles Lauritsen, made it a national center for fundamental nuclear physics. Lauritsen spent much of the thirties investigating the nuclear properties of the light elements—hydrogen and deuterium, helium, lithium, up through carbon and beyond—filling in details of energy levels and spin with a patched-together arsenal of equipment.
He was still working in Kellogg in the winter of 1951, when oracular messages started coming in by ham radio. A blind operator in Brazil would establish a link every week or so with a student at Caltech. Lauritsen would receive terse predictions: Could it be that nitrogen has two levels very close together at the lowest state, not just a single level? He would check these, and often they would prove correct. His Brazilian informant apparently had a theory …
In Chicago, Fermi, too, heard from Feynman—a long “Dear Fermi” letter just before Christmas from the Miramar Palace Hotel in Copacabana. Feynman, following the thread he had picked up in the episode of Case v. Slotnick, was working on meson theory. It was messy—divergences everywhere—but he had reached a hodgepodge of conclusions. “I should like to make some comments at the risk of saying what is obvious to everybody in the U.S.,” he wrote Fermi. Mesons are pseudoscalar … Yukawa’s theory is wrong. He had heard some experimental news via the ham-radio link—“I am not entirely in the dark in Brazil.” He had some predictions that he wanted checked. His approach to these particles, so essential to the binding of the atomic nucleus, centered increasingly on an even more abstract variant of spin: yet another quantum number called isotopic spin. So did Fermi’s approach, as it turned out. Feynman was duplicating some of the Chicago work. In their ways they were trying to take the measure of a theory that resembled quantum electrodynamics yet resisted the lion tamers’ favorite whips, renormalization, perturbation theory. “Don’t believe any calculation in meson theory which uses a Feynman diagram!” Feynman wrote Fermi. Meanwhile, as they pushed more energetically inside the atom, they were watching the breakup of the prewar particle picture. With each new particle, the dream of a manageable number of building blocks faded. In this continually subdividing world, what was truly elementary?
What was made of what? “Principles,” Feynman had written in the tiny address book he carried with him. “You can’t say A is made of B or vice versa. All mass is interaction.” That did not solve the problem, though. Cloud chamber photographs showed new kinds of forks and kinks in the trajectories—new mesons, it seemed, before anyone had understood the old. Fermi set the tone for the coming proliferation of particles with a declaration in the Physical Review.
In recent years several new particles have been discovered which are currently assumed to be “elementary,” that is, essentially structureless. The probability that all such particles should be really elementary becomes less and less as their number increases.
It is by no means certain that nucleons, mesons, electrons, neutri
nos are all elementary particles… .
Feynman had made his escape shortly after arriving in Pasadena. He accepted Caltech’s offer of an immediate sabbatical year and fled to the most exotic place he could find. The State Department subsidized his salary. For the first time since Far Rockaway he could spend days at the beach, where he looked over the crowds in sandals and bathing suits and gazed at the endless waves and sky. He had never before seen a beach where mountains loomed just behind. At night the Serra da Carioca were black humps in the moonlight. Royal palms like dressed-up telephone poles—taller by far than the palms of Pasadena—lined the coast and the broad avenues of Rio. Feynman went down to the sea for inspiration. Fermi teased him: “I wish I could also refresh my ideas by swimming off Copacabana.” Feynman liked the idea of helping build a new seat of physics at the Centro Brasiliero de Pesquisas Físicas. Fifteen years before, physics had hardly existed in Brazil or elsewhere in South America. A few lesser German and Italian physicists had grafted branches in the middle 1930s, and within a decade their students’ students were creating new facilities with the support of industry and government agencies.
Feynman taught basic electromagnetism to students at the University of Brazil in Rio, who disappointed him by meekly refusing to ask questions. Their style seemed rote and hidebound after freewheeling Americans. European influence had dominated the construction of a curriculum. The nascent graduate programs did not have the luxury of a liberal mix of confident instructors. Memorization replaced understanding, or so it seemed to Feynman, and he began to proselytize the Brazilian educational establishment. Students learned names and abstract formulations, he said. Brazilian students could recite Brewster’s Law: “Light impinging on a material of index n is 100 percent polarized with the electric field perpendicular to the plane of incidence if the tangent …” But when he asked what would happen if they looked out at the sunlight reflecting off the bay and held up a piece of polarized film and turned the film this way and that, he got blank stares. They could define “triboluminescence”—light emitted by crystals under mechanical pressure—and it made Feynman wish the professors would just send them into a dark room with a pair of pliers and a sugar cube or a Life Saver to see the faint blue flash, as he had when he was a child. “Have you got science? No! You have only told what a word means in terms of other words. You haven’t told them anything about nature—what crystals produce light when you crush them, why they produce light… .” An examination question would read, “What are the four types of telescope?” (Newtonian, Cassegrainian, …) Students could answer, and yet, Feynman said, the real telescope was lost: the instrument that helped begin the scientific revolution, that showed humanity the humbling vastness of the stars.
