The Pope of Physics

by Gino Segrè

  Building such a machine would be a major engineering effort. Fermi was extraordinarily eager to proceed, anticipating that it would lead to a wave of discoveries once it was operating. The confirmation of Yukawa’s conjecture in 1947 added impetus to its construction. A team from Bristol University had observed his meson in a cosmic ray. It was given the name pi-meson, or, more simply, pion.

  Almost simultaneously, a high-level government official came to Chicago. Such was the faith in Fermi’s record of achievements that the official only inquired how much funding Fermi needed, not to what purpose. Hearing about the prospective grant, an excited Herb Anderson asked Fermi, “What would you like? I’ll build it. An accelerator, a big computer.… You name it.” Fermi chose the accelerator, and Anderson, joined by John Marshall, began building it.

  Originally scheduled for completion in May 1950, the complicated machine did not start operating until February 1951. By April of that year it was running at full power. The usually calm Fermi was beside himself, Laura noting that her husband was “as pleased as a child who has received a new toy long dreamed of and exceeding expectations. He played with the cyclotron at all hours of day and evening during that summer of 1951. He allowed the cyclotron to upset his routine.”

  Fermi had certainly not been idle while waiting for the completion of his “new toy.” He had carried out an important set of neutron experiments with Leona Woods Marshall and others at the Argonne reactor and, in a visionary paper, had shown how intergalactic magnetic fields could provide the mechanism to accelerate cosmic rays.

  Fermi had, however, always been thinking about what experiments he might perform once the machine was ready. It would provide not just a few pions, but a whole beam of them. The beam’s energy could be varied and the pions directed toward a target of protons, subsequently making it possible to observe the angles at which the pions were scattered. The pion-proton interaction and therefore the nuclear force would become known to a previously unobtainable degree.

  When the accelerator started operating, some unexpected results in the scattering experiments appeared. Fermi had not anticipated them but was prepared for surprises. There were hints of new particles being produced. These indicated that the search for the ultimate structure of matter would be lengthy. Perhaps one day it might even be shown that pions were composites of other particles, as Fermi had conjectured in a 1949 article written with his former student Chen Ning Yang. More powerful particle accelerators would be built in the coming decades, but Fermi was convinced that the experiments he was carrying out were the gateway to making progress.

  The scattering experiments were also ensuring progress in a different direction by calling for development of novel computational tools. Fermi’s office desk calculator and his constant companion, a small slide rule, were no longer sufficient for analyzing the enormous amounts of data being produced. But computers, first introduced by the late 1940s, could perform the task. They were tools of an entirely new character and Los Alamos had one. It would prove valuable for studying the details of the thermonuclear reactions underlying the H-bomb’s functioning. Now, in a completely different vein, it allowed Fermi to analyze his experimental results. Back in 1947, Anderson had asked him if he wanted an accelerator or a big computer. In 1952, he had both.

  Looking beyond his immediate interests, Fermi also saw that computers provided a way to deal with previously intractable physics problems, ones of a nonlinear kind in which the output is not simply proportional to the input or in which the expected approach to equilibrium is not reached. Research along the lines that Fermi conducted at Los Alamos with his mathematician friend Stan Ulam and others during the summers of 1952 and 1953 is seen as pioneering work toward contemporary fields, such as chaos theory.

  Although advancing science was always Fermi’s driving force, he was optimistic that the progress along these paths would eventually benefit society as a whole. In fielding questions such as “What does it matter?” about the development of the new tools, he answered as follows in a 1952 speech at the University of Rochester:

  The history of science and technology has consistently taught us that scientific advances in basic understanding have sooner or later led to technical and industrial applications that have revolutionized our way of life. It seems to me improbable that this effort to get at the structure of matter should be an exception to this rule.

  Remembering also how physics had contributed to the development of weapons, Fermi concluded with a warning for his audience, “What is less certain, and what we all fervently hope, is that man will soon grow sufficiently adult to make good use of the powers that he acquires over nature.” It is probably as close as Fermi ever got to imparting a moral and cautionary message regarding scientific advances.

  36

  THE FERMI METHOD

  Fermi was delighted to get back to the teaching environment of a university campus after leaving Los Alamos. The quality of physics students at the University of Chicago was extraordinarily high. Suddenly physics, once a relatively dormant and obscure field, was attracting top students at both the graduate and undergraduate level. Dramatic discoveries, astonishing tools, and high-profile visionaries all added to its allure.

  Fermi’s reputation as a professor was legendary and well earned. One doctoral student, still tentative about his chosen field, recalled how “my first physics exposure at the University of Chicago was to Fermi’s famous 8:00 a.m. introductory lectures on nuclear physics. By about 8:15 I knew I had made the right decision!” In homage to his mentor, Marshall Rosenbluth later became known as “the Pope of Plasma Physics.” In 1985 he won the coveted Enrico Fermi Prize.

  Fermi’s lecture notes for his nuclear physics course, carefully crafted and painstakingly detailed, were so esteemed that three of his students decided to type them up, enter the formulas by hand, and distribute mimeographed copies. As word spread, in 1949 the University of Chicago Press photo-offset the lecture notes into a book on nuclear physics. By the time of the sixth edition, twenty thousand copies had been sold; their format was unchanged. Fermi’s lectures on quantum mechanics and thermodynamics were also published, praised, and appreciated by physics devotees not privileged to have him as a classroom teacher.

  Fermi had the further distinction of an astonishing record: six of his Chicago students and one from Rome won Nobel Prizes in Physics. To this day, the record is unmatched. All the more remarkable was the fact that these laureates represented the respective disciplines of theory and experiment. It was yet another testament to Fermi’s command of both fields. The Pope was training a cadre of future leaders; many viewed Fermi’s teaching as his greatest contribution to the physics of the postwar period. The students’ feelings were reflected in a 1954 letter one of the Nobelists wrote to Fermi, “If I am to be regarded as a decent physicist, it is mostly because of your training.”

  Re-creating the atmosphere of Via Panisperna, Fermi regularly invited advanced students to small gatherings in his office with its adjacent experimental laboratory. The setting reflected his partiality for simplicity and functionality. There were no comfortable sofas or rows of book-lined shelves in the office, only a blackboard, a plain metal desk, some chairs, and a few filing cabinets that stored stacks of notebooks. These notebooks, carefully annotated, carried a wealth of knowledge. A self-confessed nonreader of traditional texts, Fermi referred to these notebooks as his artificial memory, relying on them for information or a specific formula.

  Office discussions ranged from abstract Riemannian geometry to the practicalities of electric noise in circuits. Fermi insisted that every assumption be tested and no formula taken for granted. One of the most brilliant theory students claimed they all learned from Fermi the maxim “Physics is to be built from the ground up, brick by brick by brick, layer by layer.”

  Never seeming to lose an opportunity to teach and learn, Fermi also mixed with students by eating lunch with them and a few colleagues at a long table in the main campus dining hall. A sp
irited discussion was guaranteed. The atmosphere was casual, far from European formalities where “Herr Professors” reigned.

  Aside from the world of work, Fermi extended his relationship with students to the world of play. He joined them in their outdoor activities and sports, displaying his considerable endurance and his well-known desire to win. The short and less-than-graceful Italian was considered a ferocious tennis player who would run and hit in the midday sun until he thoroughly exhausted any opponent. Harold Agnew—who had worked with Fermi on the pile in 1942, followed him to Los Alamos, and returned to Chicago as a Ph.D. candidate—could attest to his mentor’s exuberance on the tennis court, in the waters of Lake Michigan, and, most improbably, on the dance floor.

  Square dancing was an import of the Fermis from Los Alamos days and was a frequent form of entertaining colleagues, graduate students, and occasionally undergraduates in the spacious third floor of the Chicago house. The dances were predictably lively, although bizarre to foreign students. “They were my first introduction to occidental culture,” recalled the 1957 Nobel laureate Tsung Dao Lee, who had arrived in Chicago from China in 1946 as a twenty-year-old. “Enrico’s dancing, Laura’s punch and Agnew’s energetic calling of ‘do-si-do’ all made indelible marks on my memory.” The very essence of square dancing seems antithetical to the innovative and independent personalities of physicists. Dancers obey instructions, follow patterned footsteps, and stay within the confines of a square box. More typically, physicists tend to think independently and outside the box, beyond boundaries and constraints.

  Maybe square dancing, this most American of gambols, provided some welcome respite and a semblance of normal life. Although Fermi considered himself “perfectly normal,” one can argue differently. He saw the world through a special lens, that of quantification and rationality. In the physics community, the approach was so identified with him that it is referred to as “the Fermi method.” Questions that he posed, ones that could be answered by careful order-of-magnitude reckoning, became known as “Fermi questions.”

  The idea was to arrive at an approximate answer, doing so, as one colleague said, “with a minimum of complication and sophistication.” The Fermi method combined a breadth of knowledge, mathematical acumen, a strong dose of intuition, and mental agility. The Pope’s accurate estimate at Trinity of the explosive power of the first atomic bomb was considered a classic example of the approach.

  Numbers ruled and Fermi was a master at discovering them, interpreting them, and applying them. The joys of music and art seemed lost on Fermi, who was thought to be without much aesthetic appreciation. Quantification, not the ambiguities of aesthetics and taste, was what made him happy and secure. When his Chicago protégée Leona Woods Marshall took Fermi to the Art Institute to view a portrait exhibit of immigrants, she hoped he would identify with these fellow new Americans and appreciate the artistic treatment of them. It did not take long for him to pull out his omnipresent slide rule, compute the ratio of their body to leg lengths, and happily conclude that his own measurements coincided with the center of the distribution he had just calculated.

  Other times—while hiking, for example—Fermi did not rely on a slide rule and used his thumb as a yardstick, placing it in front of his left eye while closing the right, thereby accurately calibrating mountain range distances, heights of trees, and speeds at which a bird flew. To Laura’s somewhat amused consternation, one of his favorite pastimes was classifying people, on a scale from one to four, according to intelligence. When during their courtship Enrico gallantly offered to share the classification of four with her, Laura rejoined that if he was allowing her to be a four, he must have intended for there to be a scale of five. Five was reserved for Fermi alone.

  What saved Fermi and his obsession with numbers from being overbearing was his amazing accuracy and his sense of humor. When Fermi thought, he played. This playfulness spilled over into his teaching, whether of undergraduates, graduates, or his peers. And it surfaced in sundry ways.

  To encourage students to develop their skill in estimating orders of magnitude, a sort of mental calisthenics, Fermi would pose seemingly outrageous questions. Once, pointing to the university’s lunch hall windows, he asked his students to estimate “How thick can the dirt be on the window up there before it falls off?” Another time he asked, “What is the number of sheep in Nevada?” His most cited question was “How many piano tuners are there in the city of Chicago?” In the process of answering these questions, easy or hard, the students gained confidence, coming to feel, as one put it, that “we could solve any problem.”

  Fermi seemed to have an uncanny ability to rapidly grasp a problem’s essential features. His graduate students would joke that his legendary intuition was only possible because “Fermi had an inside track to God.”

  Fermi’s method was not limited to students. Colleagues treasured his give-and-take, consulting him even when the subject was far from his expertise. However, when it came to serious personal problems, Fermi was “certainly not the person to go to.” A colleague describes him as reticent about talking about feelings, “not cold, but not warm either.” Fermi was at his best as a scientist.

  A 1983 Nobel Prize winner, the very distinguished Chicago astrophysicist Subrahmanyan Chandrasekhar, collaborated with Fermi on important problems in astrophysics regarding galactic magnetic fields. He described the impression Fermi made on him as being akin to that of “a musician who, when presented with a new piece of music, at once plays it with a perception and a discernment which one would normally associate only with long practice and study.”

  Maria Goeppert Mayer, another Chicago colleague, acknowledged in her 1963 Nobel Prize acceptance speech that her research had been turned around by a casual question Fermi posed to her about a possible interaction affecting the structure of large nuclei. Mayer was the second female laureate ever in physics, preceded only by Marie Curie. What Mayer did not know was that ten years earlier, when a prominent Harvard professor of chemistry wrote to Fermi inquiring about her, the professor started his letter, “I had the misfortune of having been made a member of a committee which is recommending a woman scholar for a distinguished appointment.” Fermi responded the next day, ignoring the gratuitous gender reference. “I believe that Maria G. Mayer is without any [reservation] an outstanding scientist,” he wrote, adding that her work was “doubtlessly the most important contribution to the physics of the nucleus in the last five years.”

  Given the reputation Fermi had acquired, physicists came from afar to benefit from his opinion on their work and seek his advice. The great theorist Freeman Dyson described an example from the spring of 1953. Then a young but already well known Cornell faculty member, Dyson traveled to Chicago to show Fermi a series of calculations he had undertaken with his graduate students. Their results matched the data from the pion-proton scattering experiments Fermi had performed with his own students. But Fermi was skeptical of the significance of such calculations. In a 1951 presentation for the twentieth anniversary of the founding of the American Institute of Physics, Fermi had stated that in attempting to understand the subject, “we must be prepared for a long pull.” He did not estimate how long that pull might be. It would be another quarter of a century before quarks and gluons provided an answer.

  When Dyson met with him in 1953, Fermi welcomed him politely, but he quickly put aside the graphs he was being shown indicating agreement between theory and experiment. His verdict, as Dyson remembered, was “There are two ways of doing calculations in theoretical physics. One way, and this is the way I prefer, is to have a clear physical picture of the process you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.”

  When a stunned Dyson tried to counter by emphasizing the agreement between experiment and the calculations, Fermi asked him how many free parameters he had used to obtain the fit. Smiling after being told “Four,” Fermi remarked, “I remember my old friend Johnny
von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” There was little to add. In retrospect, Dyson was grateful for Fermi’s rather brusque judgment, saying it “saved me and my students from getting stuck in a blind alley.”

  The Fermi method was not always applicable and sometimes could backfire. Talking once with a group that included Leo Szilard, Fermi wondered how one might determine whether there were extraterrestrial beings. What were the possibilities? After estimating the number of stars in the universe, the number of planets around them with liquid water and the evolution of some semblance of human life, Fermi asked if there could be a civilization that could communicate with Earth or even colonize it. If so, he rhetorically queried, “Where is everybody?” Szilard quickly responded, “Enrico, they are already among us. We just call them Hungarians.” He was referring to the almost simultaneous appearance on earth of Teller, von Neumann, Wigner, and of course himself.

  One of those Hungarians, the bushy-browed Teller, whose associations with other scientists were often volatile or prickly, was on good footing with his Italian co-immigrant. They taught a seminar together in Chicago, Teller often faltering in his explanations. Fermi would step in, remarking, “What Edward is trying to say is,” and then articulate the concepts in his own lucid way.

  By the end of the 1940s, their Chicago interactions were becoming far more rare. Teller was spending more time working in Los Alamos. The Super was once again becoming paramount and he was fervently promoting it. “What Edward is trying to say” was crystal clear. The zealous scientist, believed to be the inspiration for the movie Dr. Strangelove, was convinced America would be safe only if it succeeded in making a hydrogen bomb.