True Genius: The Life and Science of John Bardeen: The Only Winner of Two Nobel Prizes in Physics (2002)

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4 A Graduate Student’s Paradise I t was dark when Bardeen reached Princeton, but the campus was not deserted. Most of the buildings were still lit on that late summer night. Every now and then a bicycle headlight flickered by as a student returned from late study in the library or from a laboratory. Driving half a mile west of the main campus, Bardeen pulled up to the Graduate College, where he would live for the next two years. He stopped for a moment to admire the Gothic structure designed by Ralph Adams Cram. Another physics student, Philip Morse, described the elaborate building as “the embodiment of scholasticism.” Numerous gargoyles and entryways projected a sense of age and culture. The carillon tower beside the entry gate looked eerie and beautiful in the moonlight. The next morning Bardeen made his way to Fine Hall, the mathematics building. After registering, he walked next door into the Palmer Physics Laboratory. The department chair, Adams Trowbridge, grabbed Fred Seitz, a fourth-semester graduate student from Stanford, and said, “Here’s a new student. Could you take him to lunch?” Seitz readily agreed. Seitz and Bardeen struck up a friendship that would be life- long. John told Fred about his oil prospecting work. Fred was fasci- nated. He thought the electrical and magnetic methods that John described for seeking oil sounded more effective than the sonic 45 

46 TRUE GENIUS technique that he knew about. He also thought that Bardeen appeared mature for his age. Seitz decided this was probably because Bardeen had lived on his own for three years while “work- ing in the corporate world.” Having taken two years of graduate engineering courses at Wisconsin, Bardeen was more advanced than Seitz had been at the time the latter entered Princeton’s program for the spring 1932 semester. Bardeen and Seitz walked together to the Graduate College and into its formal dining hall, where they sat down at a long table with about half a dozen other students. Seitz knew them all. He reckoned there were only about 150 graduate students in the entire university. Across the table sat a fellow “who was much worried about passing his preliminary exams. He was in the middle of taking them and in deep trouble,” Seitz recalled. Extending over several days, the “prelims” were the major hurdle for a Princeton graduate stu- dent, the crucial step before passing to the stage of thesis writing. The ordeal included a rigorous written section and several sessions of intensive oral questioning by a committee. “This fellow looked at John and at me and said, ‘Does he know what he’s getting into? Don’t you think you should tell him?’ ” Seitz explained the home rules of the Graduate College. Dinner was served every evening in the great hall following the dean’s daily grace, which was said in Latin. He told John that he needed to buy a formal black scholastic gown to wear at dinner, adding that he could probably get one inexpensively from a graduating student. The gowns grew increasingly stained and tattered as they were passed on. “They were rags,” recalled Seitz. “We thought of them as bibs.” Bardeen nodded stiffly as he registered Seitz’s next instruction: Always wear a tie to class. The Princeton style was clearly very different from the informal one he had witnessed from the docks of Lake Mendota. Bardeen thought Princeton’s rituals might take some time to get used to, but they didn’t. Like Seitz, he would find the formalities “insignificant.” Princeton’s rituals would be less graciously accepted by Einstein, who arrived on the scene a month later with his wife, Elsa. Abraham Flexner had conceived of the Institute for Advanced Study as a haven for scholars. Its purpose was to nourish advanced research and thinking by freeing the most creative academics from their usual pressures. Oswald Veblen, one of the institute’s first 

A Graduate Student’s Paradise 47 appointed mathematicians, suggested that Flexner start by building up faculty in the area of mathematics. Accordingly, Flexner hired Hermann Weyl, whose work had helped to put quantum mechanics on a firm mathematical basis. Einstein’s subsequent acceptance of a permanent post moved the institute onto the world stage. The physicist Paul Langevin compared Einstein’s well-publicized move to Princeton with transferring the Vatican to the New World. The Einsteins, like the Quakers who had settled Princeton in the 1680s, admired the town’s physical setting, with its lush forests and many streams. “One great park with wonderful trees,” Elsa Einstein wrote to a European friend. Albert, however, deplored the aura of gentility in the Princeton community, with its endless ceremonies regulating life in that intellectual enclave. He described Princeton as “a quaint and ceremonious village of puny demigods on stilts.” He missed the coffeehouses of Berlin, where intellectu- als could relax for hours while exchanging deep ideas. Eugene Wigner, a fellow European on the faculty, also lamented Princeton’s lack of “coffeehouses in the European sense.” Bardeen didn’t care about coffeehouses, but he did care about games, such as bowling or bridge, which were readily available in Princeton. Johnny, as he was known to his Princeton friends, bowled regularly with his roommate Cassius Curtis or with his friend Robert Brattain. As in Madison, John parlayed his social encounters during games into collegial connections. Bardeen felt very comfortable with Bob Brattain, who entered the program in physics at the same time Bardeen entered in math. Raised on a cattle ranch in the state of Washington, Brattain was quite unconcerned about high culture. And, like Bardeen, he also loved games. The two bowled as a team to win the doubles graduate bowling tournament and then faced off against one another for the singles championship. In bridge they were “enemies.” Bardeen’s partner, John Vanderslice, another mathematics graduate student (who Brattain referred to as “Slice”), was an internationally ranked chess player. Occasionally Brattain invited Bardeen along to New York City to join in one of the weekend-long bridge marathons that Bob’s brother Walter sometimes hosted in his Greenwich Village apartment. “We played until everybody got so sleepy that they went to sleep. Then we’d sleep for a while, get up, eat something and play bridge. We played bridge continuously for the whole weekend.” 

48 TRUE GENIUS Bardeen immediately hit it off with Walter Brattain, an out- going experimental physicist then working in lower Manhattan at Bell Telephone Laboratories, the research and development arm of the American Telephone and Telegraph Corporation (AT&T). Walter was among the few Bell Labs researchers who already recog- nized that quantum mechanics would be important in solving AT&T’s communications problems. When Walter learned that Arnold Sommerfeld, the great European quantum theorist, would be lecturing in Ann Arbor at the 1931 Michigan summer school in theoretical physics, he convinced Bell Labs to let him attend Sommerfeld’s course. The lectures covered the new “semi- classical” electron theory of metals that Sommerfeld had devel- oped several years earlier. Brattain recognized the importance of this theory for his own physics problems and for others of interest to Bell Labs. Afterwards, when Brattain returned to Bell Labs, he summarized what he had learned in Michigan in a series of talks he offered to his colleagues. Bardeen soon encountered the same material in his studies at Princeton. John and Walter could not have known then that fourteen years later they would co-invent a device that would change the world. John did know that he greatly enjoyed socializing with Walter. He loved Walter’s good humor and colorful stories about the Brattain family’s pioneering heritage. Walter would often tell how, before entering college, he had spent an entire year “herding cattle in the mountains, with a rifle, in my own camp. I only saw my family on occasional weekends and saw practically no other individual out- side of my mother and father and brother and sister.” Walter’s and John’s stylistic differences were already clear. For example, in their bridge playing both men aimed to win, but Brattain played aggressively while Bardeen played thoughtfully. Although different in their styles, their passions, values, and inter- ests aligned. At that time they even worked on the same physics problem. “Walter and I had a common interest,” Bardeen later wrote, “the theory of the work function as derived from the quan- tum theory of metals.” A measure of the energy required to remove an electron from the surface of a metal, the work function was a concern of any technology that relied on vacuum tubes. The two also had in common John Van Vleck, who had intro- duced both to quantum mechanics. Van Vleck had been on the faculty at the University of Minnesota before moving to Madison. 

A Graduate Student’s Paradise 49 Walter had taken Van Vleck’s quantum theory course at Minnesota in the late 1920s. But at that early stage in their lifelong friendship, John and Walter “didn’t really talk that much physics,” Bardeen recalled. “It was more of a social acquaintance.” Bardeen’s closest colleague and friend at Princeton was Seitz, who after completing his Ph.D. in 1934 stayed at Princeton for an additional year with a Proctor Fellowship. In later years Bardeen and Seitz would often interact professionally. They would work together in the same department at the University of Illinois from 1951 through 1965. After Seitz, Bardeen’s closest physics friend at Princeton was Conyers Herring, who arrived in 1934, when Bardeen was starting his second year. After graduating from the University of Kansas, Herring had spent a year studying astronomy at Caltech. He trans- ferred to Princeton after changing his field to physics. Bardeen and Herring would also remain friends and colleagues. They would overlap in the late 1930s at Harvard and in the 1940s at Bell Labo- ratories. Another of Bardeen’s friends at Princeton was Walker Bleakney, a young faculty member. Bleakney had attended graduate school in Minnesota with Walter Brattain, who occasionally visited Bleakney at Princeton. They “were part of the ring with John,” Seitz recalled. “Their friendship went very deep” and they “were thick as thieves when having fun together.” Not only would they bowl and drink beer together but they also “spoke the same Midwestern language.” Bardeen’s Princeton friends also included the chemists Henry Eyring and Joseph Hirschfelder. Princeton encouraged communica- tion among students in related fields, such as chemistry and physics, or physics and mathematics. The physics and mathematics students regularly drank afternoon tea together in Fine Hall. “At 4:30,” Seitz recalled, “everyone who could walk or go on crutches met in what was called the social room and spent about twenty minutes to a half-hour talking.” Bardeen attended seminars at both the university and the Institute for Advanced Study. The institute, though institutionally separate from the university, was housed in Fine Hall. Bardeen recalled institute seminars that included such greats as Einstein, John von Neumann, Oswald Veblen, and Hermann Weyl. He later described the institute as a model of collaborative work that created “a strong synergistic effect of accomplishing much more than the 

50 TRUE GENIUS individuals could be expected to do on their own.” The notion of enhancing research through interdisciplinary collaboration appealed to Bardeen throughout his career. Princeton was then entering an extraordinary era of change. Modernization of the curriculum had brought major additions to the physics faculty, including Edward U. Condon and Howard P. Robertson in 1928. Princeton’s strengthening of its mathematics and physics offerings was part of a larger institutional growth in American universities during the 1920s and 1930s. This nation- wide trend transformed American physics, removing the earlier gap between American and Old World scientific centers that had led young theorists of the previous generation, such as J. Robert Oppenheimer or John Slater, to study in Europe. By the time Bardeen entered his graduate program, that gap was no longer noticeable. Among the European physicists who had taken an interest in building up American physics was the eminent Dutch theoretical physicist Paul Ehrenfest. He had explained to the heads of Ameri- can departments that hiring Europeans would work much better if positions were offered in pairs, preferably to researchers in close specialties, so that they would be able to speak with one another and feel less isolated in the “wilds” of America. The University of Michigan conducted the “Ehrenfest experiment” successfully in 1927, when Samuel Goudsmit and George Uhlenbeck were simul- taneously offered positions in its physics department. Princeton followed suit in 1930, hiring two Hungarian mem- bers of the Berlin circle of physics and mathematics, John von Neumann and Eugene Wigner, who were old friends. Princeton had “reluctantly” taken Wigner on to attract von Neumann, who had been in the class behind Wigner in their Budapest grade school. At Princeton the two friends enjoyed deep conversations during long walks together. The subjects they discussed ranged from popular culture to mathematics. A year later, when their one-year appointments ended, both Wigner and von Neumann were happy to accept a new five-year contract. The appointments included the condition that they both spend half the year at Princeton together, the other half anywhere else. Wigner accepted an appointment at the Technische Hochschule in Berlin for the spring semesters. But before the five years had ended, the situation in Germany for Jewish physicists 

A Graduate Student’s Paradise 51 had grown so dangerous that Wigner broke his ties with Berlin. Bardeen later wrote that of all his professors at Princeton he was “most stimulated by the two young Hungarians.” Bardeen thoroughly enjoyed his Princeton seminars on quan- tum mechanics and relativity. One of his favorites was the one that von Neumann offered on “Operator Theory” during the first and second semesters of Bardeen’s time at Princeton. The seminar dealt with Hilbert space, an infinite dimensional space of functions. Dur- ing his second year at Princeton, Bardeen sat in on Paul Dirac’s yearlong course on quantum electrodynamics, a more advanced continuation of the course Bardeen had taken from him at Wisconsin. Robertson’s course on general relativity and cosmology during the spring of 1935 impressed Bardeen so much that he would use it later as a basis for teaching his own course on relativity. “Robertson’s lectures were of supreme elegance,” Seitz later reflected. Bardeen found Robertson easy to talk with. He was “certainly one of those who made the department in terms of social inter- actions, creating a friendly atmosphere.” Bardeen recalled that he was the “sort of person who would not intimidate anyone from asking questions about anything.” Herring said that Robertson was “prominent in the beer parties,” as well as “very competent in his field of general relativity and cosmology.” Both students said the same about Condon, who Herring called “good-natured, very approachable.” Condon “always had a good physical way of explaining everything and just was very easy-going.” Bardeen, Seitz, and Herring were among the members of a small group of young physicists that gathered informally around Condon, united by their interest in theoretical physics. Their meetings typically began in the afternoon and ended in the evening at the Nassau Tavern, where the discussions continued over beer. Bardeen attended many special lectures and seminars. One dis- tinguished visitor was Ralph H. Fowler, from Trinity College, to whom John had applied unsuccessfully in 1929 for a research studentship. Others who lectured at Princeton while Bardeen was studying there included Erwin Schrödinger, the inventor of the wave mechanical formulation of quantum mechanics, and Isadore I. Rabi, whose molecular beam experiments had made it possible to measure the radio frequency spectrum of atomic nuclei. Bardeen made an effort to attend these lectures “most of the time, even 

52 TRUE GENIUS though the talks were not in areas which affected my work di- rectly,” for his goal was to gain “a broader knowledge of what sorts of problems people were interested in.” He wanted “to see what major hurdles were being faced”—in short, what it meant to be a great physicist. Although, he admitted, many of the talks were “over my head,” he was “getting a little feeling” for their subjects. The Princeton graduate students discovered that they were quite free to follow their interests. “Only a few courses were offered at the graduate level, so most of the students took what was offered,” Bardeen explained. Beyond these, students worked with individual professors to create specialized courses to help advance their careers. There were no official requirements. Routine burdens, such as homework assignments, were “minimal.” Seitz called Princeton in that period “a graduate student’s paradise.” Bardeen stayed on the fence between physics and math. He thought he had more talent in math but considered physics more interesting. In any case, choosing was unnecessary as the physics and math graduate students took the same courses. The only differ- ence between Bardeen’s program in math and Seitz’s in physics was in the oral prelims; even their written prelims were identical. Bardeen straddled the two fields as long as he could. Although his Ph.D. was in math, he selected a physics problem for his thesis. Bardeen “found that there wasn’t much opportunity of work- ing with Einstein after all.” The great man had done his major work decades ago and was then mainly devoted to relocating German- Jewish refugee physicists. The research he was doing focused on two immensely difficult projects not appropriate for a young researcher: finding the inconsistencies in quantum mechanics and developing a unifying theory for all of physics. In shopping around for a thesis advisor, Bardeen spoke first with Condon, but he found that all of Condon’s suggestions concerned filling gaps in the textbook he was then completing with G. H. Shortley, The Theory of Atomic Spectra. That “didn’t sound too interesting” to Bardeen. Seitz had had a similar experience with Condon, with whom Seitz had expected to work, given that Condon was known to be “one of the few individuals on the East Coast with a working knowledge of quantum mechanics.” Seitz found Condon “all wrapped up” with his textbook. In an effort to be fair, Condon explained to Seitz that the problems of his book were not top-level thesis projects. He helped Seitz arrange to work with 

A Graduate Student’s Paradise 53 Wigner. According to Seitz, Condon told Wigner, “Atomic theory is a cold fish by now. What we ought to see is if we can make a start on solids.” And Wigner had replied, “Yes, that has been on my mind.” Bardeen also spoke with Robertson about working on a prob- lem in relativistic quantum electrodynamics. Exploring a few prob- lems that Robertson suggested, he soon realized that the esoteric field was not ripe for progress. He thought he would be constantly frustrated by “all those infinities” that arise in relativistic quan- tum field theory, because single electrons can make a virtual tran- sition to an infinite number of states. A decade and a half later, in 1947, Julian Schwinger, Richard Feynman, and Sin-itiro Tomonaga would develop a method for avoiding the infinities using “renormalization” theory. The three would win the 1965 Nobel Prize for their contribution. The problems that Wigner was addressing, on the application of quantum mechanics to real (rather than ideal) solids, looked more manageable to Bardeen. It also appealed to Bardeen that solid- state work would be of great use in the world. Wigner thought that his interest in solids had emerged from the curious fact that each material has its unique characteristics. Attempting to explain this interest to an interviewer, Wigner reached for his keys which at first he could not find. “Maybe they’re in your overcoat, Eugene,” suggested Seitz, who was there. Wigner rushed out into the hall to check his overcoat. He returned after a short time rattling the keys. Then he raised them and let them fall. He explained: If I drop my keys, I don’t worry at all whether they will be broken. But if I drop a cup or a glass, I worry at once, and usually it is broken. That is a fundamental and noticeable difference. The explanation of these facts uses, to a very large extent, the basic fact that there are fundamental differences in the structure of different solids. Wigner wanted to know the cause of these differences in struc- ture. His childhood experience of tanning leather in his family’s shop had nurtured an interest in real materials. He claimed that he had always been attracted to problems on the borders between dis- ciplines. The problems of solids, such as why the “atoms in crys- tals are so often located on symmetry axes or in symmetry planes,” drew on several disciplines. In studying solids he could benefit from seven fields in which he had prior knowledge: atomic physics, 

54 TRUE GENIUS quantum mechanics, chemistry, chemical engineering, molecular structure, elastic vibrations, and group theory. Bardeen wondered whether Wigner, only six years Bardeen’s senior, would be a suitable advisor. He had heard rumors about the rigors Wigner imposed, in particular his expectation that students have a firm grasp of quantum mechanics. That was not a problem for Bardeen, as he wanted to gain mastery of that field. He was more concerned with the amount of time Wigner could offer. The latter was still spending only the fall semesters at Princeton, the spring semesters in Berlin. Bardeen also worried whether he and Wigner would be able to communicate effectively. The courtly Wigner was at least as quiet as Bardeen. One Princeton student judged Wigner “too polite for this informal society.” In his own office, Wigner would ask for permission to remove his jacket. Wigner’s biographer, Andrew Szanton, described a telling inter- change he had had with Wigner. When a coughing spell interrupted the conversation, Wigner apologized. “It is my fault,” he said, but “not my conscious fault.” Bardeen questioned Seitz about his experience with Wigner. Seitz was completely positive. He later called working with Wigner “one of the most remarkable experiences of my life.” Not only was Wigner the perfect mentor for Seitz, but the two also became close friends. Having recently arrived at Princeton in 1930, Wigner felt like a “fish out of water.” During long walks together, Seitz tried to address Wigner’s questions about American customs, while he in turn quizzed Wigner about European politics. Bardeen decided to throw in his lot with Wigner and never regretted it. He found he needed only occasional meetings to keep his thesis on track. Wigner later told Seitz “that he rarely commu- nicated with Bardeen.” But what Bardeen remembered about Wigner was that he always had ways to motivate him with his penetrating questions. Most importantly, Bardeen felt that Wigner instructed him in the art of choosing crucial problems. “He could see what was essential and what the important problems were.” Bardeen also felt that Wigner taught him how to go about attacking problems. The first step was to decompose the problem, either into smaller problems with less scope or into simpler prob- lems that contained the essence of the larger problem. Bardeen said that Wigner stressed reducing to “the simplest possible case, so you can understand that before you go on to something more com- 

A Graduate Student’s Paradise 55 plicated.” In other words, “You reduce a problem to its bare essen- tials, so that it contains just as much of the physics as necessary. I think that was a good lesson to learn.” However, Seitz and other colleagues later pointed out that Bardeen’s problem-solving methods differed from Wigner’s in at least one important way: While Wigner typically opted for an elegant, “very refined math- ematical approach,” Bardeen was happy “to bully through” using any method that worked. In his later years, Bardeen would sometimes note that William Shockley, his Bell Labs group leader and co-Nobel laureate, often used the same approach of simplifying problems to their essentials. But the physicist Philip Anderson, who knew both Shockley and Bardeen, pointed out that while Shockley believed in simplifying problems, he sometimes found it difficult to try alternative approaches if the first attempt failed. If Shockley’s “try simplest cases mantra failed to work, that was it.” Bardeen, Anderson said, “had, in addition to his brilliance, the persistence and judgment . . . to recognize that when one line failed one had to look deeper.” Wigner was “very encouraging about the attempts I was mak- ing towards quantum electrodynamics that didn’t go anywhere,” Bardeen recalled. When the work was superceded before Bardeen had a chance to publish it, Wigner suggested that Bardeen instead try to calculate the work function of a metal, the energy that must be added to release an electron from its surface. This problem was of great interest to industry because reducing the work function of filaments could save huge amounts of power. Bardeen took the problem up. In the early 1930s, only two other graduate programs offered training in quantum solid-state theory: one program at MIT, in Massachusetts, was directed by John Slater; the other, at the Uni- versity of Bristol in England, was led by John E. Lennard-Jones, Nevill Mott, and Harry Jones. As MIT was only a long day’s drive from Princeton, Wigner’s and Slater’s students could, and did, occa- sionally visit each other for a few days, sometimes for a whole week. Reflecting on the roles of Princeton, MIT, and Bristol in shap- ing solid-state theory during the 1930s, Bardeen felt that “practi- cally all descendents can be traced back, one way or another, to those three.” But Princeton, he smiled, was “certainly the most exciting place.” A year later Herring also made the decision to work on the 

56 TRUE GENIUS theory of solids under Wigner. Wigner later told an interviewer that “Conyers knew more solid-state physics than anybody I ever met.” Seitz, Bardeen, and Herring, in that order, Wigner’s first three gradu- ate students, were in the first handful of theoretical physicists who would refer to themselves as solid-state physicists. But while Wigner’s infectious passion for solid-state physics problems burned out after a few years, Seitz, Bardeen, and Herring all stayed within solid-state theory throughout their long careers. For the Christmas break in 1933, Bardeen followed through on his plan to drive back to Pittsburgh. As soon as he arrived, he phoned the Relines. Jane was there. Bruce put his hand over the mouth- piece and said, “It’s John Bardeen. I think he wants to ask you out but he’s forgotten your name.” It was a moment she had been hoping for. John asked Jane to a New Year’s Eve party. She had an earlier en- gagement across town. To encourage the romance, Bruce offered to get her back home in time for her date with Bardeen. Afterwards, John had to rush back to Princeton. He began to seek reasons to visit Pittsburgh. When Peters and Eckhardt invited him to work at Gulf for the summer, he readily agreed. But the time John and Jane spent together was minimal in that summer of 1934, because Jane had already arranged to work at the Woods Hole Marine Biological Research Laboratory on the Massachusetts coast. When John learned that his younger brother Tom was marry- ing his longtime sweetheart Janet Smith, he suggested that Tom apply to Gulf for a position. He figured that Tom had a good chance of being hired. Unlike John, Tom had excelled all along as a stu- dent, receiving honors at the University of Wisconsin. One story has Tom developing his own derivation on a mathematics final when he did not know the official one. Like John, Tom had also been on the swim team, serving for a time as its captain. He had been president of the Student Athletic Board. Although Tom went on to work toward his Ph.D. in electrical engineering, he was not completely satisfied with the program at Wisconsin. With a master’s degree in hand and a strong recommendation from his older brother, Tom secured a post at Gulf Labs. He arrived in time to overlap with John for a few weeks during the summer of 1934. Tom’s quick intelligence made him an instant asset at Gulf. Over the years he took responsibility for much of the company’s 

A Graduate Student’s Paradise 57 seismic instrumentation. By the time he retired he had nine pat- ents to his credit. Gulf eventually rewarded him with its senior scientist appointment, a rank equivalent in honor and pay to that of its upper-level executives. John saw Jane whenever he visited Tom in Pittsburgh. The fam- ily in Madison was not fooled by the “visiting Tom” ruse. They also teased John about the letters that arrived in Madison from a mysterious woman friend whenever John was home. John’s sister Ann recalled, “He wouldn’t say a word about them, and he was very closed-lipped about the whole thing.” When he was in Pittsburgh John also visited his former Gulf buddies, with whom he could relax and sometimes carouse. Seitz recalled a visit that he and Bardeen made in June 1934, after they passed their prelims. Having studied intensively, they were “greatly over-prepared” for the written part, Seitz recalled. He and Bardeen would work until they “thought they were safe.” Then Joseph Hirshfelder, a Wigner student in chemistry who was examined with them, “would come around with an exotic question and we all went back to the books.” The oral part proved an ordeal, however. The questions that a committee of professors threw at them were aimed at revealing the limitations of their understanding. Robertson “raised the height of the cross-bar until you tripped,” recalled Seitz. His questions high- lighted one of Bardeen’s weaknesses, his difficulty to verbalize all the steps in his reasoning. In one question, Robertson asked John to explain what “electrodynamics would look like if there were magnetic poles.” Bardeen gave the correct answer, but stumbled when asked for the details of his argument. “I was using too much intuition and could not give a convincing argument of the sort he wanted.” He passed the prelim, but never could forget the embar- rassment of having fumbled an important question. Afterwards, Bardeen and Seitz piled into Bardeen’s car for a vacation in Chicago. On the way they stopped in Pittsburgh, where they were greeted “noisily and as honored guests.” They were given rooms in an engineering fraternity house across the street from Carnegie Tech. Seitz later described the “big party for John” thrown by the fraternity on Saturday night: Without too much encouragement, he soon became the life and soul of the boisterous gathering. That night I saw John in a rare departure from his usual sober demeanor, a treat that few of his later friends 

58 TRUE GENIUS would experience in quite the way I did. I might add that I was put quietly to bed long before John was ready to quit. Bardeen realized that he would have to grasp much of what was known about the physics of solids. He would have to learn how the electrons in metals interact with one another and with the crystal lattice. These were issues that concerned him throughout his career. Back at Princeton, he retired to the library and looked up everything he could find on work functions. Wigner, who encour- aged all his students to immerse themselves in the literature of their field, reported “No one in my experience ever became ac- quainted more quickly with a rather complicated subject.” Bardeen added the habit of spending daily time in the library to his arsenal of problem-solving tools. Over the years he built up an enor- mous fund of knowledge about solid-state physics. He had to decide how far back to go in the literature. Since the beginnings of civilization, the properties of materials had been studied by blacksmiths, potters, jewelry makers, and other artisans. Artists and builders also knew much about the materials they used. But at the end of the nineteenth century, there was still no frame- work for answering many basic questions, such as why do metals and insulators behave so differently in transporting heat and electricity? Paradoxically, as the metallurgist and historian of technology Cyril Stanley Smith once noted, physicists interested in explaining real materials were forced to leave the domain of real materials for a period of time. For almost three decades, from 1905 until 1933, they had puzzled over the more abstract problem of explaining ideal materials, much simpler models of metals, insulators, and the like. Here was a historical example of Wigner’s principle of approaching complex problems by considering simpler cases first. By starting with these hypothetical cases, physicists could get to the heart of the matter and develop a basic machinery for dealing with the full range of properties and conditions that characterize real materials. Bardeen realized that it was the work of these three decades that he needed to zoom in on. The work had left many problems unaddressed—a field ripe for progress. He also recognized that he was standing on the edge of a frontier. Since the birth of the quantum in 1900, the physicists who studied solids had limited their work to ideal materials. This restriction had allowed them to 

A Graduate Student’s Paradise 59 make much progress, especially during the seven years following the invention of quantum mechanics in 1925. The new mechanics had offered the tools for studying atoms, molecules, and solids. But until 1933—until the work that Wigner and Seitz were just then doing—the theory was incapable of dealing with real solids, “far more complex things than have been allowed in the domain of respectable physics in the past,” as Cyril Smith wrote. Wigner and Condon were among the first to recognize the opportunity to ad- dress real problems of real solids, such as the structure, cohesion, plasticity, diffusion, strength, electrical conduction, and magnetism of materials like sodium or copper. For the first time in history, one could go beyond treating such problems of ideal materials and move into the real world. Wigner offered this opportunity to his first graduate students. The problem of the photoelectric effect, which Einstein had studied in 1905, was in some ways analogous to the problem of the work function. Einstein had computed the energy in the form of light quanta needed to release an electron from a metal’s surface. In exploring the photoelectric effect he had paved the way for viewing all forms of radiation in terms of Max Planck’s revolutionary quanta, the irreducible bits that comprise electromagnetic energy. It was for solving this problem—not for his theory of relativity— that Einstein won the 1921 Nobel Prize. Another important model for Bardeen was Einstein’s 1907 cal- culation of the specific heat. Using quantum concepts Einstein had derived the amount of energy needed to raise the temperature of one gram of material by one degree Centigrade. And to understand the crystal structure of a metal, it was necessary to go back only to 1912, when Max von Laue, Walther Friederich, and Paul Knipping demonstrated in their Munich experiments that crystals can dif- fract X rays. Their work offered the first startling look at the crys- tal structure inside metals. Bardeen realized that he needed a thorough understanding of the quantum theory framework on which he and others in his generation would construct the theory of real solids. Statistical methods were essential because solids contain multitudes of atoms—over a thousand billion billion (1021)—in every cubic centi- meter. By the end of 1926, two different quantum statistics were available: the Fermi-Dirac and the Bose-Einstein statistics. Fermi- Dirac statistics apply to particles, such as electrons, that obey the 

60 TRUE GENIUS Pauli exclusion principle, the electron zoning ordinance that Wolfgang Pauli proposed in 1925 to explain the closure of electron shells in atoms. The principle states that two identical particles in the class later referred to as “fermions” cannot occupy the same quantum state. The other statistics apply to “bosons,” particles of radiation, like photons, or X rays, that don’t obey the Pauli prin- ciple. In 1926 Pauli began the development of the quantum theory of solids with a quantum-mechanical calculation of one of the phenomena that experimenters were studying, the weak para- magnetism of metals. He used this problem as a test case to address the fundamental question: Which of the two quantum statistics describes matter? Ample data were available on paramagnetism. He performed the calculation both ways, using Fermi-Dirac and Bose-Einstein statistics. He found that Fermi-Dirac statistics worked and Bose-Einstein did not. This simple triumph pointed to the need for reworking the ex- isting formulation of the theory of metals, then based on classical Maxwell-Boltzmann statistics. Pauli could see the utility of doing this, but he also realized that the calculation would be exceedingly messy. He turned in disgust from the approximations needed to tailor the theory to real phenomena, warning his students against working in what he called the “physics of dirt,” an area he cau- tioned “one shouldn’t wallow in.” Fortunately, Wigner, Seitz, and Bardeen disagreed with Pauli. Arnold Sommerfeld, who had been Pauli’s professor in Munich and whose Michigan lectures Brattain had heard in 1931, consid- ered solid-state physics beautiful because its problems were real. In his classic calculations of 1927, Sommerfeld followed Pauli’s program and structured a “semi-classical” quantum theory of solids. Avoiding the full use of the quantum-mechanical machinery based on Schrödinger’s wave equation, and employing the Fermi- Dirac statistics only as needed in modifying the classical theory, Sommerfeld was able to address a whole range of problems that had previously been insoluble. Still it remained a puzzle why Sommerfeld’s theory should work at all, as it was based on the unreal assumption that electrons in metals move freely. This ques- tion would nag Bardeen for years. A partial answer was offered in the brilliant 1928 doctoral dissertation of Heisenberg’s graduate student, Felix Bloch. Bloch 

A Graduate Student’s Paradise 61 discovered that when electrons move through a perfect crystal (in which the atoms are evenly spaced), they behave as though they are free particles. On this basis he constructed the conceptual framework known as “band theory.” Just as the electrons in atoms are confined to energy levels, the electrons in metals are confined to energy bands (extended levels). Other physicists, including Léon Brillouin and Rudolf Peierls, elaborated on Bloch’s theory. Bardeen especially admired the theoretical bridge that Alan Wilson erected in 1931 between the theoretical works of Bloch and Peierls and the practical problems encountered by experimenters. Wilson’s tour de force was to assemble the available pieces of the band theory to explain the difference between metals and insula- tors. His simple answer was: insulators have completely filled bands; metals have partially filled bands. Within the partially filled bands, electrons can move and carry current. Wilson’s work also clarified the ghostlike notion of the “hole,” a concept of solids that Peierls first described in 1928. An empty electron state near the top of an otherwise filled energy band, the hole behaves as though it were a positively charged particle. The hole in a solid is like the moving empty seat in a large garden party, where guests are seated at various tables. As one guest who had been seated at a certain table with all chairs filled moves over into a previously empty seat at another table, she leaves her former seat vacant. Then when someone else leaves a different chair to move into her seat, he leaves his former seat vacant, and so on. To one observing the scene from a helicopter, it would appear that the empty place is moving. For the case of semiconductors and semi- metals, the moving holes can be treated as positive charges, be- cause the electrons are negatively charged. Wilson also explained the behavior of semiconductors, materials with properties that are partway between those of metals and insu- lators. Semiconductors were enormously controversial in the early 1930s; some physicists were convinced they did not exist. Wilson pictured them as materials having a gap between their highest filled energy band and their lowest unfilled one. Under ordinary circum- stances, electrons cannot jump the gap. Therefore, the material behaves like an insulator. But when energy is added in the form of light or heat, some electrons gain enough energy to traverse the gap. Conduction begins when an electron enters the first unfilled band. In the 1940s experimenters would find that adding impuri- 

62 TRUE GENIUS ties (“doping”) can enhance conduction by creating shallow levels, in effect offering stepping stones for the electrons. Bardeen realized that the most dramatic moment in this little- known history was occurring just then—at Princeton! Seitz’s doc- toral thesis of 1933 was the first step in a revolution that would bring the quantum theory of solids to the study of real materials. Until then no one had been able to calculate any real band struc- tures. Focusing on sodium, the simplest metal, Wigner and Seitz began by dividing the crystal into small cells associated with indi- vidual ions. In each cell they assumed that the electrical potential was spherically symmetrical. This simplifying assumption made the mathematics able to compute such properties of real metals as cohesive force, elastic constants, compressibilities, thermal and electrical conductivities, and various optical properties. To Bardeen the Wigner-Seitz work “looked like it would open up a new area.” At MIT, Slater, who made the Wigner-Seitz method central to his training of graduate students, wrote of the Wigner- Seitz papers, “There were so many approximations that it was hard to accept the numerical results very seriously. However, for the first time they had given a usable method for estimating energy bands in actual crystals.” Within a decade the first crude methods for calculating the properties of metals would lead to better ones. The new frame- work became an umbrella covering many subfields—including crystallography, electrical conduction, semiconductors, ferroelec- tricity, and magnetism—that were earlier thought to be indepen- dent. Considered together the subfields became known as solid- state physics. Most scientific fields arise through differentiation from other broader fields. Solid-state physics, however, arose by a conglomeration of fields, as the historian Spencer Weart pointed out. At least a dozen major reviews of the new field of physics were in print or in press by 1933. The most comprehensive was the monumental, almost 300-page article by Hans Bethe and Arnold Sommerfeld in the 1933 Handbuch der Physik. Graduate seminars on solid-state physics soon began to be offered at universities. One of the earliest was Wigner’s seminar, “Theory of the Solid State,” first taught in 1932. He covered a wide variety of topics, including the distinctions between different solids, symmetry groups in rela- tion to the different kinds of crystals, aspects of the growth of crys- 

A Graduate Student’s Paradise 63 tals, and approximation methods. Seitz prepared the course notes for this seminar in 1934, the year in which he, Bardeen, and about a dozen other students attended. Bardeen learned that designing the best approximations for a theory of solids was an art in itself. It was not at all clear how to represent the electrons inside solids. Were they to be thought of as tied to individual atoms (or ions)? Or were they better represented as swarms of particles that move without allegiance to any single ion? The true picture had to fall between these extremes. Numerous approximation schemes grew up around these questions. The effort to deal with the interactions between electrons, or between electrons and ions, set the stage for a new field that became known as “many-body” theory. In many-body problems, the inter- actions are so crucial to the description that ignoring them misses important observed phenomena. The art in solving such problems involved representing the interactions and deciding which inter- actions to include in the theory. Such problems would engage Bardeen throughout his career. In his thesis calculation, Bardeen first needed to make work- able approximations for the electron interactions. Starting with a method pioneered by Douglas Hartree and Vladimir Fock, Bardeen wrote down a wave function that described each electron approxi- mately, with its own single-electron wave function. He next modeled the distribution of electrons at the surface of the metal, including higher contributions arising from electron forces that cor- related electrons with other electrons. It was a heroic early work in the field. He was ready to write up the thesis by the spring of 1935, publishing it as a joint work with Wigner. “Wigner actually did most of the work,” Bardeen later claimed. But Wigner said that Bardeen “started to work on his own line and has worked practically independently.” He added that Bardeen “has not needed exaggerated mathematical equipment but rather the handling of physical ideas and this he has done in an unusually original manner.” As Bardeen began writing up his thesis, he was surprised to learn that Harvard’s Society of Fellows, recently established in 1933, was considering him for their third class of junior fellows. It was an extraordinary opportunity. If he could land the prestigious fellowship, he would be able to concentrate entirely on research for three years. Harvard was an outstanding physics center. So was 

64 TRUE GENIUS nearby MIT. But first he had to be interviewed by a group of senior fellows of the Harvard Society. The purpose of this formidable ritual was “to see the man beyond the scholar, if possible a man with a long view.” Bardeen was completely tongue-tied during the ordeal. His interviewing committee included the famous philosopher and mathematician Alfred North Whitehead, the internationally known historian Samuel Eliot Morison, and the leading biological chemist Lawrence J. Henderson. “I was placed before this very distinguished group of people who asked me questions. I think I was too scared to hardly say a word.” When Bardeen failed to make much of an impression at the interview, John Van Vleck stepped in. Van Vleck had recently left the University of Wisconsin and was now on Harvard’s physics fac- ulty. His intervention succeeded, and Bardeen’s fellowship began in the fall of 1935. “I’m sure it was Van Vleck that got me in,” Bardeen admitted years later. As it turned out, Bardeen had the luxury of choosing between two attractive fellowships, for Princeton also offered him one of its prestigious Proctor fellowships for 1935–1936. As the Harvard fellowship paid substantially more ($1,500 a year plus board at Harvard’s Lowell House) and was guaranteed for three years, the choice was easy to make. “Three years of job security was no small item at the time.” Another consideration was that Harvard’s fellow- ship was in physics, whereas Princeton’s was in mathematics. By then “it was obvious that I was going in the direction of physics.” Harvard junior fellows were expected to arrive with doctorate in hand. For Bardeen this proved impossible. In May 1935 he received an urgent request to come home to Madison immediately. His father Charles was jaundiced and very ill. He was not expected to survive long. Two years earlier he had had his thyroid removed because of a cancerous growth. The cancer had returned. Charles passed away on June 12, a few weeks after John came home. A postmortem discovered a difficult-to-diagnose form of pan- creatic cancer that had spread to Charles’s liver. He was buried beside Althea, under a boulder from Lake Mendota. Charles Bardeen’s obituaries highlight many features that John came to share with his father. One said that the older Bardeen’s “relaxations came through walks or picnics with his family, a game of golf with some old cronies, conversation or dinner with a group 

A Graduate Student’s Paradise 65 of friends.” Although Charles had been “endowed with a brilliant mind,” he was, like John, “sympathetic with those less gifted.” The morning after Dean Bardeen’s death, a janitor said he “had lost a good pal.” Later reminiscences of Charles Bardeen expanded the analogy between him and his son John. In 1957, at the dedication of a new medical school building to Charles Bardeen, Harold Bradley described Charles as “a prodigious worker,” with “a deep dislike of public acclaim or personal recognition.” He referred to him as “a quiet giant, given to few words; modest, self-effacing, shunning praise and public approbation.” Paul Clark subsequently wrote in a history of the Wisconsin Medical School that “Dr. Bardeen spoke in a somewhat mumbling fashion, moving his lips only slightly, but he thought with clarity and there was no mumbling in his deci- sions.” He, too, referred to Charles as “a prodigious worker, a patient, tolerant man, simple in his tastes, keenly intellectual . . . reserved and persevering almost to stubbornness.” Among Dean Bardeen’s lasting educational contributions was his establishment of a preceptorship in which medical students worked closely with one of a dozen highly competent practicing physicians. In the weeks after his father’s funeral John was intensely anxious to finish his thesis. He worked on it whenever possible, but he could not complete the arduous calculations that summer. Not only was it difficult to concentrate, but also Wigner was in Europe and thus unable to approve the thesis before fall. Bardeen did not receive his Ph.D. until January 1936. That Harvard allowed Bardeen to complete his doctorate during his first semester as a junior fellow was perhaps another result of Van Vleck’s continuing influence. At the end of that long and difficult summer of 1935, when Bardeen’s extended family of stepmother, siblings, aunts, uncles, and cousins offered him comfort and stability, John set out for Harvard. Despite some uneasiness about not completing his thesis, he was filled with excitement.