Quantum Legacies: Dispatches From an Uncertain World Read online

  The pedagogical shift was closely correlated with enrollment patterns. Whereas Oppenheimer had lectured to about two dozen students at a time in his Berkeley course during the 1930s, after the war enrollments rapidly began to rise. By the mid-1950s, courses on quantum mechanics aimed at first-year graduate students typically had forty to sixty students enrolled; in the nation’s largest departments, at Berkeley and MIT, the number edged over one hundred, “a disgrace [that] should not be tolerated at any respectable university,” Berkeley’s department chair complained to the dean. In a handful of departments, however, enrollments in first-year graduate-level quantum mechanics courses remained fairly small during the early 1950s or began to grow only later. Reading through lecture notes from these various departments reveals some remarkable differences. In short, an increase by a factor of three in enrollments was correlated with a decrease by a factor of five in the proportion of time devoted to the conceptual puzzles or philosophical challenges of quantum theory.16

  Beyond the numbers and statistics, the lecture notes themselves provide some stark contrasts. Consider the course that Lothar Nordheim taught at Duke University in the spring of 1950. Like so many of his colleagues across the country, Nordheim had spent the war years working on the Manhattan Project. He had served as section chief at the Oak Ridge laboratory in Tennessee (principal site for isolating the fissionable isotope of uranium, U-235), rising to direct its physics division between 1945 and 1947. He left Oak Ridge for Duke in 1947 but did not stay long: by autumn 1950, he had begun to work full-time on the top-secret hydrogen-bomb project and later chaired the theoretical physics division at the major nuclear-related defense contractor General Atomics. In short, Nordheim was no stranger to the new realities of the military-industrial complex, and he excelled at wringing practical results, often under extreme time pressures, from the equations of quantum theory.17

  Yet when he taught his course on quantum mechanics at Duke in 1950, Nordheim insisted that his students focus on its conceptual challenges. Working with a small class of a dozen students, he launched into the stubborn strangeness of quantum mechanics in his very first lecture. Given the new restriction to probabilities, he asked his students: “What does this do to causality?” A student recorded in his notes, simply, “Ans[wer]. It Fucks it!” To drive the point home, Nordheim devoted two more lectures to the fabled double-slit experiment—a favorite example that Heisenberg and Schrödinger had each introduced in his own teaching, back in the early days of quantum theory, to emphasize such quintessential quantum features as wave-particle duality, superposition, and the uncertainty principle. Likewise for Nordheim’s treatment of a quantum particle tunneling through a barrier. As he described the counterintuitive process, he pressed his students, “it is meaningless to ask, ‘Is there causality?,’ because we can never know the state completely at any time, because of [the] uncertainty relation. Hence, we discard the classical physical ideas of idealized observations.”18

  In other classrooms across the country, physicists who had shared many of Nordheim’s worldly experiences—the secret, massive wartime projects, major consulting for defense projects after the war—charted a very different course when lecturing on quantum mechanics to their own graduate students. Where Nordheim lectured to a dozen students, most of these others faced classes that had already grown several times larger. At Chicago, Enrico Fermi spent twice as long deriving properties of the Laguerre polynomials—mathematical functions that quantify the behavior of an electron in a hydrogen atom—as he did on Heisenberg’s uncertainty principle. At Cornell, Hans Bethe observed, with one passing remark, that trying to circumvent the uncertainty principle was as fruitless as designing perpetual motion machines, full stop. Even Richard Feynman, full of exuberance about bringing quantum theory to younger and younger students, made clear in his own classroom that the real purpose was to learn to calculate. In the lecture notes from his graduate-level course on quantum mechanics, he admonished that interpretive issues—of the sort that had filled Oppenheimer’s lectures before the war and Nordheim’s lectures after it—were all “in the nature of philosophical questions. They are not necessary for the further development of physics.” While Nordheim had paused to consider conceptual sticking points of quantum tunneling, Freeman Dyson, lecturing to a class at Cornell with nearly three times as many students as Nordheim’s class at Duke, plowed forward, adapting the usual calculation to treat various states of nuclear matter, such as deuterons. Dyson made clear, in his first lecture, that he would not follow the chosen textbook very closely. “Too much philosophy.”19

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  Two well-known textbooks, both published soon after the war, further illustrate the trend: Leonard Schiff’s Quantum Mechanics (1949) and David Bohm’s Quantum Theory (1951). Schiff and Bohm had each studied with Oppenheimer in Berkeley during the 1930s; both authors acknowledged how influential Oppenheimer’s course had been for their own teaching. Yet what seemed like complementary models for teaching the subject—remarkably different in their emphases, yet equally hailed as great successes upon publication—soon collapsed under the pressure of rising student numbers.20

  Leonard Schiff had been a postdoc with Oppenheimer between 1937 and 1940. He later joined the faculty at Stanford, and his Quantum Mechanics first appeared in 1949 to rave reviews. Schiff’s book exemplified the toolkit approach to quantum mechanics. Whereas Oppenheimer had made his way slowly to the details of the Schrödinger equation, pausing at length to entertain many of the conceptual quandaries that arose along the way, Schiff largely dispensed with such philosophical niceties. (“We shall discuss physics, not philosophy,” he announced on the first day of one of his courses in 1959.)21 What had occupied nearly 20 percent of Oppenheimer’s lecture notes, Schiff dispatched in a few opening pages of his book. In its place, Schiff provided what was widely hailed as the best collection of homework problems to calculate, of just the right level of difficulty for his target readers.22

  David Bohm completed his PhD under Oppenheimer’s direction in 1942 and published his Quantum Theory in 1951 after teaching at Princeton for a few years. He had tested out the material for his book in classes during 1947 and 1948, before Princeton’s physics department had swelled too large. (His enrollments in those years were around twenty students in each class, similar in size to Oppenheimer’s course at Berkeley in the 1930s.) Like Schiff’s book, Bohm’s book received glowing reviews at first—“a rare example of expressive, clear scientific writing,” proclaimed one satisfied reviewer. In contrast to Schiff’s approach, Bohm devoted several opening chapters to the kinds of philosophical challenges and conceptual puzzles that Oppenheimer, too, had emphasized. The Schrödinger equation didn’t even appear until page 191 in Bohm’s book; Schiff had first introduced the equation on page 21.23

  The conceptual care that Bohm had taken when composing his textbook impressed several of his earliest reviewers. One praised “the concise and well balanced interplay, point-counterpoint, between formalism and interpretation.” Another compared Bohm’s and Schiff’s books side by side—Schiff’s being the only obvious American competitor published since the war—and offered the following balance sheet. Though only two-thirds as long, Schiff’s book treated many more applications of the formalism in greater detail. Yet for those topics treated by both authors, this reviewer continued, “it is to the credit of Bohm’s book that, for example, it gives the clearer and more physically understandable explanation.”24

  Despite their equally promising starts, the two books—like their authors—suffered quite different fates. Schiff became department head at Stanford and soon editor of the influential textbook series published by McGraw-Hill in which his own book had appeared. Bohm, meanwhile, was forced from his position at Princeton—and soon forced out of the country—just months after his book had been published. He had refused to name names when subpoenaed to testify before the House Un-American Activities Committee, during its headline-grabbing investigation into alleged “Communist in
filtration” of the wartime Manhattan Project. Bohm fled to Brazil—where, in between crippling bouts of nausea, he was compelled to forfeit his US passport—before moving a few years later to Israel, eventually settling in London. Schiff’s book saw two widely heralded, updated editions (in 1955 and 1968); Bohm’s book was never reissued during his lifetime, and his efforts to publish a follow-up textbook on quantum mechanics were rebuffed.25

  It fell to a third veteran of Oppenheimer’s Berkeley group, Edward Gerjuoy, to make sense of the diverging paths. He took up the comparison in a review of the second edition of Schiff’s book, in the mid-1950s. In expanding his book, Schiff had devoted even less space to conceptual or interpretive discussion; to Gerjuoy’s taste, each edition of Schiff’s book devoted too little attention to “such questions as correspondence, uncertainty, complementarity, and causality”—precisely the topics that had filled so much of Bohm’s book. (Gerjuoy noted that “the contrast with Bohm’s Quantum Theory is interesting, even amusing.”) But Gerjuoy could understand Schiff’s decision not to amplify these topics in his revised edition. “With these subjects lecturing is of little avail—the baffled student hardly knows what to write down, and what notes he does take are almost certain to horrify the instructor, who perspicaciously usually resolutely refuses to question his students on these topics.” So, instead, Schiff focused on a cache of worked examples: too soon, the student “is well into detailed algebraic complexities verifying which, he readily persuades himself to believe, means he is learning quantum mechanics.” Though Gerjuoy could understand Schiff’s pedagogical choices, he wondered—perhaps thinking back to his experiences as a student in Oppenheimer’s famous course at Berkeley—whether it was “necessary, as Schiff does, to leap so rapidly over the philosophical issues raised by quantum mechanics that the student never has a chance to gauge their depth.”26

  Despite Gerjuoy’s cautions, Schiff’s textbook rapidly became the standard-bearer, its collection of homework problems especially well geared to teaching large classes of students. When asked to evaluate whether a third edition of Schiff’s book would be warranted, a professor at Berkeley responded with a sixteen-page memorandum on why the previous two editions had been so successful. “I believe that the explanation is that Schiff is a very practical book,” the reviewer began. “The reader who goes through the book really obtains a working knowledge of quantum mechanics.” A student using the book, this reviewer continued, is “taken through a number of well chosen applications, and he is shown, through these examples how it all works out.” It was an approach that the Berkeley physicist could appreciate; he had learned the subject from the first edition of Schiff’s book. “As a student I was perfectly happy with this mode of presentation, and the book kept me sufficiently busy to prevent pseudo-philosophical speculations about the True Meaning of quantum mechanics.”27

  Many other physicists across the United States offered similar appraisals. Where once reviewers had evaluated textbooks on quantum mechanics at least in part on the basis of their philosophical stance, reviewers throughout the 1950s and 1960s routinely praised the latest offerings for “avoid[ing] philosophical discussion” and for omitting “philosophically tainted questions” that distracted from the business of learning to calculate. Enough with the “musty atavistic to-do about position and momentum,” stormed MIT’s Herman Feshbach.28

  The new approach shaped the contents of the books as well. Between 1949 and 1979, physicists in the United States published thirty-three textbooks on quantum mechanics aimed at first-year graduate students. Together, these books included 6,261 homework problems (including, of course, many duplicate problems that appeared in several books). Most required students to manipulate the equations in the text: make a change of variables in the Schrödinger equation or evaluate various integrals. Only about 10 percent of the problems pressed students to go beyond the equations, to discuss their calculations in words. The pattern alarmed at least some older physicists, who, like Oppenheimer, had witnessed the remarkable conceptual transformations of quantum theory firsthand. In the early 1960s, one grumbled that with the spate of new textbooks, his colleagues had confused what was “easy to teach”—the “technical mathematical aspects of the theory”—with the conceptual understanding that students needed most.29

  After the enrollments had crashed, however, newer textbooks began to appear, with a markedly different mix of homework problems. For example, Robert Eisberg and Robert Resnick pulled together a draft of their massive book, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, in the early 1970s. By the time their book was published in 1974, first-year graduate enrollments in physics—the population to whom the book was directed—had fallen more than 60 percent from their 1960s peak. Eisberg and Resnick’s book reflected the new classroom realities. In addition to hundreds of quantitative problems, akin to the classics that filled all three editions of Leonard Schiff’s book, Eisberg and Resnick also included long lists of “discussion questions” at the end of each chapter. “Does a blackbody always appear black? Explain the term blackbody” was one early example. “What is the fallacy in the following statement? ‘Since a particle cannot be detected while tunneling through a barrier, it is senseless to say that the process actually happens’”—hearkening back to one of Lothar Nordheim’s favorite examples from his course at Duke. In a similar way, more than half of the homework problems within Quantum States of Atoms, Molecules, and Solids (1976), written by a trio of physicists at Rice University, were of this qualitative, essay-type form.30

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  During the early 1950s, a young theoretical physicist at Berkeley learned the hard way how bloated class sizes could affect research and teaching styles. Having been on the faculty in Berkeley’s physics department for a year and a half, the theorist was let go, not because he was unproductive in research or unconscientious in his teaching—the department chair insisted that the young professor had performed more than adequately at both. Rather, the theorist’s chosen research topic fit poorly with the new pedagogical realities. He had focused on rather abstruse points in quantum field theory. Though the topic could well prove important—the department chair considered it too early to say—it had failed an important test. Junior faculty members, the chair explained, needed to select research topics for themselves that could provide appropriate spin-off projects for their graduate students: “subjects that are not trivial, but at the same time are not unduly difficult or too time-consuming.” Whether or not the young physicist’s research would pan out in the long term, “it is not the sort of work that can readily be used for Ph.D. theses.” With more than two hundred graduate students enrolled, Berkeley’s physics department needed “someone who will be more useful to us.” Only recently, in fact, the department chair had fast-tracked the promotion case for a different junior faculty member largely on the basis of his ability to craft appropriate problems for his many graduate students.31

  Though few departments swelled as large or as quickly as Berkeley’s, most felt the strain of the postwar enrollment boom. At nearby Stanford, physics faculty had prided themselves on the small-group intimacy their department could offer, compared with the “factory” at Berkeley. During the early 1950s, when the incoming cohorts included ten to twelve new students each year, Stanford faculty kept detailed notes on how individual students fared on their oral exams, the standard gateway between coursework and dissertation research: “Rather limited knowledge; shy, hesitant in answers; nervous,” for example, or “well composed and thinks on his feet.” Yet as the number of incoming students rose—soon up to thirty per year by the late 1950s, peaking at thirty-seven in 1969—the individualized note-taking stopped. The written exams shifted from essays to problems to calculate; faculty even flirted with administering true-false exams, to keep the burden of grading under control.32 Physicists at the University of Illinois, facing similar pressures, jokingly called for a “test-ban treaty” in 1963—between faculty and students rather than the
United States and Soviet Union—while students there lobbied for a “flunk-out shelter.”33

  Then the bottom fell out: only eighteen graduate students entered Stanford’s department in 1970, and sixteen in 1972. Just as suddenly, the department once again undertook a sweeping reform of its comprehensive exams, restoring “a significant fraction of essay and discussion questions.” In September 1972, the revised exam featured short-answer or essay questions in 40 percent of the problems, nearly double the proportion in the previous decade’s exams. That same year, the department introduced a new, informal seminar on “speculations in physics”—just the sort of thing that had cost the young theorist at Berkeley his position twenty years earlier.34 Richard Feynman took similar advantage of the transformed pedagogical realities at Caltech. He began to offer an informal course known as “Physics X,” open to any undergraduates who were eager to puzzle through juicy scientific questions. One of my favorite photographs shows Feynman gesturing at the blackboard in 1976—the suit and tie from his early-1960s Feynman Lectures days replaced by an open, wide collar—while a handful of students look on, some sporting headbands, feet propped up on a desk.35