Quantum Legacies: Dispatches From an Uncertain World Read online

  DeWitt had, in fact, included data on graduation rates in the natural sciences and mathematics for both countries, presented just as clearly as the information on agricultural and health specialists had been. Playing the numbers game with these data produced a rather different picture. Up through the mid-1950s (and, indeed, into the early 1960s, as DeWitt’s follow-up study found), the United States maintained a two-to-one lead over the Soviet Union, rather than a deficit, in numbers of students who completed degrees in science and math each year. Lumping science, mathematics, and engineering graduates together and dropping agriculture and health, the ratio came out as 4:3 in favor of the Soviets—a lead that included a large fraction of students who earned their diplomas armed with a textbook and a mailbox. So much for the Soviets’ “two to three times” advantage.22

  None of these points were hidden in classified reports, sealed in a CIA safe; all were as plain on the page as the “two to three times” data had been. Amid a drumbeat of news about the Korean War, the launch of Sputnik, and nuclear brinksmanship, however, certain calculations proved persuasive. The sober rationality of economic analysis—so often honored in the breach—had succumbed to exuberance.

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  The physicists’ bubble, so sharply pronounced between 1945 and 1975, was not a one-shot deal. In fact, graduate enrollments in physics within the United States rebounded during the 1980s, bid higher and higher by many of the same mechanisms that had inflated the first bubble. A resurgence of defense-related spending under the Reagan administration—including the sprawling Strategic Defense Initiative, or “Star Wars” program—combined with new fears of economic competition from Japan drove enrollments in physics and neighboring fields up exponentially once more, nearly matching the late-1960s peak. They fell sharply a decade later with the end of the Cold War. Just as during the early 1970s, shared conditions across fields led to an overall decline in graduate-level enrollments. By the time PhD conferrals in the United States bottomed out in 2002, annual numbers of PhDs granted across all fields had fallen by more than 6 percent from their 1990s peak. As before, though, some fields fell more sharply than others. Annual numbers of PhDs granted across all of science and engineering fell by 10 percent, while annual numbers of PhDs in physics plummeted by 26 percent. Once again, dire predictions of shortfalls in the scientific labor supply had been stupendously mistaken; once again, physics marked the extremes of a general pattern throughout American universities.23

  Figure 7.3. Number of physics PhDs granted per year by US institutions, 1900–2005. (Source: Figure by Alex Wellerstein, based on data from the US National Science Foundation.)

  The dynamics behind the second bubble were remarkably similar to the earlier example. Beginning in 1986, officials at the National Science Foundation had sounded the alarm again that the United States would soon face a devastating shortage of scientists and engineers. Foundation projections indicated that there would be 675,000 too few scientists and engineers in the United States by the year 2010. Just as in response to the DeWitt and Korol studies from the 1950s—especially the stripped-down ratio of “two to three times more” science and engineering graduates per year in the Soviet Union than in the United States—the dramatic projection of shortages during the 1980s helped to unleash generous federal spending.24

  Unlike the DeWitt and Korol studies, the 1980s study by the National Science Foundation did not impress many close observers. In keeping with broader economic modeling during the Reagan administration, the study had neglected to consider demand at all, sticking only with supply-side variables. Yet few skeptics came forward until the early 1990s, after the Soviet Union had dissolved and the Cold War ground to an unexpected halt.25

  Just as in the earlier era, reality checks that could easily have been applied were not, while the scarcity talk looped from hype to amplification to feedback all over again. And just as in the early 1970s, the second bubble burst, triggering double-digit unemployment rates among PhD-level scientists and mathematicians across the United States. The glut of freshly minted scholars—many of whom had been lured to graduate school with federally funded fellowships and promises of plentiful academic jobs to come—occasioned testy hearings in Congress. The pushback ultimately led to the dismantling of the Policy Research and Analysis Division within the National Science Foundation, which had developed the faulty supply-side projections.26

  I witnessed this second bubble—or, rather, its sudden bursting—up close, having entered graduate school in 1993. Though I was just beginning my studies, I watched nervously as slightly older peers tried to navigate their way into academic careers. Whereas just a few years earlier there had been several faculty positions advertised each year across various subfields of physics, suddenly the best-trained students found themselves competing for a single position in a given specialty, often at an out-of-the-way university. A few years into my graduate studies, as the academic job market became ever more bleak, every single member of the latest batch of PhDs in particle physics from my department decamped for Wall Street, taking jobs as “quants” for the financial industry.27 (My sister had recently begun working for a Wall Street firm and she, too, encouraged me to join her. “They love physicists here,” she explained. “You can work on derivatives.” When I told her that I worked on derivatives every day—confusing my calculus-laden homework problems with exotic creations like “collateralized debt obligations” that she had in mind—she just rolled her eyes.) Little could those young physicists know that they were fleeing one bubble only to help provoke another.

  8

  Training Quantum Mechanics

  In the autumn of 1961, Richard Feynman launched a new experiment. Together with several colleagues at Caltech, he aimed to overhaul the curriculum for physics students. Their main goal was to introduce students to some of the most exciting—yet abstruse—aspects of modern physics as early as possible, right in their first year as undergraduates. That way, they hoped, they could fire the young students’ imaginations, rather than making them wade through important but staid topics first. The capstone of the new syllabus, filling the final third of the yearlong course, centered on quantum theory.1

  Feynman and his colleagues, Robert Leighton and Matthew Sands, feverishly composed the new lectures. Feynman delivered each one with his usual gusto, after which Leighton and Sands transcribed the recordings. Before long, rumors of the new course reached several textbook publishers. Feynman and his colleagues got to name their own terms. Leighton drew up a form letter, instructing interested publishers to submit written proposals to the authors within three weeks—a reversal of the normal procedure, in which authors submitted proposals to the publishers! The publishers were to describe how quickly they would be able to produce the books, at what price the new textbooks would be sold, what share of the royalties would be paid to Caltech, and what additional expenses the publishers proposed to absorb.2

  In the end, Feynman and his colleagues chose to work with Addison-Wesley. Before the books came out, a sales representative took galleys on a tour to gauge interest among other physics faculty. Writing to the president of the press, the sales rep could hardly contain himself. “Comments: Great enthusiasm,” began his long memo. “Where? In every department of physics, of course.” Several faculty seemed to be amazed by the new book. “It took me a life time to leave his room with the Feynman book, he just wanted to read another chapter and another one!!” Another professor tried to brush him off, until the crafty salesman flashed the book’s red covers. “Well . . . we had a nice talk for fifteen minutes and made an appointment for next spring. Of course he wanted a copy of the book.” And so it went, town after town during the sales representative’s two-week tour. “Give me a Feynman once or twice a year and I will do my job!” he closed. “I do not know who signed up Feynman, but I suggest that you owe him (not Feynman) a fine Turkey for his Christmas dinner!”3

  The sales rep’s instincts proved accurate. The Feynman Lectures on Physics sold more than 1
30,000 copies within six years of publication—even though Feynman himself later conceded that the pedagogical experiment had been a bit too ambitious. Some of the material really did prove to be too advanced for first-year undergraduates. Yet sales remained brisk—indeed, the books remain in print today—driven largely by demand from more advanced students, and even faculty, who have continued to snatch up copies for self-study.4

  Figure 8.1. Richard Feynman lectures before a large undergraduate class at Caltech, ca. 1956. Recordings of lectures like these formed the basis for The Feynman Lectures on Physics, first published in 1963–65. (Source: Courtesy of the Archives, California Institute of Technology. Used with permission of the Melanie Jackson Agency, LLC.)

  Though Feynman, Leighton, and Sands might have gotten a bit ahead of the curve, by the early 1960s most of their colleagues shared their impulse to teach quantum theory to younger and younger students. Given how slowly university curricula usually evolve, the changes typified by The Feynman Lectures were extraordinary. Just twenty years before Feynman began lecturing on quantum theory to first-year undergraduates, many physicists in the United States had earned their PhDs without taking a single course in the subject.5

  Amid the rapid-fire changes, some expressed alarm that too much was changing too quickly. A professor at Vanderbilt University, calling himself “one of those old-fashioned persons,” suggested that “children should eat a reasonably good meal before partaking of dessert”—and, for this instructor at least, quantum theory was “distinctly dessert,” which “could easily cause intellectual indigestion if not preceded by a properly balanced diet.”6

  Others, like J. Robert Oppenheimer, observed a more subtle shift: not just in what was being taught but how. Ever since the earliest work on quantum theory by the likes of Einstein and Schrödinger, Heisenberg and Dirac, the subject had inspired heated debate. So many of its core notions—the uncertainty principle, Schrödinger’s cat, quantum entanglement—seemed to be at odds with other leading physical theories, let alone common sense. Yet when Oppenheimer surveyed how his colleagues taught quantum theory just a few years before Feynman, Leighton, and Sands launched their new course, he noted that the subject was by then “taught not as history, not as a great adventure in human understanding, but as a piece of knowledge, as a set of techniques, as a scientific discipline to be used by the student in understanding and exploring new phenomena.” Quantum mechanics had become “an instrument of the scientist to be taken for granted by him, to be used by him, to be taught as a mode of action, as we teach our children to spell and add.”7

  How much things had changed. Oppenheimer had been among the first to bring working knowledge of the still-new quantum theory back to the United States, following his studies in Europe in the mid-1920s; before long, his course on the subject at Berkeley had become legendary. Yet by the time most of his colleagues began to offer their own courses on the subject, after the Second World War, the dramas of the wartime projects and the ensuing hyperinflation of physics enrollments had affected nearly every aspect of young physicists’ training. The transition that Oppenheimer noted, perhaps a bit wistfully, in the 1950s—teaching quantum mechanics more as a toolkit than an adventure—became emblematic of broader shifts in the field after the war. Facing runaway enrollments, many physicists across the United States winnowed the range of what would count as “quantum mechanics” in the classroom. Where once-fabled teachers like Oppenheimer had relished talking through thorny conceptual challenges with small groups of students, instructors after the war—their intimate classrooms by then replaced by large lecture halls, tiered rows of seats teeming with students—increasingly aimed to train quantum mechanics: skilled calculators of the atomic domain.

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  Oppenheimer’s own entry into physics had been meteoric. Born in 1904 to a family of wealthy Jewish immigrants in New York City, he skipped several grades during his secondary schooling and entered Harvard for his undergraduate studies. (He later described his young self as “an unctuous, repulsively good little boy.”) At Harvard he piled on extra courses each semester, graduating in just three years. During his first year as an undergraduate, he was invited to skip the introductory physics courses and dive directly into doctoral-level coursework.8

  As was typical at the time for the best American students who were interested in theoretical physics, Oppenheimer next set off for Europe to pursue his PhD, studying first at Cambridge before transferring to Göttingen. There he studied under Max Born, just as Born was collaborating with Werner Heisenberg and others to craft the new quantum mechanics and working frantically to try to make sense of the strange new formalism. Oppenheimer absorbed the emerging material quickly, publishing a dozen research articles while in Göttingen. He completed his PhD in the spring of 1927, a month shy of his twenty-third birthday.9

  After a brief postdoctoral fellowship, Oppenheimer accepted teaching appointments in 1929 at both the University of California at Berkeley and at Caltech—more than 370 miles apart. Each department was so eager to hire him that they reached a compromise: Oppenheimer would teach at Berkeley in the fall and then decamp to Caltech for the winter and spring terms. During his first semester at Berkeley, he taught an elective course for graduate students on quantum mechanics. One student registered for credit, while twenty-five signed on to listen. During that first course, Oppenheimer raced through the material so quickly that students complained to the department chair; Oppenheimer grumbled, in turn, that he had to crawl so slowly through the syllabus. Before long, however, he developed an engaging lecturing style.10 Graduate students routinely sat through his Berkeley course on quantum mechanics more than once; one desperate student staged a hunger strike until Oppenheimer relented and allowed her to attend the class for a fourth time.11

  As late as 1939—the year that one of Oppenheimer’s graduate students transcribed the lectures and made hectographed copies, which quickly saw wide circulation—Oppenheimer still introduced quantum mechanics as a “radical solution” to problems that were as much philosophical as physical. Lecture after lecture, he focused not only on the new mathematical formalism, centered on Schrödinger’s wave function, ψ, but also on its curious physical interpretation. He lingered over Born’s interpretation of |ψ|2 as yielding probabilities for various outcomes, emphasizing the remarkable conceptual break from the rigid determinism of classical physics. Wielding Newton’s laws or even Einstein’s relativity, physicists had long since been able to calculate that B strictly followed A. In the newer world of quantum theory, on the other hand, physicists could calculate only likelihoods: B had certain odds to follow A, and physicists remained utterly stymied from saying more. Oppenheimer even indulged in Einstein-styled attempts to circumvent Heisenberg’s uncertainty principle—revealing, with a flourish each time, how such clever efforts were destined to fail—all before walking his students through the first practical calculations with the formalism.12

  Oppenheimer’s pedagogical approach was hardly unique at the time. Felix Bloch, a Jewish émigré from Switzerland who had studied with Heisenberg before fleeing Nazism in 1934, taught his graduate-level course on quantum mechanics at Stanford University in a remarkably similar way. Throughout the 1930s, meanwhile, Caltech graduate students faced tough questions about the interpretation of quantum mechanics on their qualifying examinations. For years, beginning in 1929, the Caltech students kept communal notebooks in which they recorded how they had prepared for their oral exams and what questions various examiners had posed. Well into the late 1930s, faculty had pressed students to talk “all about [the] ψ function, physical meaning, etc.” or had asked, “What is [the] interpretation of ψ(x)? Does the Schrödinger equation describe the rate of change for all time?”—a subtle question about how the range of probabilities encoded in the wave function reduces to a single, measured result. Then came the follow-up: “Discuss the nature of observation in quantum mechanics and in classical mechanics.”13

  The first textbooks on quantu
m mechanics by physicists in the United States likewise emphasized in their opening pages that students would need to confront “philosophical difficulties,” which could not be “exorcised.” Some even paused, in the midst of what would soon become a standard calculation of an electron’s energy levels within a hydrogen atom, to assess whether various mathematical solutions could be considered physically meaningful if no experiment could distinguish between them. Others included entire chapters with titles like “Observation and Interpretation.” Reviewers of the textbooks during the 1930s agreed that an overtly philosophical register was appropriate when it came to teaching quantum mechanics. They often disagreed with specific points of interpretation in the books under review, but not with the notion that textbooks should broach such interpretive issues.14

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  Soon after the war, as more physics departments across the country began offering courses on quantum mechanics, the style of instruction began to shift. Few instructors during the 1950s lingered over how best to interpret the uncertainty principle or the place of probabilities in the quantum-mechanical formalism. Fewer still paused to dissect the philosophical standing of various hydrogenic wave functions.

  The changes came on quickly. Some Caltech students, having studied reports of earlier oral exams, were caught by surprise. One complained in 1953 that the effort he had “invested in analysis of paradoxes and queer logical points was of no use in the exam.” Instead, he had faced “straightforward questions” about then-standard calculations. Others similarly advised their fellow students to “give the usual spiel” or the “standard response” when asked to perform various quantum-mechanical calculations. One student suggested that his peers should simply “memorize” and “rehearse” answers to what had by then emerged as the standard calculations. Across the country, graduate students experienced a similar shift. Expansive essay-style questions about matters of interpretation, which had been common as late as the 1940s on the written qualifying exams, from Stanford and Berkeley to the Universities of Chicago and Pennsylvania, Columbia University, and MIT, were replaced by the mid-1950s by a collection of standard calculations.15