Uncertainty

by David Lindley

  In the interim, Heisenberg went to the annual meeting of the Society of German Scientists and Physicians in Leipzig in September, where he hoped in particular to meet Einstein. But anti-Semitism and the campaign against Jewish science were gaining momentum. In June, shortly after Bohr’s triumphant lectures in Göttingen, right-wing militants in Berlin gunned down the German foreign minister, Walther Rathenau, a Jew and a friend of Einstein’s. Workers, trade unionists, and socialists organized and protested. Rightist groups in turn shouted louder against communists and Jews. In this delicate, dangerous atmosphere, Einstein chose not to go to Leipzig.

  Heisenberg’s visit was eye-opening. At the first session he attended, a leaflet was thrust into his hand, which proved to be a circular from the German science movement decrying the polluting influence of Jewish thought. In his memoirs Heisenberg professed to be shocked at this intrusion of coarse politics and prejudice into the tight world of science. But he could hardly have been unaware of these vicious hatreds. His shock was that he could no longer wish them away, or pretend they were some sort of transient aberration that would collapse under the pressure of reason. Scientists could be as irrational and vituperative, as opportunistic and selfish, as the mobs in the streets. Science was not the citadel Heisenberg dreamed of.

  After that first session, he returned to his lodgings to find that everything he had brought with him had been stolen. Left only with the clothes he wore and the return half of his train ticket, he skipped straight back to Munich and thence, a little later, to Göttingen. There, at least, he could hope to find sanctuary in a university town that took pride in its intellectual detachment from the travails of the world outside.

  Pauli had spent the previous winter semester at Göttingen. Born wrote to Einstein that “young Pauli is very stimulating—I shall never get another assistant as good,” but he was miffed to find he had to send a maid to get Pauli out of bed at 10:30 every morning. Nor did Pauli’s brusque independence and sharp tongue endear him to the quiet and formal Born. Pauli made snide reference to the excessive brand of rigor and pedantry he called Göttingen Gelehrsamkeit—Göttingen scholarliness. Years later Born said of Pauli, “I was, from the beginning, quite crushed by him…He would never do what I told him to do—he did it his own way, and generally he was right.”

  Though Born, as the aging Sommerfeld began to retire from the front lines, would oversee an equally influential school of quantum theory in Göttingen, he never attained the general respect and affection that Sommerfeld inspired. He had been a shy, sensitive child, easily discouraged by small slights, and grew into a reserved, rather timorous, occasionally peevish adult. His original intention to be a pure mathematician had faltered when, after a brief undergraduate spell in Göttingen, he felt overawed by the mathematical talent around him. Moving into physics, he proved adept and versatile—a dilettante, to use a word he applied to himself—but always remained both diffident about his abilities and quick to take offense if his contributions went unnoticed. During the war years he was appointed a professor in Berlin, where he became close to Einstein as the general theory of relativity burst upon the world. “I was so impressed by the greatness of his conception,” Born wrote later, “that I decided never to work in this field.”

  He became a good teacher and mentor but, as his experience with Pauli illustrates, he could be cowed by students sharper and more confident than he felt himself to be. Unlike Pauli, Heisenberg proved capable of getting up in the mornings unaided, and showed proper respect. He was, Born recalled, “quite different; he was like a little peasant boy when he came, very quiet and friendly and shy…Very soon I discovered he was just as good in brains as the other one.”

  From Born, Heisenberg learned yet a third attitude toward the development of quantum theory. Sommerfeld forged ahead by solving problems, troubled little by either mathematical nicety or philosophical profundity. Bohr tried to force vague concepts and dimly perceived suggestions into rational shape, and only then started looking for a mathematical formulation. Born, by contrast, was reluctant to say anything that he couldn’t yet express in a formal mathematical way. Though he had abandoned any desire to be a true mathematician, his thinking retained a powerful strain of the mathematician’s desire for strict reasoning and watertight logic.

  In Göttingen, traces of the old ethos remained. Observing the increasing use of rarefied mathematics in physical theory, David Hilbert, the presiding mathematical genius, made the not-quite-joking remark that physics was becoming too difficult for physicists—the implication being that only mathematicians could be trusted to do the job properly. Born at least half agreed. He didn’t share Bohr’s belief in the importance of working out the concepts first. “I always thought mathematics was cleverer than we are—one has first to find the correct formalism before one should philosophize about it,” he said. Heisenberg formed a distinctly different view. “Born was very conservative in some ways,” he said. “He would only state things which he could prove mathematically…[He] had not so much feeling about how things worked in atomic physics.”

  That was Born’s unfortunate role: to the physicists, too much the mathematician; to the mathematicians, not enough.

  Still, Heisenberg acquired a new degree of mathematical sophistication from his time with Born, who conducted a regular seminar at his house with half a dozen eager students. But even in these early days, as a mere undergraduate judging an established professor, he was far from convinced that Born had the right kind of imagination to push science forward.

  Under Born’s guidance, Heisenberg tried to apply his ideas, including the half-quantum system, to neutral helium—two electrons orbiting a doubly charged nucleus. Spectroscopically, helium displayed all kinds of complications. It had both single and multiple lines, and when electric or magnetic fields were applied, those lines split in hopelessly complex ways. Heisenberg and Born concluded before very long that they could not understand helium at all, even with all the augmentations and ornamentations of the Bohr-Sommerfeld atom that were now floating about. The same conclusion emerged from Bohr’s institute.

  Meanwhile Alfred Landé, having already beaten Heisenberg to the punch with the half-quantum business, rolled out a further elaboration in which he added more peculiar rules to produce a scheme that mimicked yet more curiosities of the Zeeman effect. Pauli despaired of this strategy. He couldn’t deny that Landé’s tricks and devices appeared to fit various complicated sets of spectroscopic data, but as far as the search for an underlying theory was concerned, these efforts struck him as fatuous.

  Having taken a position in Hamburg, Pauli quickly excused himself to spend some months in Copenhagen, where he could learn quantum theory from Bohr. One day, Pauli recalled, he was stumping about the streets when a friend came across him and said he looked glum. “How can one be happy when one is thinking about the anomalous Zeeman effect?” Pauli responded smartly, and went on his way.

  For all his earlier enthusiasm over Sommerfeld’s elaborate atomic models, Bohr was increasingly unimpressed by the Munich game of mindlessly fitting quantum numbers and odd numerical systems to all manner of spectroscopic lines. Such efforts brought no real enlightenment, but seemed rather to degenerate into mere tinkering, in which each new spectroscopic puzzle was answered by some arbitrary theoretical adjustment. To Heisenberg and Pauli too it frequently seemed that a line had been crossed; a model can stand only so much ornamentation before its conceptual integrity falls apart. Heisenberg recalled that “some of us had begun to feel that the earlier successes of the theory might have been due to the use of particularly simple systems, and that the theory would break down in a slightly more complicated one.”

  It was as if physicists, attempting to uncloak the capricious nature of the quantum atom, were resorting to irrationality themselves.

  Chapter 8

  I WOULD RATHER BE A COBBLER

  In September 1923, Niels Bohr made his first visit to North America, speaking at Harvard, Princeton, Colum
bia, and elsewhere and concluding with a series of six lectures at Yale. This event The New York Times found noteworthy enough to report, though it didn’t manage to spell the speaker’s name right. “Dr. Nils Bohr,” the story ran, would explain “his theory of the structure of the atom, which has been accepted by many scientists as the most plausible hypothesis yet put forward.” A helpful subhead added: “He pictures the atom with nucleus corresponding to sun, and electrons to planets.”

  By this time, of course, the idea of the atom as a miniature solar system was barely tenable even as a loose analogy. At Yale, Bohr described the history of theories of the atom, explained how spectroscopy had become the essential tool for probing the modern atom’s structure, talked of how electrons were supposed to inhabit and move within atoms, and hinted at the numerous puzzles theorists currently faced. In words reported by the Times, Bohr confessed his inability to clearly describe the quantum atom in familiar language: “I hope I have succeeded in giving an impression that we are dealing with some sort of reality—a kind of connecting up of experimental evidence, with the prediction of new experimental evidence. Of course we cannot offer a picture of the same kind as we have been used to in natural philosophy. We are in a new field where we find that the old methods do not help, and we are trying to develop new methods.”

  Despite occasional attention from the newspapers, Bohr would never acquire the celebrity and glamorous aura that came Einstein’s way. The previous year Bohr had won the Nobel physics prize for his insight into the structure of atoms, but even then he had been overshadowed by Einstein, who was at the same time awarded the delayed 1921 prize. There had been no shortage over the years of Nobel nominations for Einstein, but the Nobel committee, a cautious outfit, was slow to embrace relativity, which still had vehement critics and for which direct evidence remained meager. Einstein almost won the prize in 1920, but last-minute doubts and reservations led the committee to reward instead Charles Guillaume of Switzerland, who had invented a nickel steel with a low coefficient of thermal expansion, cited for its great utility in precision measuring instruments. Einstein’s prize, when it finally came, was for his theory of the photoelectric effect, which Millikan’s experiments had verified a few years earlier, even though Millikan himself refused to accept that his results demonstrated the reality of light quanta.

  The Nobel awards to Bohr and Einstein highlighted a glaring contradiction. Einstein, as he had done for many years now, accepted at face value the reality of light quanta, but then was unhappy at the way they contaminated physics with elements of discontinuity and chance. In sharp contrast, Bohr had invented an atomic model that explained how atoms emitted and absorbed dollops of light at specific frequencies, but then ran into trouble because he refused to accept that these packets of light were truly fundamental to physics.

  Just a few weeks later, there came news of an experiment that seemed to settle the question. At Washington University in St. Louis, Arthur Compton succeeded in bouncing X-rays off electrons and found precisely what the quantum model predicted. When a quantum of radiation hits an electron, it bounces off with less energy. But Planck’s rule says that the energy per quantum is proportional to the radiation’s frequency, so reduced energy means lower frequency or longer wavelength. Compton’s careful measurements bore this prediction out. “This remarkable agreement between our formulas and the experiments can leave but little doubt,” he concluded, “that the scattering of X rays is a quantum phenomenon.”

  Sommerfeld, teaching in Madison at the time, relayed the news to Bohr, and as he traveled about America giving lectures on quantum theory, he urged upon his listeners the importance of the experiment. Compton’s decisive findings appeared in May 1923 in the American Physical Review, now the world’s preeminent journal of physics but one that Europeans in those days barely knew. (Heisenberg, interviewed in 1962, recalled that in the early days no one in Germany read the Physical Review because of course it didn’t exist back then; in fact it was already three decades old.)

  Compton scattering stands in the history books as the crucial evidence that light quanta had to be taken seriously. Probably the majority of physicists, like Sommerfeld, reacted to the announcement with enthusiasm and gratitude. Others were more grudging in their acceptance. Niels Bohr’s reaction, though, went beyond skepticism into outright hostility. With a stubbornness bordering on blockheadedness, he insisted more strenuously than ever that light quanta could not possibly be real and spent a year working up a sketchy theory of atomic emission and absorption that denied them any role. This episode reveals the dark side of Bohr’s character. Convinced that he alone could see the truth, he was intransigent, overbearing, and immune to reason.

  Bohr’s antipathy to Compton’s discovery was, it later emerged, not purely a matter of scientific judgment. He reacted fiercely for the simple reason that he had heard and dismissed the same idea several months earlier, when his own assistant in Copenhagen figured out the theory of what became known as the Compton effect. Bohr had angrily squelched the idea then, and so was instantly ready to do battle when Compton made his announcement.

  Bohr’s assistant was Hendrik Kramers, a native of Rotterdam. In 1916, Kramers had shown up on Bohr’s doorstep in Copenhagen, equipped with a degree in physics and an eagerness to learn quantum theory. The match proved perfect. A quick study and a sharp mathematician, Kramers had a capacity to grasp Bohr’s opaquely articulated thoughts and turn them into quantitative theoretical statements. And he could lecture clearly. Only a couple of years after arriving in Copenhagen, Kramers became an informal emissary for Bohr, speaking persuasively to audiences that were often still reserved and skeptical. Kramers offered precise arguments and specific calculations, not the obscure philosophical musing that Bohr favored.

  “Bohr is Allah and Kramers is his prophet,” pronounced Wolfgang Pauli, notwithstanding that he liked Bohr’s assistant a good deal. Kramers, proud and a little insecure, could be prickly and sarcastic. Pauli detected a congenial spirit.

  Bohr encouraged Kramers to look into a question that had thus far received little attention. If the most notable characteristic of spectral lines was their wavelength or frequency, a second obvious quality was their intensity. Some lines are brighter than others. The germ of an explanation could be found in Einstein’s prescient 1916 paper, in which he showed that atomic transitions followed a law of probability identical to Rutherford’s probability rule for radioactive decay. The more probable a transition, Bohr suggested to Kramers, the brighter the corresponding spectral line ought to be.

  But Einstein’s analysis of the abrupt, probabilistic way in which atoms emitted light also provided further reason to believe that light quanta were genuine physical entities. Following in these footsteps, Kramers could not help but absorb the same lesson.

  Sometime in 1921, according to a story unearthed only recently by his biographer Max Dresden, Kramers must have been thinking about the way a light quantum would interact with a particle such as an electron. In short order, he came up with the pleasingly simple collision law that Compton would soon employ to such great effect. In the recollection of his wife, a singer who had acquired the nickname Storm on account of her tempestuous personality, Kramers came home one day “insanely excited.” The next day he took his momentous discovery to Bohr. And then, Storm recalled, Bohr went to work on her husband, explaining and insisting and maintaining over and over, in any number of different ways, that the idea of a light quantum was untenable, that it had no place in physics, that it would mean throwing away the hugely successful classical theory of electromagnetism, that it simply would not do. Bohr wouldn’t let up. Against Kramers’s straightforward calculation, Bohr could put up any number of weighty but elusive arguments, physical, philosophical, historical in nature. Bohr had the trick of being powerfully persuasive even when he was not entirely reasonable. Whenever, by dint of his impressive but inscrutable reasoning, he saw the right answer ahead of all the mathematicians and calculators, his reputa
tion as the mystic of quantum theory only grew. When he was equally relentless in pursuit of a mistaken idea, he could be a bully, plain and simple.

  So great was the pressure that Kramers became ill, taking refuge in the hospital for a few days. By the time he came out, he had yielded utterly to Bohr’s will. Kramers suppressed his discovery of what would soon be called the Compton effect, to the extent of destroying his notes. He became as vehement as Bohr, if not more so, in his denunciation and ridicule of the light quantum. When Compton published his results, Kramers further repressed the knowledge that he had already calculated exactly what Compton had now disclosed to the world, and joined with his boss in looking for a way to continue the fight against an unacceptable conclusion.

  Bohr’s adamancy on this point remains genuinely mysterious. It seems to have become fixed in his mind that accepting the existence of discrete light quanta would fatally undermine the wave theory of classical electromagnetism. Others, notably Einstein, saw well enough that there was a basic mismatch between the two points of view but decided this was a problem physics would have to set aside for the time being, until all these new ideas were better assimilated.

  Bohr and Kramers, at any rate, set themselves to salvaging their viewpoint. A third young collaborator was drawn into this web. John C. Slater, after earning a doctorate from Harvard, set out in the fall of 1923 on a European tour, stopping in Cambridge for a few months before moving on to Copenhagen. Like most younger physicists, Slater embraced light quanta without reservation, but while in Cambridge, the ancestral home of the classical theory of radiation, he saw dimly how it might be possible to live with light quanta while not throwing away all the undeniable successes of light waves. Both must exist, he thought. He imagined a radiation field, roughly along classical lines, but repurposed. It existed to guide light quanta around and to facilitate their dealings with atoms.