There is something of a joke in the way that, just as physicists began warring over the truth of physical law, the rest of the world’s avant-garde was insisting that their subjects were lawful, too. Nonphysicists have, for centuries, looked jealously at the order and solidity of physical foundations and have lusted after it for their own fields. Lavoisier’s physics-envy brought reasoned order to chemistry. Lyell’s imported it into geology. There were also efforts to bring systematic law and order into the study of human affairs—Karl Marx in history, John Watson in psychology, and heaven knows how many thinkers in economics. Most of these efforts to link people and natural law were failures. And when it was tried in politics, as with bolshevism and Nazism, it became literally criminal. In the arts, however, particularly in literature, the fruit was sometimes more satisfying.
Proust’s first volume tells of a certain Monsieur Swann who traveled in France’s most elegant circles, dining at the Jockey Club, playing cards with the Prince of Wales, and yet never speaking of these connections. His neighbors in the small town of Combray have no idea of the distinguished company he keeps. In volume 2, readers immediately learn that Swann is to be avoided because he is always bragging about the nobodies who have entertained him and his wife. No, Swann’s character has not changed. It turns out that Swann has exactly
the same character he had before, but he lives in new circumstances and is seen by himself and by others in a new way. Poor Proust, he hoped that there was some relation between his account of time and Einstein’s. There was none. He died without knowing that when it came to a belief in a natural law that underlay seemingly contradictory events, he and Einstein were one.
But there was another move afoot that was equally modern and, because it was more practical, had already seized hold on the lives of millions. This was the effort to give technical rationality to the operation of social systems. The moderns behind this transformation based their laws on efficiency rather than meaning; naturally, that kept their focus narrow. Yet it let them go deep into the details, so they could scorn the broad-minded generalists who lacked their expertise.
Straddling these two modernisms was Niels Bohr. He was born in the late nineteenth century, when meaningful systems appeared triumphant: Species had been linked through an evolutionary history, chemical elements through a periodic chart, and even the impulses of the mind through a psychoanalytic theory. Bohr had no instinct for such systematic thinking, as was probably best shown in his distaste for mathematics. It seems hard to believe that such an anti-arithmetician could have risen so high in theoretical physics, and it often startled the wonderlads of physics when they first met him. Paul Dirac heard Bohr when he spoke in Cambridge in May, 1925. “People were pretty well spellbound by what Bohr said,” he remembered, “While I was very much impressed … his arguments were mainly of a qualitative nature and I was not able really to pinpoint the facts behind them. What I wanted was statements which could be expressed in terms of equations, and Bohr’s work very seldom provided such statements…. He certainly did not have a direct influence because he did not stimulate one to think of new equations.”
If Bohr was ever to sympathize with quantitative arguments, the new mathematics of Heisenberg, Born, and Dirac provided the sorts of equations that best suited him. They allowed great feats without pointing toward deeper physical truths, and Bohr was enthusiastic about this practical math from the start. He first learned of Heisenberg’s quantum mechanics from a letter in which Heisenberg made a brief,
happy reference to his new paper. At a mathematics congress, Bohr then reported that Heisenberg had made a breakthrough, “probably of extraordinary scope.” Bohr’s immediate embrace of quantum mechanics came on the heels of the collapse of the Copenhagen achievement in quantum theory. The success of the Compton effect and the defeat of the BKS strategy had been a great blow. Similarly, his 1913 model of the atom had become increasingly hard to credit, and his protégés were saying to his face that they doubted its key feature—electrons following fixed orbits around an atomic nucleus.
“The most important question seems to me,” Pauli wrote Bohr, “to be this: to what extent may definite orbits of electrons in the stationary states be spoken of at all. I believe this can in no way be assumed as self-evident.” By getting rid of geometry, the new quantum mechanics abolished Bohr’s famous electron orbits and jumps just as decisively as Schrödinger’s wave mechanics would do. Yet Bohr embraced it all, and without a fight.
Not everybody followed his example. In November, 1925, Heisenberg told Pauli that Göttingen physicists had already fallen into two camps, those who welcomed the success of matrix algebra, regardless of its abstractions, and those who denied it was even physics. Bohr was with Heisenberg because he liked unambiguous abstractions. Physicists were always treating their abstractions as real—like energy, so real it could be conserved. But with matrices there was no danger of that temptation toward realism.
Bohr’s anti-realism prejudices are often attributed to one philosophy or another, but that is the suspicion of people with very few such tendencies of their own. It is like thinking a religious person must have fallen under the sway of some preacher, and disregarding the possibility of private experience and personal taste. Einstein was the one who read philosophers for his own entertainment. Years later, when the heroic age of quantum physics was well in the past, Bohr did attend a conference of philosophers. He reported afterward, “I have made a great discovery, a very great discovery. All that philosophers have ever written is pure drivel.”
Instead of the organizing logic that Einstein hoped for, Bohr wanted techniques that would allow him to consider particular physi-
cal problems. His great technique had been the correspondence principle, the rule of thumb that allowed him to approximate quantum results by thinking in classical terms. He was not interested in resolving the contradictions between quantum and classical physics so much as he was in using them. And his students, all of whom were more mathematically oriented than their teacher, absorbed this attitude.
Heisenberg once said, “I learned optimism from Sommerfeld, mathematics in Göttingen, and physics from Bohr.” And the physics that Bohr taught was the unambiguous, unrealistic variety. Theoretical contradictions—Einstein’s key to progress—were not a worry to Bohr. He later recalled that in those days of struggle, when nothing worked, his students at the Institute consoled themselves with the joke that along with “statements so simple and clear that the opposite assertion obviously could not be defended” there were also “‘deep truths’ in which the opposite also contains deep truth.”
Bohr looked for this attitude in students. He finally invited Pauli to come to Copenhagen when Pauli wrote that quantum physics was mired in two great bits of nonsense and that “the physicist who finally succeeds in adding these two nonsenses will gain the truth!”
The taste for nonsense probably lay behind the skepticism that Bohr displayed about electron spin when he arrived to celebrate Lorentz’s 50 years as a doctor of philosophy. Spin had first been proposed in Copenhagen by a German-American physicist named Ralph Kronig. Heisenberg and Pauli immediately hated the idea. They had just chased all imaginable actions out of quantum mechanics. Now Kronig was proposing to set the electron rotating in space. Faced with such fierce criticism by Bohr’s stars, Kronig grew silent and the idea of electron spin had to wait for a second coming, this time under Ehrenfest’s encouraging eye.
That was the state of physics during this period. With new ideas coming as regularly as the full moon, nobody’s method could absorb them all. It was a predicament that suited Bohr’s practicality. Heisenberg’s method was to stick with his matrix calculations, confident that eventually it must lead to “all the right answers.” Schrödinger held the same attitude toward his wave mechanics. But Bohr’s attitude, as summed up by Heisenberg was, “Well, there’s one mathematical
tool—that’s matrix mechanics. There’s another one, that’s wave mechanics. And there may still be other ones.” Bohr was entirely flexible in this matter because, unlike every other physicist struggling to understand quantum changes, his ultimate interest lay in finding an unambiguous, qualitative physics.
Bohr was explicit about his preference for nonquantitative physics. When he was finally persuaded to publicly endorse the concept of electron spin, he wrote that spin “opens up a very hopeful prospect of our being able to account more extensively for the properties of elements by means of mechanical models, at least in a qualitative way characteristic of applications of the correspondence principle.” As so often the case with Bohr’s remarks, this passage’s meaning seems to dissolve when examined closely, but we can get its sprit. Spin offers hope of more qualitative understanding, and more support for the beloved “magic wand,” the correspondence principle.
Mathematically oriented physicists were perhaps surprised by Bohr’s remark, because Schrödinger’s equation had given quantitative rigor to the correspondence principle and thereby done away with the need for a rule of thumb. In the spring of 1926, the rising popularity and strength of Schrödinger’s equation looked to mark the ceiling for Bohr’s fame and achievement. The old quantum theory, in which he had been a founding revolutionary, was being replaced by a new mechanics that digested the best of his old ideas, giving them a rigor they never had before. And then in early May came the surprise that ultimately set Einstein to defiance and raised Bohr to a sage.