“A new reality is in the air,” began the title song of one of Berlin’s hit revues of 1926. The idea of a new reality, the Neue Sachlichkeit, was part of the mid-1920’s mood that shaped Berliners. The war had smashed the old social order. The inflation had destroyed middle-class morals based on saving for a rainy day. Change was everywhere and Berliners believed in progress. They had not been this confident and optimistic since the war’s early days. Construction work was peppered across the city. Radio broadcasts sounded from apartment windows. Women bobbed their hair and, in 1926, the rising hemline reached the knee. The style was, to use a term favored by the Germans, “American”—meaning the style was up-to-date, rational, functional, secular, successful.
Hindsight knows this optimism was another lie. A different modernity was soon to come, but the new Weimar reality might not have been an impossible dream. It was open, complex, human and, therefore, sorely resented by the millions who had loved the old lies and missed them still. Who would be quicker on their feet, the republic’s beneficiaries or its enemies? The enemies were organizing themselves just offstage. Hitler had tried to blast his way into the spotlight and failed, but he had not given up hope, and he fought to strengthen his grip over the Nazi movement. His rivals in the party were supported
by an energetic and adept young rabble-rouser named Joseph Goebbels. In early 1926, Hitler won Goebbels to his side. The new loyalist would prove himself a liar extraordinaire and would begin feeding Germany’s old addiction to falsehoods.
But we are getting ahead of ourselves. At the time, internal shifts in crackpot organizations were too common and trivial to notice. The more promising struggle, the one that held Einstein’s full attention, was a search for the truth. Einstein in this new Berlin was both modern and old-fashioned. He participated in the changes as a man-about-town. He went to the shows, met the stylish people, and discussed the newest ideas. Yet he was also an old-style savant, a thinker who had not become a journalist, a visionary who did not turn to photography, a musician who did not enjoy the new dissonance. That old-fashioned seeker after truth was the enduring part; Einstein’s modernity was merely part of his Berlin wardrobe, and his clothes were never that important to him.
A few days after receiving Schrödinger’s letter, Einstein sent him a second note, “I am convinced that you have made a decisive advance with your formulation of the quantum condition, just as I am equally convinced that the Heisenberg-Born route is off the track.” That reference to a rival approach reflected the peculiar state of quantum physics in the spring of 1926—after years of bafflement, physicists all over Europe were having their bathtub moments and shouting “Eureka.” Heisenberg had developed a “quantum mechanics” at Göttingen, which his advisor, Max Born, had given a more coherent mathematical form. A graduate student in Cambridge, Paul Dirac, had proposed a mathematical theory of quantum behavior that has become known as q-number algebra. A few months later, Erwin Schrödinger announced from Zürich his new undulatory theory. The quantum revolution that Einstein had been anticipating for a quarter of a century had begun at last, and, as in any revolution, past experience provided only the crudest guide to its course.
Science was well acquainted with the phenomenon of separate discoveries of the same thing. Darwin was shocked when he read Alfred Wallace’s paper and found that his own chapter titles appeared as phrases in Wallace’s theory. But the quantum eurekas of 1925 and
1926 appeared, in a startling way, mutually contradictory. All these new ideas were being born, all of them appeared to work—in the sense that they correctly predicted changes in quantum states—and each of them meant something profoundly different. There had not been such confusion in physics since Galileo’s time, when three rival theories of the universe stood side by side. The available data supported each of the theories. Choosing one depended on instinct. Intelligence alone could not point the way.
By the spring of 1926, when Einstein congratulated Schrödinger for making “a decisive advance,” the role of instinct had returned to science. By praising Schrödinger, Einstein meant what he always meant when he spoke of a step or a stride forward: theory had combined with meaning to give a new ability to understand phenomena. When Einstein said others had gone “off the track,” he was objecting to the absence of meaning from their theories.
Even the staunchest defenders of Heisenberg’s and Dirac’s new ideas did not pretend that they had yet clarified underlying meaning. They worked in the tradition of Bohr’s atom, replacing explanation with mathematical decrees. Dirac’s q-number algebra, for example, was almost completely abstract. Dirac had devised a new type of number with all manner of unusual properties. Number a, for instance, was different from number b, but neither one was bigger than the other. How then, one might ask, did they differ? Whatever the answer, it was quite divorced from the familiar experience of counting or measuring. Dirac provided rules for manipulating his numbers, and when physicists followed the rules they got results that matched experiment, but as for understanding what it all meant, the physicists might just as well have been consulting the hieroglyphs of a lost language. Meanwhile, the quantum mechanics of Heisenberg and Born that Einstein had dismissed in his note to Schrödinger was hardly less abstract. Its most remarkable feature was that the order of calculation suddenly mattered. If, so to speak, you multiplied 2 times 3, you got a different answer than if you had multiplied 3 times 2. “A real sorcerer’s multiplication table,” Einstein laughed.
Heisenberg prefaced his system with the remark, “The present paper seeks to establish a basis for theoretical quantum mechanics
founded exclusively upon relationships between quantities which in principle are observable.” Focusing “exclusively” on “quantities” meant that Heisenberg had taken the astonishingly bold step of removing geometry from his physics. His method took a quantum state such as its energy level, performed a mathematical manipulation, and reported a new quantum state. How the particle got from one state to the other was unspecified.
Einstein was immediately offended by this notion and demanded of Heisenberg, “You don’t seriously believe that none but observable magnitudes must go into a physical theory?”
The challenge seems to have caught Heisenberg by surprise. As he recalled it many years later, he replied that Einstein had done exactly the same thing in his theory of relativity.
Einstein might have shrieked, “I did not.” Neither the relativity principle nor the constant speed of light, his famous theory’s axioms, were observable magnitudes. However, as Heisenberg recalled it, Einstein muttered something about, “A good trick should not be tried twice,” but then he added, “In reality the very opposite happens; it is theory that decides what we can observe.” The retort appears to have silenced Heisenberg, at least for the moment. “Measuring observables” sounds like it is free of theory, but theory defines the measurement. For centuries astronomers had measured Mars’s position in the sky and believed they were recording the absolute motion of Mars around the earth. Then Kepler made measurements, believing them to trace Mars’s orbit around the sun, relative to the earth, and a new physics of the sky was born. It was this long experience that had led Einstein to tell the Prussian Academy during his inaugural address that, without principles, “the individual empirical fact is of no use to the theorist; indeed he cannot do anything with isolated general laws abstracted from experience.”
This new quantum mechanics had lain in the background of the November 1925 meeting between Bose and Einstein. When Einstein had asked Bose if he could press his statistical approach further to present a new explanation of quantum change, he was asking if Bose could connect a new quantum theory with the old quantum facts.
At the Lorentz celebration in December, quantum mechanics had
been the great new idea behind many discussions. Every month the revolution brought new techniques for manipulating quantum data. November produced the “three-man paper” of Max Born, Werner Heisenberg, and Pasqual Jordan. It constructed a firm mathematical foundation for Heisenberg’s approach, but this foundation rested on a branch of mathematics called matrix calculus that was new to physics. Most physicists had no idea how it worked, and the joke going around the labs that season was that physics was getting too difficult for the physicists. So in early 1926, when Schrödinger’s wave mechanics offered a more familiar mathematics and its meaning that particles are, at root, wave packets, there was a sigh of relief from physicists who liked their science meaningful and doable.
Five years earlier, instinct had held a much more subtle role in physics. It made some people experimentalists and some theorists. It pointed some quantum investigators toward radiation and some toward matter, but authority had always come from the facts. The fact of the Compton effect and follow-up experiments had settled the issue of light quanta, no matter what a person might have preferred. The Bose-Einstein statistics had met little resistance because they were based on those photons that were fully supported by the experimental data. The facts about quanta and matter, however, were different. They pointed nowhere—you had one quantum state, then another. Without a theory to explain those facts, scientists were free to use whichever technique they preferred for calculating the changes. As most people are pragmatists about their methods and anti-revolutionary by temperament, the mass of physicists preferred to use Schrödinger’s equation. Its form was more familiar than matrices or q-numbers, and it was also easier to use. Matrix methods challenged the intellectual habits of a lifetime by abolishing any role for geometry from its calculations. Yes, Einstein had already demanded extensive rethinking of space and time, and he had gotten it, but Schrödinger’s wave equation made that kind of radicalism unnecessary.
Still, there were physicists whose motives were more personal than practical or professional. Einstein was never one to favor the easier or more familiar pathway. Neither was Max Born nor Niels Bohr. Those who joined Einstein in preferring Schrödinger for other than practical
reasons usually agreed that they wanted to understand the fundamentals and to know what sat at the base of reality. For them, facts by themselves were trivial, interesting only for their ability to point at the deeper truth of what lies at the bottom of natural events. It was that ambition that led Planck to speak enthusiastically to Einstein about the Schrödinger papers. Wilhelm Wien made himself the most public spokesman for this attitude.
These battles became so bitter that each group characterized the other so crudely they might have been hack political propagandists. Even today it is too easy to find accounts of the quantum revolution that portray it as a battle between conservatives and progressives, or old versus young, or of students of Kant against modern positivists. None of that rhetoric helps us much in understanding the behavior of particular scientists. It seems absurd to speak of skeptical Einstein as a conservative, or his contemporary Max Born as a youth, or of philosophically indifferent Heisenberg as anticipating the positivism of the Vienna Circle. The split was much more sharply focused on the nature of physics. The Einstein side was the heir to the Euclid-Newton tradition that systematized facts and gave them meaning for the nontechnical world.
The unEinsteinian school was more technically oriented and was more dubious about finding general truth. Their attitude had been suppressed during Newton’s long glory, but for most of the history of science, theirs was the dominant notion. They wanted rules that worked and let them do their physics; they did not want to bother with the larger meaning of it all.
This difference explains why—with the exception of his discovery of the photon—Einstein always denied that his work was revolutionary. True, he had demoted both Newton and Euclid from the ranks of divinely inspired prophets, but he had also kept to their goals of understanding the meaning of laws. When he toppled Euclid, Einstein immediately set an alternate geometry in its place. Surely he never expected to read, as one could find in the three-man-paper, “Admittedly … a system of quantum-theoretical relations between observable quantities … [labors] under the disadvantage of not being … geometrically visualizable since the motion of electrons cannot be
described in terms of the basic concepts of space and time.” For Einstein and the other opponents of quantum mechanics, this was no step forward. Embracing it meant throwing out rational, accessible nature.
During the battle over the Compton effect, Wien had published his newspaper article that insisted no true physicist would ever accept the BKS theory of random, arbitrary motions. Later, in November, 1925, at about the same time that Bose and Einstein met, Wien gave a speech in Munich that proclaimed how Newton’s laws “had revealed to man for the first time the possibility of comprehending nature by the logical force of his intellect.” The following June, at Munich University’s Founder’s Day celebrations, Wien insisted that no part of physics is barred from human understanding. Physicists, he insisted, would not rest until they understood atomic processes. Rejecting mathematical manipulation, he promised that “number mysticism would be supplanted by the cool logic of physical thought.”
It was in that confident expectation of being on the road to finding the universe’s rational basis that Einstein wrote his old chum from college and patent-office days, Michael Besso, bringing him up to date and telling him, “Schrödinger has come out with a pair of wonderful papers on the quantum rules.” That letter was written on May Day, 1926. It was the last time Einstein would make an unambiguously enthusiastic remark about the progress of the quantum revolution.