Einstein in Paris, 1922

It seemed obvious that Einstein would someday win the Nobel Prize for Physics. He had, in fact, already agreed to transfer the money to his first wife, Mileva Mari, when that occurred. The questions were: When would it happen? and, For what?

Once it was announced—in November 1922, awarding him the prize for 1921—the questions were: What took so long? and, Why “especially for his discovery of the law of the photoelectric effect”?

It has been part of the popular lore that Einstein learned that he had finally won while on his way to Japan. “Nobel Prize for physics awarded to you. More by letter,” read the telegram sent on November 10. In fact, he had been alerted as soon as the Swedish Academy made the decision in September, well before he left on his trip.

The chairman of the physics award committee, Svante Arrhenius, had heard that Einstein was planning to go to Japan in October, which meant that he would be away for the ceremony unless he postponed the trip. So he wrote Einstein directly and explicitly: “It will probably be very desirable for you to come to Stockholm in December.” Expressing a principle of pre–jet travel physics, he added, “And if you are then in Japan that will be impossible.”¹ Coming from the head of a Nobel Prize committee, it was clear what that meant. There are not a lot of other reasons for physicists to be summoned to Stockholm in December.

Despite knowing that he would finally win, Einstein did not see fit to postpone his trip. Partly it was because he had been passed over so often that it had begun to annoy him.

He had first been nominated for the prize in 1910 by the chemistry laureate Wilhelm Ostwald, who had rejected Einstein’s pleas for a job nine years earlier. Ostwald cited special relativity, emphasizing that the theory involved fundamental physics and not, as some Einstein detractors argued, mere philosophy. It was a point that he reiterated over the next few years as he resubmitted the nomination.

The Swedish committee was mindful of the charge in Alfred Nobel’s will that the prize should go to “the most important discovery or invention,” and it felt that relativity theory was not exactly either of those. So it reported that it needed to wait for more experimental evidence “before one can accept the principle and in particular award it a Nobel prize.”²

Einstein continued to be nominated for his work on relativity during most of the ensuing ten years, gaining support from distinguished theorists such as Wilhelm Wien, although not yet from a still-skeptical Lorentz. His greatest obstacle was that the committee at the time was leery of pure theorists. Three out of the committee’s five members throughout the period from 1910 to 1922 were experimentalists from Sweden’s Uppsala University, known for its fervent devotion to perfecting experimental and measuring techniques. “Swedish physicists with a strong experimentalist bias dominated the committee,” notes Robert Marc Friedman, a historian of science in Oslo. “They held precision measurement as the highest goal for their discipline.” That is one reason Max Planck had to wait until 1919 (when he was awarded the delayed prize for 1918) and why Henri Poincaré never won at all.³

The dramatic announcement in November 1919 that the eclipse observations had confirmed parts of Einstein’s theory should have made 1920 his year. By then Lorentz was no longer such a skeptic. He along with Bohr and six other official nominators wrote in support of Einstein, mostly focusing on his completed theory of relativity. (Planck wrote in support as well, but his letter arrived after the deadline for consideration.) As Lorentz’s letter declared, Einstein “has placed himself in the first rank of physicists of all time.” Bohr’s letter was equally clear: “One faces here an advance of decisive significance.”⁴

Politics intervened. Up until then, the primary justifications for denying Einstein a Nobel had been scientific: his work was purely theoretical, it lacked experimental grounding, and it putatively did not involve the “discovery” of any new laws. After the eclipse observations, the explanation of the shift in Mercury’s orbit, and other experimental confirmations, these arguments against Einstein were still made, but they were now tinged with more cultural and personal bias. To his critics, the fact that he had suddenly achieved superstar status as the most internationally celebrated scientist since the lightning-tamer Benjamin Franklin was paraded through the streets of Paris was evidence of his self-promotion rather than his worthiness of a Nobel.

This subtext was evident in the internal seven-page report prepared by Arrhenius, the committee chairman, explaining why Einstein should not win the prize in 1920. He noted that the eclipse results had been criticized as ambiguous and that scientists had not yet confirmed the theory’s prediction that light coming from the sun would be shifted toward the red end of the spectrum by the sun’s gravity. He also cited the discredited argument of Ernst Gehrcke, one of the anti-Semitic antirelativists who led the notorious 1920 rally against Einstein that summer in Berlin, that the shift in Mercury’s orbit could be explained by other theories.

Behind the scenes, Einstein’s other leading anti-Semitic critic, Philipp Lenard, was waging a crusade against him. (The following year, Lenard would propose Gehrcke for the prize!) Sven Hedin, a Swedish explorer who was a prominent member of the Academy, later recalled that Lenard worked hard to persuade him and others that “relativity was really not a discovery” and that it had not been proven.⁵

Arrhenius’s report cited Lenard’s “strong critique of the oddities in Einstein’s generalized theory of relativity.” Lenard’s views were couched as a criticism of physics that was not grounded in experiments and concrete discoveries. But there was a strong undercurrent in the report of Lenard’s animosity to the type of “philosophical conjecturing” that he often dismissed as being a feature of “Jewish science.”⁶

So the 1920 prize instead went to another Zurich Polytechnic graduate who was Einstein’s scientific opposite: Charles-Edouard Guillaume, the director of the International Bureau of Weights and Measures, who had made his modest mark on science by assuring that standard measures were more precise and discovering metal alloys that had practical uses, including making good measuring rods. “When the world of physics had entered upon an intellectual adventure of extraordinary proportions, it was remarkable to find Guillaume’s accomplishment, based on routine study and modest theoretical finesse, recognized as a beacon of achievement,” says Friedman. “Even those who opposed relativity theory found Guillaume a bizarre choice.”⁷

By 1921, the public’s Einstein mania was in full force, for better or worse, and there was a groundswell of support for him from both theoreticians and experimentalists, Germans such as Planck and non-Germans such as Eddington. He garnered fourteen official nominations, far more than any other contender. “Einstein stands above his contemporaries even as Newton did,” wrote Eddington, offering the highest praise a member of the Royal Society could muster.⁸

This time the prize committee assigned the task of doing a report on relativity to Allvar Gullstrand, a professor of ophthalmology at the University of Uppsala, who had won the prize for medicine in 1911. With little expertise in either the math or the physics of relativity, he criticized Einstein’s theory in a sharp but unknowing manner. Clearly determined to undermine Einstein by any means, Gullstrand’s fifty-page report declared, for example, that the bending of light was not a true test of Einstein’s theory, that the results were not experimentally valid, and that even if they were there were still other ways to explain the phenomenon using classical mechanics. As for Mercury’s orbit, he declared, “It remains unknown until further notice whether the Einstein theory can at all be brought into agreement with the perihelion experiment.” And the effects of special relativity, he said, “lay below the limits of experimental error.” As one who had made his name by devising precision optical measuring instruments, Gullstrand seemed particularly appalled by Einstein’s theory that the length of rigid measuring rods could vary relative to moving observers.⁹

Even though some members of the full Academy realized that Gullstrand’s opposition was unsophisticated, it was hard to overcome. He was a respected and popular Swedish professor, and he insisted both publicly and privately that the great honor of a Nobel should not be given to a highly speculative theory that was the subject of an inexplicable mass hysteria that would soon deflate. Instead of choosing someone else, the Academy did something that was less (or more?) of a public slap at Einstein: it voted to choose nobody and tentatively bank the 1921 award for another year.

The great impasse threatened to become embarrassing. His lack of a prize had begun to reflect more negatively on the Nobel than on Einstein. “Imagine for a moment what the general opinion will be fifty years from now if the name Einstein does not appear on the list of Nobel laureates,” wrote the French physicist Marcel Brillouin in his 1922 nominating letter.¹⁰

To the rescue rode a theoretical physicist from the University of Uppsala, Carl Wilhelm Oseen, who joined the committee in 1922. He was a colleague and friend of Gullstrand, which helped him gently overcome some of the ophthalmologist’s ill-conceived but stubborn objections. And he realized that the whole issue of relativity theory was so encrusted with controversy that it would be better to try a different tack. So Oseen pushed hard to give the prize to Einstein for “the discovery of the law of the photoelectric effect.”

Each part of that phrase was carefully calculated. It was not a nomination for relativity, of course. In fact, despite the way it has been phrased by some historians, it was not for Einstein’s theory of light quanta, even though that was the primary focus of the relevant 1905 paper. Nor was it for any theory at all. Instead, it was for the discovery of a law.

A report from the previous year had discussed Einstein’s “theory of the photoelectric effect,” but Oseen made clear his different approach with the title of his report: “Einstein’s Law of the Photoelectric Effect” (emphasis added). In it, Oseen did not focus on the theoretical aspects of Einstein’s work. He specified instead what he called a fundamental natural law, fully proven by experiment, that Einstein propounded: the mathematical description of how the photoelectric effect was explained by assuming that light was absorbed and emitted in discrete quanta, and the way this related to the frequency of the light.

Oseen also proposed that giving Einstein the prize delayed from 1921 would allow the Academy to use that as a basis for simultaneously giving Niels Bohr the 1922 prize, because his model of the atom built on the laws that explained the photoelectric effect. It was a clever coupled-entry ticket for making sure that the two greatest theoretical physicists of the time became Nobel laureates without offending the Academy’s old-line establishment. Gullstrand went along. Arrhenius, who had met Einstein in Berlin and been charmed, was now also willing to accept the inevitable. On September 6, 1922, the Academy voted accordingly, and Einstein and Bohr were awarded the 1921 and 1922 prizes, respectively.

Thus it was that Einstein became the recipient of the 1921 Nobel Prize, in the words of the official citation, “for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect.” In both the citation and the letter from the Academy’s secretary officially informing Einstein, an unusual caveat was explicitly inserted. Both documents specified that the award was given “without taking into account the value that will be accorded your relativity and gravitation theories after these are confirmed in the future.”¹¹ Einstein would not, as it turned out, ever win a Nobel for his work on relativity and gravitation, nor for anything other than the photoelectric effect.

There was a dark irony in using the photoelectric effect as a path to get Einstein the prize. His “law” was based primarily on observations made by Philipp Lenard, who had been the most fervent campaigner to have him blackballed. In his 1905 paper, Einstein had credited Lenard’s “pioneering” work. But after the 1920 anti-Semitic rally in Berlin, they had become bitter enemies. So Lenard was doubly outraged that, despite his opposition, Einstein had won the prize and, worse yet, done so in a field that Lenard pioneered. He wrote an angry letter to the Academy, the only official protest it received, in which he said that Einstein misunderstood the true nature of light and was, in addition, a publicity-seeking Jew whose approach was alien to the true spirit of German physics.¹²

Einstein was traveling by train through Japan and missed the official award ceremony on December 10. After much controversy over whether he should be considered German or Swiss, the prize was accepted by the German ambassador, but he was listed as both nationalities in the official record.

The formal presentation speech by Arrhenius, the committee chair, was carefully crafted. “There is probably no physicist living today whose name has become so widely known as that of Albert Einstein,” he began. “Most discussion centers on his theory of relativity.” He then went on to say, almost dismissively, that “this pertains essentially to epistemology and has therefore been the subject of lively debate in philosophical circles.”

After touching briefly on Einstein’s other work, Arrhenius explained the Academy’s position on why he had won. “Einstein’s law of the photoelectrical effect has been extremely rigorously tested by the American Millikan* and his pupils and passed the test brilliantly,” he said. “Einstein’s law has become the basis of quantitative photo-chemistry in the same way as Faraday’s law is the basis of electro-chemistry.”¹³

Einstein gave his official acceptance speech the following July at a Swedish science conference with King Gustav Adolf V in attendance. He spoke not about the photoelectric effect, but about relativity, and he concluded by emphasizing the importance of his new passion, finding a unified field theory that would reconcile general relativity with electromagnetic theory and, if possible, with quantum mechanics.¹⁴

The prize money that year amounted to 121,572 Swedish kronor, or $32,250, which was more than ten times the annual salary of the average professor at the time. As per his divorce agreement with Mari, Einstein had part of it sent directly to Zurich to reside in a trust for her and their sons, and the rest went into an American account with the interest directed for her use.

This prompted another row. Hans Albert complained that the trust arrangement, which had previously been agreed to, made only the interest on the money accessible to the family. Once again, Zangger intervened and calmed the dispute. Einstein jokingly wrote to his sons, “You all will be so rich that some fine day I may ask you for a loan.”The money was eventually used by Mari to buy three homes with rental apartments in Zurich.¹⁵

“Anything truly novel is invented only during one’s youth,” Einstein lamented to a friend after finishing his work on general relativity and cosmology. “Later one becomes more experienced, more famous—and more blockheaded.”¹⁶

Einstein turned 40 in 1919, the year that the eclipse observations made him world-famous. For the next six years, he continued to make important contributions to quantum theory. But after that, as we shall see, he would begin to seem, if not blockheaded, at least a bit stubborn as he resisted quantum mechanics and embarked on a long, lonely, and unsuccessful effort to devise a unified theory that would subsume it into a more deterministic framework.

Over the ensuing years, researchers would discover new forces in nature, besides electromagnetism and gravity, and also new particles. These would make Einstein’s attempts at unification all the more complex. But he would find himself less familiar with the latest data in experimental physics, and he thus would no longer have the same intuitive feel for how to wrest from nature her fundamental principles.

If Einstein had retired after the eclipse observations and devoted himself to sailing for the remaining thirty-six years of his life, would science have suffered? Yes, for even though most of his attacks on quantum mechanics did not prove to be warranted, he did serve to strengthen the theory by coming up with a few advances and also, less intentionally, by his ingenious but futile efforts to poke holes in it.

That raises another question: Why was Einstein so much more creative before the age of 40 than after? Partly, it is an occupational hazard of mathematicians and theoretical physicists to have their great breakthroughs before turning 40.¹⁷ “The intellect gets crippled,” Einstein explained to a friend, “but glittering renown is still draped around the calcified shell.”¹⁸

More specifically, Einstein’s scientific successes had come in part from his rebelliousness. There was a link between his creativity and his willingness to defy authority. He had no sentimental attachment to the old order, thus was energized by upending it. His stubbornness had worked to his advantage.

But now, just as he had traded his youthful bohemian attitudes for the comforts of a bourgeois home, he had become wedded to the faith that field theories could preserve the certainties and determinism of classical science. His stubbornness henceforth would work to his disadvantage.

It was a fate that he had begun fearing years before, not long after he finished his famous flurry of 1905 papers. “Soon I will reach the age of stagnation and sterility when one laments the revolutionary spirit of the young,” he had worried to his colleague from the Olympia Academy, Maurice Solovine.¹⁹

Now, many triumphs later, there were young revolutionaries who felt this fate had indeed befallen him. In one of his most revealing remarks about himself, Einstein lamented, “To punish me for my contempt of authority, Fate has made me an authority myself.”²⁰

Thus it is not surprising that, during the 1920s, Einstein found himself scaling back on some of his bolder earlier ideas. For example, in his 1905 special relativity paper he had famously dismissed the concept of the ether as “superfluous.” But after he finished his theory of general relativity, he concluded that the gravitational potentials in that theory characterized the physical qualities of empty space and served as a medium that could transmit disturbances. He began referring to this as a new way to conceive of an ether.“I agree with you that the general relativity theory admits of an ether hypothesis,” he wrote Lorentz in 1916.²¹

In a lecture in Leiden in May 1920, Einstein publicly proposed a reincarnation, though not a rebirth, of the ether. “More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether,” he said. “We may assume the existence of an ether, only we must give up ascribing a definite state of motion to it.”

This revised view was justified, he said, by the results of the general theory of relativity. He made clear that his new ether was different from the old one, which had been conceived as a medium that could ripple and thus explain how light waves moved through space. Instead, he was reintroducing the idea in order to explain rotation and inertia.

Perhaps he could have saved some confusion if he had chosen a different term. But in his speech he made clear that he was reintroducing the word intentionally:

To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view . . . Besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real . . . The conception of the ether has again acquired an intelligible content, although this content differs widely from that of the ether of the mechanical wave theory of light ... According to the general theory of relativity, space is endowed with physical qualities; in this sense, there exists an ether. Space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any spacetime intervals in the physical sense. But this ether may not be thought of as endowed with the qualities of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.²²

So what was this reincarnated ether, and what did it mean for Mach’s principle and for the question raised by Newton’s bucket?* Einstein had initially enthused that general relativity explained rotation as being simply a motion relative to other objects in space, just as Mach had argued. In other words, if you were inside a bucket that was dangling in empty space, with no other objects in the universe, there would be no way to tell if you were spinning or not. Einstein even wrote to Mach saying he should be pleased that his principle was supported by general relativity.

Einstein had asserted this claim in a letter to Schwarzschild, the brilliant young scientist who had written to him from Germany’s Russian front during the war about the cosmological implications of general relativity. “Inertia is simply an interaction between masses, not an effect in which ‘space’ of itself is involved, separate from the observed mass,” Einstein had declared.²³ But Schwarzschild disagreed with that assessment.

And now, four years later, Einstein had changed his mind. In his Leiden speech, unlike in his 1916 interpretation of general relativity, Einstein accepted that his gravitational field theory implied that empty space had physical qualities. The mechanical behavior of an object hovering in empty space, like Newton’s bucket, “depends not only on relative velocities but also on its state of rotation.” And that meant “space is endowed with physical qualities.”

As he admitted outright, this meant that he was now abandoning Mach’s principle. Among other things, Mach’s idea that inertia is caused by the presence of all of the distant bodies in the universe implied that these bodies could instantly have an effect on an object, even though they were far apart. Einstein’s theory of relativity did not accept instant actions at a distance. Even gravity did not exert its force instantly, but only through changes in the gravitational field that obeyed the speed limit of light. “Inertial resistance to acceleration in relation to distant masses supposes action at a distance,” Einstein lectured. “Be-cause the modern physicist does not accept such a thing as action at a distance, he comes back to the ether, which has to serve as medium for the effects of inertia.”²⁴

It is an issue that still causes dispute, but Einstein seemed to believe, at least when he gave his Leiden lecture, that according to general relativity as he now saw it, the water in Newton’s bucket would be pushed up the walls even if it were spinning in a universe devoid of any other objects. “In contradiction to what Mach would have predicted,” Brian Greene writes, “even in an otherwise empty universe, you will feel pressed against the inner wall of the spinning bucket . . . In general relativity, empty spacetime provides a benchmark for accelerated motion.”²⁵

The inertia pushing the water up the wall was caused by its rotation with respect to the metric field, which Einstein now reincarnated as an ether. As a result, he had to face the possibility that general relativity did not necessarily eliminate the concept of absolute motion, at least with respect to the metric of spacetime.²⁶

It was not exactly a retreat, nor was it a return to the nineteenth-century concept of the ether. But it was a more conservative way of looking at the universe, and it represented a break from the radicalism of Mach that Einstein had once embraced.

This clearly made Einstein uncomfortable. The best way to eliminate the need for an ether that existed separately from matter, he concluded, would be to find his elusive unified field theory. What a glory that would be! “The contrast between ether and matter would fade away,” he said, “and, through the general theory of relativity, the whole of physics would become a complete system of thought.”²⁷

By far the most important manifestation of Einstein’s midlife transition from a revolutionary to a conservative was his hardening attitude toward quantum theory, which in the mid-1920s produced a radical new system of mechanics. His qualms about this new quantum mechanics, and his search for a unifying theory that would reconcile it with relativity and restore certainty to nature, would dominate—and to some extent diminish—the second half of his scientific career.

He had once been a fearless quantum pioneer. Together with Max Planck, he launched the revolution at the beginning of the century; unlike Planck, he had been one of the few scientists who truly believed in the physical reality of quanta—that light actually came in packets of energy. These quanta behaved at times like particles. They were indivisible units, not part of a continuum.

In his 1909 Salzburg address, he had predicted that physics would have to reconcile itself to a duality in which light could be regarded as both wave and particle. And at the first Solvay Conference in 1911, he had declared that “these discontinuities, which we find so distasteful in Planck’s theory, seem really to exist in nature.”²⁸

This caused Planck, who resisted the notion that his quanta actually had a physical reality, to say of Einstein, in his recommendation that he be elected to the Prussian Academy, “His hypothesis of light quanta may have gone overboard.” Other scientists likewise resisted Einstein’s quantum hypothesis. Walther Nernst called it “probably the strangest thing ever thought up,” and Robert Millikan called it “wholly untenable,” even after confirming its predictive power in his lab.²⁹

A new phase of the quantum revolution was launched in 1913, when Niels Bohr came up with a revised model for the structure of the atom. Six years younger than Einstein, brilliant yet rather shy and inarticulate, Bohr was Danish and thus able to draw from the work on quantum theory being done by Germans such as Planck and Einstein and also from the work on the structure of the atom being done by the Englishmen J. J. Thomson and Ernest Rutherford. “At the time, quantum theory was a German invention which had scarcely penetrated to England at all,” recalled Arthur Eddington.³⁰

Bohr had gone to study with Thomson in Cambridge. But the mumbling Dane and brusque Brit had trouble communicating. So Bohr migrated up to Manchester to work with the more gregarious Rutherford, who had devised a model of the atom that featured a positively charged nucleus around which tiny negatively charged electrons orbited.³¹

Bohr made a refinement based on the fact that these electrons did not collapse into the nucleus and emit a continuous spectrum of radiation, as classical physics would suggest. In Bohr’s new model, which was based on studying the hydrogen atom, an electron circled a nucleus at certain permitted orbits in states with discrete energies. The atom could absorb energy from radiation (such as light) only in increments that would kick the electron up a notch to another permitted orbit. Likewise, the atom could emit radiation only in increments that would drop the electron down to another permitted orbit.

When an electron moved from one orbit to the next, it was a quantum leap. In other words, it was a disconnected and discontinuous shift from one level to another, with no meandering in between. Bohr went on to show how this model accounted for the lines in the spectrum of light emitted by the hydrogen atom.

Einstein was both impressed and a little jealous when he heard of Bohr’s theory. As one scientist reported to Rutherford, “He told me that he had once similar ideas but he did not dare to publish them.” Einstein later declared of Bohr’s discovery, “This is the highest form of musicality in the sphere of thought.”³²

Einstein used Bohr’s model as the foundation for a series of papers in 1916, the most important of which, “On the Quantum Theory of Radiation,” was also formally published in a journal in 1917.³³

Einstein began with a thought experiment in which a chamber is filled with a cloud of atoms. They are being bathed by light (or any form of electromagnetic radiation). Einstein then combined Bohr’s model of the atom with Max Planck’s theory of the quanta. If each change in an electron orbit corresponded to the absorption or emission of one light quantum, then—presto!—it resulted in a new and better way to derive Planck’s formula for explaining blackbody radiation. As Einstein boasted to Michele Besso, “A brilliant idea dawned on me about radiation absorption and emission. It will interest you. An astonishingly simple derivation, I should say the derivation of Planck’s formula. A thoroughly quantized affair.”³⁴

Atoms emit radiation in a spontaneous fashion, but Einstein theorized that this process could also be stimulated. A roughly simplified way to picture this is to suppose that an atom is already in a high-energy state from having absorbed a photon. If another photon with a particular wavelength is then fired into it, two photons of the same wavelength and direction can be emitted.

What Einstein discovered was slightly more complex. Suppose there is a gas of atoms with energy being pumped into it, say by pulses of electricity or light. Many of the atoms will absorb energy and go into a higher energy state, and they will begin to emit photons. Einstein argued that the presence of this cloud of photons made it even more likely that a photon of the same wavelength and direction as the other photons in the cloud would be emitted.³⁵ This process of stimulated emission would, almost forty years later, be the basis for the invention of the laser, an acronym for “light amplification by the stimulated emission of radiation.”

There was one part of Einstein’s quantum theory of radiation that had strange ramifications. “It can be demonstrated convincingly,” he told Besso, “that the elementary processes of emission and absorption are directed processes.”³⁶ In other words, when a photon pulses out of an atom, it does not do so (as the classical wave theory would have it) in all directions at once. Instead, a photon has momentum. In other words, the equations work only if each quantum of radiation is emitted in some particular direction.

That was not necessarily a problem. But here was the rub:there was no way to determine which direction an emitted photon might go. In addition, there was no way to determine when it would happen. If an atom was in a state of higher energy, it was possible to calculate the probability that it would emit a photon at any specific moment. But it was not possible to determine the moment of emission precisely. Nor was it possible to determine the direction. No matter how much information you had. It was all a matter of chance, like the roll of dice.

That was a problem. It threatened the strict determinism of Newton’s mechanics. It undermined the certainty of classical physics and the faith that if you knew all the positions and velocities in a system you could determine its future. Relativity may have seemed like a radical idea, but at least it preserved rigid cause-and-effect rules. The quirky and unpredictable behavior of pesky quanta, however, was messing with this causality.

“It is a weakness of the theory,” Einstein conceded, “that it leaves the time and direction of the elementary process to ‘chance.’ ” The whole concept of chance—“Zufall” was the word he used—was so disconcerting to him, so odd, that he put the word in quotation marks, as if to distance himself from it.³⁷

For Einstein, and indeed for most classical physicists, the idea that there could be a fundamental randomness in the universe—that events could just happen without a cause—was not only a cause of discomfort, it undermined the entire program of physics. Indeed, he never would become reconciled to it. “The thing about causality plagues me very much,” he wrote Max Born in 1920. “Is the quantumlike absorption and emission of light ever conceivable in terms of complete causality?”³⁸

For the rest of his life, Einstein would remain resistant to the notion that probabilities and uncertainties ruled nature in the realm of quantum mechanics. “I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will not only its moment to jump off but also its direction,” he despaired to Born a few years later. “In that case, I would rather be a cobbler, or even an employee of a gaming house, than a physicist.”³⁹

Philosophically, Einstein’s reaction seemed to be an echo of the attitude displayed by the antirelativists, who interpreted (or misinterpreted) Einstein’s relativity theory as meaning an end to the certainties and absolutes in nature. In fact, Einstein saw relativity theory as leading to a deeper description of certainties and absolutes—what he called invariances—based on the combination of space and time into one four-dimensional fabric. Quantum mechanics, on the other hand, would be based on true underlying uncertainties in nature, events that could be described only in terms of probabilities.

On a visit to Berlin in 1920, Niels Bohr, who had become the Copenhagen-based ringleader of the quantum mechanics movement, met Einstein for the first time. Bohr arrived at Einstein’s apartment bearing Danish cheese and butter, and then he launched into a discussion of the role that chance and probability played in quantum mechanics. Einstein expressed his wariness of “abandoning continuity and causality.” Bohr was bolder about going into that misty realm. Abandoning strict causality, he countered to Einstein, was “the only way open” given the evidence.

Einstein admitted that he was impressed, but also worried, by Bohr’s breakthroughs on the structure of the atom and the randomness it implied for the quantum nature of radiation. “I could probably have arrived at something like this myself,” Einstein lamented, “but if all this is true then it means the end of physics.”⁴⁰

Although Einstein found Bohr’s ideas disconcerting, he found the gangly and informal Dane personally endearing. “Not often in life has a human being caused me such joy by his mere presence as you did,” he wrote Bohr right after the visit, adding that he took pleasure in picturing “your cheerful boyish face.” He was equally effusive behind Bohr’s back.“Bohr was here, and I am just as keen on him as you are,” he wrote their mutual friend Ehrenfest in Leiden. “He is an extremely sensitive lad and moves around in this world as if in a trance.”⁴¹

Bohr, for his part, revered Einstein. When it was announced in 1922 that they had won sequential Nobel Prizes, Bohr wrote that his own joy had been heightened by the fact that Einstein had been recognized first for “the fundamental contribution that you made to the special field in which I am working.”⁴²

On his journey home from delivering his acceptance speech in Sweden the following summer, Einstein stopped in Copenhagen to see Bohr, who met him at the train station to take him home by streetcar. On the ride, they got into a debate. “We took the streetcar and talked so animatedly that we went much too far,” Bohr recalled. “We got off and traveled back, but again rode too far.” Neither seemed to mind, for the conversation was so engrossing. “We rode to and fro,” according to Bohr, “and I can well imagine what the people thought about us.”⁴³

More than just a friendship, their relationship became an intellectual entanglement that began with divergent views about quantum mechanics but then expanded into related issues of science, knowledge, and philosophy. “In all the history of human thought, there is no greater dialogue than that which took place over the years between Niels Bohr and Albert Einstein about the meaning of the quantum,” says the physicist John Wheeler, who studied under Bohr. The social philosopher C. P. Snow went further. “No more profound intellectual debate has ever been conducted,” he proclaimed.⁴⁴

Their dispute went to the fundamental heart of the design of the cosmos: Was there an objective reality that existed whether or not we could ever observe it? Were there laws that restored strict causality to phenomena that seemed inherently random? Was everything in the universe predetermined?

For the rest of their lives, Bohr would sputter and fret at his repeated failures to convert Einstein to quantum mechanics.Einstein, Einstein, Einstein, he would mutter after each infuriating encounter. But it was a discussion that was conducted with deep affection and even great humor. On one of the many occasions when Einstein declared that God would not play dice, it was Bohr who countered with the famous rejoinder: Einstein, stop telling God what to do!⁴⁵

Unlike the development of relativity theory, which was largely the product of one man working in near solitary splendor, the development of quantum mechanics from 1924 to 1927 came from a burst of activity by a clamorous congregation of young Turks who worked both in parallel and in collaboration. They built on the foundations laid by Planck and Einstein, who continued to resist the radical ramifications of the quanta, and on the breakthroughs by Bohr, who served as a mentor for the new generation.

Louis de Broglie, who carried the title of prince by virtue of being related to the deposed French royal family, studied history in hopes of being a civil servant. But after college, he became fascinated by physics. His doctoral dissertation in 1924 helped transform the field. If a wave can behave like a particle, he asked, shouldn’t a particle also behave like a wave?

In other words, Einstein had said that light should be regarded not only as a wave but also as a particle. Likewise, according to de Broglie, a particle such as an electron could also be regarded as a wave. “I had a sudden inspiration,” de Broglie later recalled. “Einstein’s wave-particle dualism was an absolutely general phenomenon extending to all of physical nature, and that being the case the motion of all particles—photons, electrons, protons or any other—must be associated with the propagation of a wave.”⁴⁶

Using Einstein’s law of the photoelectric affect, de Broglie showed that the wavelength associated with an electron (or any particle) would be related to Planck’s constant divided by the particle’s momentum. It turns out to be an incredibly tiny wavelength, which means that it’s usually relevant only to particles in the subatomic realm, not to such things as pebbles or planets or baseballs.*

In Bohr’s model of the atom, electrons could change their orbits (or, more precisely, their stable standing wave patterns) only by certain quantum leaps. De Broglie’s thesis helped explain this by conceiving of electrons not just as particles but also as waves. Those waves are strung out over the circular path around the nucleus. This works only if the circle accommodates a whole number—such as 2 or 3 or 4—of the particle’s wavelengths; it won’t neatly fit in the prescribed circle if there’s a fraction of a wavelength left over.

De Broglie made three typed copies of his thesis and sent one to his adviser, Paul Langevin, who was Einstein’s friend (and Madame Curie’s). Langevin, somewhat baffled, asked for another copy to send along to Einstein, who praised the work effusively. It had, Einstein said, “lifted a corner of the great veil.” As de Broglie proudly noted, “This made Langevin accept my work.”⁴⁷

Einstein made his own contribution when he received in June of that year a paper in English from a young physicist from India named Satyendra Nath Bose. It derived Planck’s blackbody radiation law by treating radiation as if it were a cloud of gas and then applying a statistical method of analyzing it. But there was a twist: Bose said that any two photons that had the same energy state were absolutely indistinguishable, in theory as well as fact, and should not be treated separately in the statistical calculations.

Bose’s creative use of statistical analysis was reminiscent of Einstein’s youthful enthusiasm for that approach. He not only got Bose’s paper published, he also extended it with three papers of his own. In them, he applied Bose’s counting method, later called “Bose-Einstein statistics,” to actual gas molecules, thus becoming the primary inventor of quantum-statistical mechanics.

Bose’s paper dealt with photons, which have no mass. Einstein extended the idea by treating quantum particles with mass as being indistinguishable from one another for statistical purposes in certain cases. “The quanta or molecules are not treated as structures statistically independent of one another,” he wrote.⁴⁸

The key insight, which Einstein extracted from Bose’s initial paper, has to do with how you calculate the probabilities for each possible state of multiple quantum particles. To use an analogy suggested by the Yale physicist Douglas Stone, imagine how this calculation is done for dice. In calculating the odds that the roll of two dice (A and B) will produce a lucky 7, we treat the possibility that A comes up 4 and B comes up 3 as one outcome, and we treat the possibility that A comes up 3 and B comes up 4 as a different outcome—thus counting each of these combinations as different ways to produce a 7. Einstein realized that the new way of calculating the odds of quantum states involved treating these not as two different possibilities, but only as one. A 4-3 combination was indistinguishable from a 3-4 combination; likewise, a 5-2 combination was indistinguishable from a 2-5.

That cuts in half the number of ways two dice can roll a 7. But it does not affect the number of ways they could turn up a 2 or a 12 (using either counting method, there is only one way to roll each of these totals), and it only reduces from five to three the number of ways the two dice could total 6. A few minutes of jotting down possible outcomes shows how this system changes the overall odds of rolling any particular number. The changes wrought by this new calculating method are even greater if we are applying it to dozens of dice. And if we are dealing with billions of particles, the change in probabilities becomes huge.

When he applied this approach to a gas of quantum particles, Einstein discovered an amazing property: unlike a gas of classical particles, which will remain a gas unless the particles attract one another, a gas of quantum particles can condense into some kind of liquid even without a force of attraction between them.

This phenomenon, now called Bose-Einstein condensation,* was a brilliant and important discovery in quantum mechanics, and Einstein deserves most of the credit for it. Bose had not quite realized that the statistical mathematics he used represented a fundamentally new approach. As with the case of Planck’s constant, Einstein recognized the physical reality, and the significance, of a contrivance that someone else had devised.⁴⁹

Einstein’s method had the effect of treating particles as if they had wavelike traits, as both he and de Broglie had suggested. Einstein even predicted that if you did Thomas Young’s old double-slit experiment (showing that light behaved like a wave by shining a beam through two slits and noting the interference pattern) by using a beam of gas molecules, they would interfere with one another as if they were waves. “A beam of gas molecules which passes through an aperture,” he wrote, “must undergo a diffraction analogous to that of a light ray.”⁵⁰

Amazingly, experiments soon showed that to be true. Despite his discomfort with the direction quantum theory was heading, Einstein was still helping, at least for the time being, to push it ahead. “Einstein is thereby clearly involved in the foundation of wave mechanics,” his friend Max Born later said, “and no alibi can disprove it.”⁵¹

Einstein admitted that he found this “mutual influence” of particles to be “quite mysterious,” for they seemed as if they should behave independently. “The quanta or molecules are not treated as independent of one another,” he wrote another physicist who expressed bafflement. In a postscript he admitted that it all worked well mathematically, but “the physical nature remains veiled.”⁵²

On the surface, this assumption that two particles could be treated as indistinguishable violated a principle that Einstein would nevertheless try to cling to in the future: the principle of separability, which as serts that particles with different locations in space have separate, independent realities. One aim of general relativity’s theory of gravity had been to avoid any “spooky action at a distance,” as Einstein famously called it later, in which something happening to one body could instantly affect another distant body.

Once again, Einstein was at the forefront of discovering an aspect of quantum theory that would cause him discomfort in the future. And once again, younger colleagues would embrace his ideas more readily than he would—just as he had once embraced the implications of the ideas of Planck, Poincaré, and Lorentz more readily than they had.⁵³

An additional step was taken by another unlikely player, Erwin Schrödinger, an Austrian theoretical physicist who despaired of discovering anything significant and thus decided to concentrate on being a philosopher instead. But the world apparently already had enough Austrian philosophers, and he couldn’t find work in that field. So he stuck with physics and, inspired by Einstein’s praise of de Broglie, came up with a theory called “wave mechanics.” It led to a set of equations that governed de Broglie’s wavelike behavior of electrons, which Schrödinger (giving half credit where he thought it was due) called “Einstein–de Broglie waves.”⁵⁴

Einstein expressed enthusiasm at first, but he soon became troubled by some of the ramifications of Schrödinger’s waves, most notably that over time they can spread over an enormous area. An electron could not, in reality, be waving thus, Einstein thought. So what, in the real world, did the wave equation really represent?

The person who helped answer that question was Max Born, Einstein’s close friend and (along with his wife, Hedwig) frequent correspondent, who was then teaching at Göttingen. Born proposed that the wave did not describe the behavior of the particle. Instead, he said that it described the probability of its location at any moment.⁵⁵ It was an approach that revealed quantum mechanics as being, even more than previously thought, fundamentally based on chance rather than causal certainties, and it made Einstein even more squeamish.⁵⁶

Meanwhile, another approach to quantum mechanics had been developed in the summer of 1925 by a bright-faced 23-year-old hiking enthusiast, Werner Heisenberg, who was a student of Niels Bohr in Copenhagen and then of Max Born in Göttingen. As Einstein had done in his more radical youth, Heisenberg started by embracing Ernst Mach’s dictum that theories should avoid any concepts that cannot be observed, measured, or verified. For Heisenberg this meant avoiding the concept of electron orbits, which could not be observed.

He relied instead on a mathematical approach that would account for something that could be observed: the wavelengths of the spectral lines of the radiation from these electrons as they lost energy. The result was so complex that Heisenberg gave his paper to Born and left on a camping trip with fellow members of his youth group, hoping that his mentor could figure it out. Born did. The math involved what are known as matrices, and Born sorted it all out and got the paper published.⁵⁷ In collaboration with Born and others in Göttingen, Heisenberg went on to perfect a matrix mechanics that was later shown to be equivalent to Schrödinger’s wave mechanics.

Einstein politely wrote Born’s wife, Hedwig, “The Heisenberg-Born concepts leave us breathless.” Those carefully couched words can be read in a variety of ways. Writing to Ehrenfest in Leiden, Einstein was more blunt. “Heisenberg has laid a big quantum egg,” he wrote. “In Göttingen they believe in it. I don’t.”⁵⁸

Heisenberg’s more famous and disruptive contribution came two years later, in 1927. It is, to the general public, one of the best known and most baffling aspects of quantum physics: the uncertainty principle.

It is impossible to know, Heisenberg declared, the precise position of a particle, such as a moving electron, and its precise momentum (its velocity times its mass) at the same instant. The more precisely the position of the particle is measured, the less precisely it is possible to measure its momentum. And the formula that describes the trade-off involves (no surprise) Planck’s constant.

The very act of observing something—of allowing photons or electrons or any other particles or waves of energy to strike the object—affects the observation. But Heisenberg’s theory went beyond that. An electron does not have a definite position or path until we observe it. This is a feature of our universe, he said, not merely some defect in our observing or measuring abilities.

The uncertainty principle, so simple and yet so startling, was a stake in the heart of classical physics. It asserts that there is no objective reality—not even an objective position of a particle—outside of our observations. In addition, Heisenberg’s principle and other aspects of quantum mechanics undermine the notion that the universe obeys strict causal laws. Chance, indeterminacy, and probability took the place of certainty. When Einstein wrote him a note objecting to these features, Heisenberg replied bluntly, “I believe that indeterminism, that is, the nonvalidity of rigorous causality, is necessary.”⁵⁹

When Heisenberg came to give a lecture in Berlin in 1926, he met Einstein for the first time. Einstein invited him over to his house one evening, and there they engaged in a friendly argument. It was the mirror of the type of argument Einstein might have had in 1905 with conservatives who resisted his dismissal of the ether.

“We cannot observe electron orbits inside the atom,” Heisenberg said.“A good theory must be based on directly observable magnitudes.”

“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudes must go into a physical theory?”

“Isn’t that precisely what you have done with relativity?” Heisenberg asked with some surprise.

“Possibly I did use this kind of reasoning,” Einstein admitted, “but it is nonsense all the same.”⁶⁰

In other words, Einstein’s approach had evolved.

Einstein had a similar conversation with his friend in Prague, Philipp Frank. “A new fashion has arisen in physics,” Einstein complained, which declares that certain things cannot be observed and therefore should not be ascribed reality.

“But the fashion you speak of,” Frank protested, “was invented by you in 1905!”

Replied Einstein: “A good joke should not be repeated too often.”⁶¹

The theoretical advances that occurred in the mid-1920s were shaped by Niels Bohr and his colleagues, including Heisenberg, into what became known as the Copenhagen interpretation of quantum mechanics. A property of an object can be discussed only in the context of how that property is observed or measured, and these observations are not simply aspects of a single picture but are complementary to one another.

In other words, there is no single underlying reality that is independent of our observations. “It is wrong to think that the task of physics is to find out how nature is,” Bohr declared. “Physics concerns what we can say about nature.”⁶²

This inability to know a so-called “underlying reality” meant that there was no strict determinism in the classical sense. “When one wishes to calculate ‘the future’ from ‘the present’ one can only get statistical results,” Heisenberg said, “since one can never discover every detail of the present.”⁶³

As this revolution climaxed in the spring of 1927, Einstein used the 200th anniversary of Newton’s death to defend the classical system of mechanics based on causality and certainty. Two decades earlier, Einstein had, with youthful insouciance, toppled many of the pillars of Newton’s universe, including absolute space and time. But now he was a defender of the established order, and of Newton.

In the new quantum mechanics, he said, strict causality seemed to disappear. “But the last word has not been said,” Einstein argued. “May the spirit of Newton’s method give us the power to restore union between physical reality and the profoundest characteristic of Newton’s teaching—strict causality.”⁶⁴

Einstein never fully came around, even as experiments repeatedly showed quantum mechanics to be valid. He remained a realist, one who made it his creed to believe in an objective reality, rooted in certainty, that existed whether or not we could observe it.

So what made Einstein cede the revolutionary road to younger radicals and spin into a defensive crouch?

As a young empiricist, excited by his readings of Ernst Mach, Einstein had been willing to reject any concepts that could not be observed, such as the ether and absolute time and space and simultaneity. But the success of his general theory convinced him that Mach’s skepticism, even though it might be useful for weeding out superfluous concepts, did not provide much help in constructing new theories.

“He rides Mach’s poor horse to exhaustion,” Einstein complained to Michele Besso about a paper written by a mutual friend.

“We should not insult Mach’s poor horse,” Besso replied. “Didn’t it make possible the tortuous journey through the relativities? And who knows, in the case of the nasty quanta, it may also carry Don Quixote de la Einsteina through it all!”

“You know what I think about Mach’s little horse,” Einstein wrote Besso in return. “It cannot give birth to anything living. It can only exterminate harmful vermin.”⁶⁵

In his maturity, Einstein more firmly believed that there was an objective “reality” that existed whether or not we could observe it. The belief in an external world independent of the person observing it, he repeatedly said, was the basis of all science.⁶⁶

In addition, Einstein resisted quantum mechanics because it abandoned strict causality and instead defined reality in terms of indeterminacy, uncertainty, and probability. A true disciple of Hume would not have been troubled by this. There is no real reason—other than either a metaphysical faith or a habit ingrained in the mind—to believe that nature must operate with absolute certainty. It is just as reasonable, though perhaps less satisfying, to believe that some things simply happen by chance. Certainly, there was mounting evidence that on the subatomic level this was the case.

But for Einstein, this simply did not smell true. The ultimate goal of physics, he repeatedly said, was to discover the laws that strictly determine causes and effects. “I am very, very reluctant to give up complete causality,” he told Max Born.⁶⁷

His faith in determinism and causality reflected that of his favorite religious philosopher, Baruch Spinoza. “He was utterly convinced,” Einstein wrote of Spinoza, “of the causal dependence of all phenomena, at a time when the success of efforts to achieve a knowledge of the causal relationship of natural phenomena was still quite modest.”⁶⁸ It was a sentence that Einstein could have written about himself, emphasizing the temporariness implied by the word “still,” after the advent of quantum mechanics.

Like Spinoza, Einstein did not believe in a personal God who interacted with man. But they both believed that a divine design was reflected in the elegant laws that governed the way the universe worked.

This was not merely some expression of faith. It was a principle that Einstein elevated (as he had the relativity principle) to the level of a postulate, one that guided him in his work. “When I am judging a theory,” he told his friend Banesh Hoffmann, “I ask myself whether, if I were God, I would have arranged the world in such a way.”

When he posed that question, there was one possibility that he simply could not believe: that the good Lord would have created beautiful and subtle rules that determined most of what happened in the universe, while leaving a few things completely to chance. It felt wrong. “If the Lord had wanted to do that, he would have done it thoroughly, and not kept to a pattern . . . He would have gone the whole hog. In that case, we wouldn’t have to look for laws at all.”⁶⁹

This led to one of Einstein’s most famous quotes, written to Max Born, the friend and physicist who would spar with him over three decades on this topic. “Quantum mechanics is certainly imposing,” Einstein said. “But an inner voice tells me that it is not yet the real thing. The theory says a lot, but it does not really bring us any closer to the secrets of the Old One. I, at any rate, am convinced that He does not play dice.”⁷⁰

Thus it was that Einstein ended up deciding that quantum mechanics, though it may not be wrong, was at least incomplete. There must be a fuller explanation of how the universe operates, one that would incorporate both relativity theory and quantum mechanics. In doing so, it would not leave things to chance.