20
It Might Look Crazy
Not quite two months after 1924’s Solvay Conference, Einstein received a letter from a young, unknown Hindu named Satyendra Bose, a physics teacher at the University of Dacca. Writing in English, Bose included a manuscript. Anybody near the public eye occasionally receives unsolicited letters that introduce a manuscript. Einstein, in a perpetual spotlight, got them all the time. Many people feel overwhelmed by far less of this sort of material than was piled up on Einstein’s desk, but he read through his mountain of stuff and did not turn away just because the contents were unorthodox.
Bose’s letter bore several marks of the crank and had a secret trait besides. Bose did not mention that his manuscript had already been rejected by one respected journal, Philosophical Magazine. The rejection is not surprising, because, although the article presented a statistical theory, it violated several rules of statistical thinking. Bose—and this is also typical of crackpot authors—did not realize how far he had strayed from proper reasoning and later conceded, “I had no idea that what I had done was really novel…. I was not a statistician to the extent of really knowing that I was doing something which was really different.” That part about “I was not a statistician” is another trait of the crank. Crackpots typically are not well acquainted with the field they have
encroached and do not have the training to appreciate their own radicality.
Just as cranky as the manuscript’s secret history and unknowing heresy was the letter-writer’s outrageous sense of entitlement. “I do not know sufficient German to translate the paper. If you think the paper worth publication I shall be grateful if you arrange for its publication in Zeitschrift für Physik.” Grateful indeed. Bose added from his outpost on the floodplains beneath the Himalayan wall, “Though a complete stranger to you, I do not feel any hesitation in making such a request. Because we are all your pupils though profiting only by your teaching through your writings.” And in that remark Bose expressed what leads all these strangers to contact and make demands on the more-famous. Modern communications has deluded the anonymous millions into feeling a relationship between themselves and a celebrity. Einstein recognized the delusion, yet remained mensch enough to take these letters seriously and to study them.
Bose’s letter did include a mathematical reference that might have encouraged Einstein’s reading. It used one of those mathematical formulae that make the untrained want to turn their eyes away, as though exposed to a painful light. “I have ventured to deduce the coefficient 8πυ2/c3,” Bose wrote, tipping the fact that he had learned some real physics somewhere. So Einstein read the manuscript and then began translating it into German. Neither incompetent nor crazy, Bose’s paper was the first revolutionary contribution to quantum theory in a dozen years, and if Bose had not realized how revolutionary he was, that was also part of the quantum tradition. Planck had had no inkling of the kind of trouble he was setting off when he first proposed the quantum.
Bose’s paper—like Louis de Broglie’s still unknown work—began by taking Einstein’s photon seriously. He proposed that radiation be thought of as a kind of gas. Possibly the Philosophical Magazine’s reader stopped right there. Gases, after all, have mass and are made of molecules scattered loosely across space. Photons have neither mass nor molecules. Einstein kept going.
“Your ideas are interesting,” Langevin had told Louis de Broglie when he had proposed a similar gas-radiation analogy, “but your gas
has nothing to do with true light.” De Broglie rarely could get a hearing for his ideas. Einstein was more respectful with Bose, agreeing that the challenge lay in getting beyond the simple gas-radiation analogy to something physically meaningful.
Technically, Bose’s novelty lay in the way he derived Planck’s equation. Planck’s work imagined waves emerging from oscillators (like bedsprings); Bose’s reasoning assumed radiation particles in the manner of Einstein’s photons, but these particles had several odd qualities. First, Bose’s photons are as temporary as the waves that washed over the foundering Titanic. Classical particles cannot be destroyed, although waves can be absorbed and disappear. Thus, with the “non-conservation of photons,” wave-particle duality begins to take on mathematical form. Bose’s particles were also indistinguishable from one another. This detail, too, gives mathematical expression to the mystery of wave-particle duality. Classical particles can always be distinguished from one another, at least by differences in position. Waves, however, are spread out over time and space and, as everybody’s home stereo system shows, two or more waves can be in the same place at the same time. This mathematical union of wave and particle properties was real progress beyond the bald, dumbfounding statement that experiments show light to be both particle and wave. Einstein recognized that achievement, even if Bose himself was not quite sure of it.
Einstein’s English was not perfect, but he went to work that summer translating. When he told his secretary cum mistress that he was abandoning her to pursue happiness in the stars, the Bose statistics were the immediate stars of his attention. While Bohr, Heisenberg, and the rest of the Copenhagen-Göttingen axis were still looking for a way to wriggle out from under the Compton effect, Einstein was a mile further along the road, examining the photon’s mathematical nature.
Einstein had spent years looking for the step that would make sense of photons, and then it turned out that this puzzle was so subtle that it required Bose and Einstein to dance together in a two-step trot. Bose’s step dealt with a quantum’s radiation side while Einstein advanced its material side. Bose provided a natural explanation for Planck’s 25-year-old quantum equation. In Bose’s picture, light par-
ticles come pouring out of their source like clowns out of a circus car. It seems impossible for so many to fit into anything so tiny. Photon indistinguishability allows them to press together in a way unseen in the material world, where two objects cannot be crammed into the same place at the same time. Freed from one of nature’s normal limits, a radiation “gas” can flow in densities forbidden to atomic and molecular gases.
Einstein could never look at such an idea without tinkering. He saw the formal similarity between Bose’s radiation gas and a real gas, and—while the Bose paper was still waiting for publication—Einstein went before his favorite intellectual club, the Prussian Academy, to once again read aloud a startling paper that shifted the ground of physics. He told the members about Bose’s work and what it meant about ideal gases. In this first paper he introduced a modification into Bose that recognized the most notable difference between photons and true particles: the way photons come and go while particles last forever. The atoms in the wire of a photographer’s flash, for example, were cooked billions of years earlier in some lost star, but the photons that the wire emits are born and absorbed in less than a second. Einstein adjusted Bose’s equation to reflect that difference between particle and photon, transforming Bose statistics into Bose-Einstein statistics.
He tinkered some more and, thanks to our knowledge of de Broglie, we can see where he was headed. For decades, Einstein and the occasional disciple had been looking for particle properties in light waves. The photoelectric law, Compton effect, and Bose’s statistics had settled that hunt. The new idea, in both Paris and Berlin, was to look for wave properties in particles. Einstein wanted to get beyond a formal, mathematical analogy between gas and radiation, to a complete, physically coherent linkage. This was, of course, the same Einstein who had believed that atoms had to be real, and quanta had to be real, and the equivalency principle had to be real; so naturally Bose’s gas had to be real as well.
Many years later, Einstein dismissed the Bose-Einstein work as “by the way,” and it was a distraction from his interest in a unified field theory, but only somebody of Einstein’s standing could say such a
thing. It was like Shakespeare downplaying Othello as a distraction from his real work on King Lear. You can see his point, but goodness gracious! and it was hardly fair to Bose, whose career had just reached its apex.
Bose’s step, his explanation of nature in terms of nature, was so much at the heart of scientific achievement that it is easy to overlook how rare it is. Many scientists pass their whole careers without taking such a stride. Bose never again managed such a step, but these rare insights are what makes science so persuasive, and so unlike other rational fields—philosophy, criticism, theology, law, politics, and so on—in which explanations provoke division. Bose had kept his eye on the target, explaining photon action in terms of photon properties without ever jumping to some other subject. Many people, of course, like those explanatory jumps and cannot conceive of an explanation that omits them, considering as no explanation at all anything that leaves out God’s will, or subconscious motivation, or class interests, or what-you-wish. That might have been science’s most remarkable trait—its attempt to explain nature without changing the subject.
By refusing to jump to some other terminology, science never moves outside nature. Many people, probably even most people, cannot believe that nature is the whole story. “The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena,” the philosopher Ludwig Wittgenstein complained in his notebook while he was posted to the Austrian front lines, “Thus people today stop at the laws of nature, treating them as something inviolable, just as God and Fate were treated in past ages.” Einstein, however, looked only to nature, and when he was, so to speak, folding nature into itself—showing, say, that radiation and matter really were bound by the same laws—he was as happy as his heart allowed.
For some reason, or perhaps for no reason at all, it could have been entirely by chance, that season saw a stirring and climaxing of many great efforts to find a way to truth. Besides Einstein’s statistical portrait of photons, the bankers had restored the money to order; the lunatic right had been quieted; Hitler was in jail. Thomas Mann had a frenzied month (September, 1924) in which he finally finished his Magic Moun-
tain. The publisher then had an equally frenzied time of it and at the end of November sent copies of the thousand-page novel into bookstores. Dada metamorphosed as well when André Breton wrote The Surrealist Manifesto, which described an expression “free from any control by the reason and of any aesthetic or moral preoccupation.”
While he was working on the physical meaning of Bose’s gas analogy, Einstein received a letter from Paul Langevin in Paris telling him about de Broglie’s work. Langevin was undecided about accepting de Broglie’s thesis and, because so much of it was founded on Einstein’s ideas, Langevin wondered what Einstein thought about the manuscript. Einstein read de Broglie’s thesis and discovered that, in some ways, his latest work had been foreshadowed. At once, Einstein became an advocate for de Broglie. He urged Langevin to accept the thesis, and he began recommending the document to others.
“Read it,” Einstein urged Max Born, “even though it might look crazy, it is absolutely solid.” Einstein’s behavior in this matter was so absolutely right and decent that we can forget how tempting it is for established scientists, when they find themselves headed off at the pass, to use their own prestige to claim to have been there first. Johannes Stark was always making that sort of claim. Even a giant like Newton was perpetually embroiled in battles over priority to an idea. Einstein seems to have been beyond that style of temptation, and in his second paper on Bose-Einstein statistics he added a footnote urging the world of physics to pay attention to de Broglie.
That second paper was read before the Prussian Academy in early 1925 and startled its audience with predictions of undiscovered behavior by gases. When matter approaches a temperature of absolute zero, said Einstein, its atoms will become as indistinguishable as photons and a new kind of quantum gas will replace the classically observed one. As usual with Einstein’s theoretical spectaculars, he was far ahead of the experimentalists. The first laboratory confirmation would not appear until 1928, and it took almost 70 more years to demonstrate that molecules really can condense into a gas with indistinguishable parts. Einstein’s paper also showed that his statistical approach to matter and de Broglie’s wave approach corresponded exactly, so the two theories snapped into place like the two sides of an arch.
Shortly afterward, Einstein read the Academy still a third paper about quantum statistics. This time he settled the question of whether the third law of thermodynamics applies to gases. The third law states that as temperatures approach absolute zero, the loss of usable energy (the entropy) also approaches zero. According to classical statistics, gases contradict this law, but Einstein showed that the law holds under the new quantum statistics.
Einstein’s papers on quantum statistics appeared at the same time that German physics was awash with rumors of laboratory confirmation of the Compton effect and disproof of its rival BKS theory. It was a time of great professional triumph for Einstein. His quantum theories now had a clear factual basis in photoelectricity and X-ray scattering, and a coherent explanatory basis in quantum statistics. Among physicists this achievement was quickly recognized and admired, but it contributed nothing to the Einstein legend, which by then was fixed in hardened cement and now focused much more on the person than on his work.
That spring Einstein toured South America, visiting Buenos Aires, Rio de Janeiro, and Montevideo. He was hailed, of course, and praised for relativity and his antiwar politics. Einstein always thought it odd that ordinary people cared anything about relativity, so he was not puzzled that his quantum work went ignored. The enthusiasm over his politics was equally bizarre, because Einstein well knew that the masses of people are not antiwar. A reminder of that reticence over peace came in Buenos Aires when a local reporter proved to be an old acquaintance from Berlin named Otto Buek. Einstein and Buek had formed half of a group of four Berliners who dared to sign a “Manifesto to Europeans” that protested the outbreak of the Great War. As Buek recalled, they “had overestimated the courage and integrity of German professors.” Yet the Germans of 1925 boasted of their Einstein and in Buenos Aires the German ambassador spoke enthusiastically about him. Einstein laughed to himself that although Germans commonly saw him as “a foul smelling flower” they stuck him in their “buttonholes.” Isn’t life preposterous? Einstein always thought so.
