Einstein and the Quantum

by Stone, A. Douglas

  But this is the perspective of a man who knows how the story will turn out: he knows it will end with an atomic theory he cannot fully accept. The Einstein of 1915 was still in hot pursuit of the new “fusion theory,” as he himself had dubbed it, in which light would be both a particle and a wave, and Newtonian mechanics would be replaced by a theory of particle motion that naturally incorporated quantum discontinuity. In February of 1916 he wrote to Sommerfeld, waxing poetic about Sommerfeld’s recent theory of atomic spectral lines, which he said had “enchanted me. A revelation!” even calling it, a few months later, “among my finest experiences in physics.” By the end of May 1916, six months after completing general relativity, he already was presenting new work on an application of quantum theory to physical chemistry, a proof that any chemical reaction that requires the input of light to proceed, absorbs energy in the amount of hυ per molecular reaction. By early July of 1916 his next great quantum breakthrough had materialized. He published an initial report that month and was polishing it for a more definitive presentation on August 11, 1916, when he wrote to Besso: “A brilliant idea has dawned on me about radiation absorption and emission; it will interest you.” That idea would be the foundation of the modern quantum theory of radiation, the first chapter in every modern textbook on the subject.

  The Einstein who wrote those lines was living a very different life from the expatriate professor in Prague who in 1911 had temporarily left quantum theory to the lunatics and raised his intellectual gaze from the atom to the cosmos. Recall that in July of 1912 the newly eminent physicist A. Einstein, father of two young boys and husband of one increasingly unhappy spouse, had returned to Zurich as a full professor of theoretical physics at the Poly, now upgraded in status to the Swiss Federal Institute of Technology (ETH). The Einstein family loved Zurich and had many close friends there, but a variety of forces were conspiring to attract Professor Einstein to a different equilibrium state.

  Already, two years before this, the formidable Nernst had begun pulling the levers that would pry Einstein out of Switzerland and into Germany. In this effort he had gained by 1912 a powerful ally in his colleague Fritz Haber, the assimilated German-Jewish chemist who was responsible for the development of the ammonia extraction process, a process that would be critical to Germany’s military strength and, ultimately, to the agricultural revolution of the twentieth century. In April of 1912, even before returning to take up the post at Zurich, Einstein had visited Berlin and spoken with Nernst, Planck, Haber, Rubens, and Warburg; and job possibilities were already being floated. As an intellectual center of the new quantum physics, Berlin outshone not only Zurich but any place else on the planet as well, and this clearly interested Einstein. However, with his famous intellectual independence, he hardly needed to move yet again simply to improve his scientific neighbors. But then two new factors entered the equation.

  On that very first trip to Berlin in April of 1912 he renewed his acquaintance with a female cousin, Elsa Einstein, whom he remembered fondly from childhood visits. Elsa, a divorcée, three years his senior with two daughters from her marriage, was Albert’s cousin through both her father’s and mother’s family; but, by the customs of the time, this would not have hindered at all an amorous relationship between the two. Later Elsa would claim that she had fallen in love with Albert when she knew him as a boy because of his beautiful violin playing. She was as comfortable and familiar to Einstein as Mileva had been different and intriguing. Born in the Einstein ancestral home of Hechingen,2 she shared his Swabian dialect and prized the Swabian value of gemütlichkeit, which narrowly refers to a cozy domestic environment but more generally denotes warmth, good humor, and acceptance. While contemporaries judged her prettier than Mileva, she was not a beauty, but shared Einstein’s stocky build and curly hair to the extent that later in life people commented on how much they looked alike. Einstein was drawn to her, it seems, as someone who would understand his needs and take care of him, which in fact is exactly what transpired.

  How Elsa and Albert reconnected on that first visit to Berlin in April 1912 is not known in detail, but their reunion had an immediate effect on both. Within days of his return Elsa wrote to Einstein at his work address (to avoid Mileva’s surveillance). While Elsa’s letters from the time have not survived, Albert’s were lovingly preserved by Elsa, who clearly saw the prospect of a rewarding future life with him. In his reply to her first letter he wrote, “I can’t even begin to tell you how fond I have become of you during these few days…. I am in seventh heaven when I think of our trip to Wannsee [the forest near Berlin].” In this very first letter he seems already to have fixed his mind on a future romantic relationship, continuing quite boldly, “I have to have someone to love, otherwise life is miserable. And this someone is you; you cannot do anything about it, as I am not asking you for permission.” And, finally, he warns her not to assume that he is unmanly because he defers to Mileva in public: “Let me categorically assure you that I consider myself a full-fledged male. Perhaps I will sometime have the opportunity to prove it to you.”

  During the same visit to Berlin at which he kindled the relationship with Elsa, Einstein was courted for a position in the Physikalisch-Technische Reichsanstalt, the laboratory at which many of the fundamental studies on blackbody radiation had been done. However, this position did not materialize and in any case would not have held much attraction for Einstein. In fact he had told Elsa in that first letter that “the chances of my getting a call to Berlin are, unfortunately, rather slight.” And, perhaps for this reason, Einstein rapidly backtracked on his overture to Elsa, saying just three weeks later, “it will not be good for the two of us as well as for others if we form a closer attachment.” However, his judgment on his prospects in Berlin was overly pessimistic; by July of the next year (1913) Walther Nernst and Max Planck had traveled to Zurich to make him an offer he could not refuse.

  Unless they were independently wealthy, as in the case of Maxwell and Lord Rayleigh, even the greatest physicists had to earn their keep by teaching, administration, or supervision of projects of practical utility. However, Nernst, Haber, and Planck had convinced the Prussian authorities that Einstein would be such a jewel in their crown that he should be an exception. He was offered a professorship at the University of Berlin with no teaching duties (except by his own choice) as well as the directorship of a new theoretical physics institute, which did not yet exist and which he could run with as little structure as he saw fit. And, finally, he was to be elected to the august Royal Prussian Academy of Sciences as its youngest member.3 This last honor was considered so great that when he told the news to an esteemed older colleague at Zurich, Aurel Stodola, it brought a “tear of joy” to Stodola’s eyes, “because ideal justice had been meted out to somebody on this earth.”

  FIGURE 19.1. Einstein playing the violin along with the daughter of his ETH colleague Adolph Hurwitz, who is conducting, in 1913. Einstein’s triumphant return to Zurich would be short-lived, as he was soon lured away to Berlin. ETH-Bibliothek Zurich, Image Archive.

  It is not likely that Einstein cared for this honor nearly as much as others did. Philipp Frank recounts a jest Einstein made when a colleague at Zurich remarked that admission to the academy always came so late in life that it no longer made the honoree happy; Einstein replied that then he should be eligible for immediate admission “because it would not make me happy even now.” But while Einstein was unimpressed by such vanities, the offer of complete intellectual freedom came at the perfect time. He was halfway through his historic struggle with the theory of gravitation, aware that he was on the verge of changing mankind’s view of the universe, but not at all confident of success. Moreover he was closely following the developments in quantum theory, where Berlin was the center. At the same time, he found his teaching duties at ETH increasingly taxing, draining time from his epoch-making research. And now the offer came to be simply left alone in Berlin to think as he pleased! To the consternation of Mileva, he accepted
the offer.

  In speaking to scientific colleagues, Einstein always cited freedom to focus on his research as his motivation for moving. To Lorentz he wrote, “I couldn’t resist the temptation of a post in which I would be free from all obligations and be able to indulge wholly in my musings.” To Ehrenfest he spoke more plainly, “I accepted this odd sinecure because lecturing in class was getting oddly on my nerves, and there I won’t have to do any lecturing.” All the perquisites for this life of untroubled scientific contemplation were put into place as promised by Nernst and Planck, and by April of 1914 Einstein had arrived in Berlin, traveling separately from his family. Barely two months later Mileva and his sons had come and gone, returned to Zurich. Mileva had “howled unceasingly” against the move and hated the city at first sight. Their relationship had become frigid and hostile, and her departure began a separation from him, which would prove permanent, although not accepted as such for many more years. Einstein wept copiously at the train station seeing them off and had to be supported by Haber as he walked home. For years he bemoaned the estrangement from his children but nonetheless quickly adapted to a new, less-encumbered lifestyle in Berlin. Barely a year later he wrote to his old friend Zangger, “In personal respects I have never been so at peace and happy as now. I am living a very secluded and yet not lonely life, thanks to the loving care of my cousin, who had drawn me to Berlin in the first place, of course” (italics added).

  1 “Experimental Proof of the Existence of Ampere’s Molecular Currents,” by A. Einstein and Wander J. de Haas, Koninklijke Akademie van Wettenschappen te Amsterdam, Section of Science Proceedings, vol. 18, pp. 696–711 (1915–1916).

  2 Einstein’s “certificate of presidency” for the Olympia Academy (figure 8.1) had labeled him “the man of Hechingen.”

  3 The nominators, Planck, Nernst, Rubens. and Warburg wrote: “The undersigned are aware that their proposal to accept so young a scholar as a regular member of the Academy is unusual; but they are of the opinion not only that the unusual circumstances adequately justify the proposal, but also that the interests of the Academy really require that the opportunity … to obtain such an extraordinary person be taken advantage of.” The academy also took the highly unusual step of granting Einstein a generous salary for this nominally honorific post.

  CHAPTER 20

  BOHR’S ATOMIC SONATA

  Europe in its madness has now embarked on something incredibly preposterous. At such times one sees to what deplorable breed of brutes we belong. I am musing serenely along in my peaceful meditations and feel only a mixture of pity and disgust.

  —ALBERT EINSTEIN, AUGUST 19, 1914

  Einstein had not only changed his domestic situation by moving to Berlin; he had radically changed his social and political environment. Within a month of his inaugural address at the Prussian Academy of Sciences he found himself surrounded by a flood of militaristic German nationalism, alone on a tiny island of pacifist universalism. The Great War had begun, and his admired German colleagues—Nernst, Haber, and even the mild-mannered Planck—rushed to show their devotion to the fatherland. They and many other academics signed an ill-conceived “Appeal to the Cultured World” denying documented German war crimes in Belgium and asserting the unity of German culture with German militarism. Einstein joined with a physician friend, George Nicolai, to respond with a counter-manifesto titled “Appeal to the Europeans” denouncing the attitude of their colleagues as “unworthy of what until now the whole world had understood by the word culture.” No one of consequence agreed to sign their version. For the next four years Einstein maintained his critical stance toward both sides in the war but mainly expressed it, as he put it, through the Socratic method—posing questions to his peers that others did not dare raise. Because of his intellectual stature and his identity as an outsider he was indulged as an eccentric genius, and suffered no major consequences (as he would later when anti-Semitism joined forces with postwar nationalism).

  However, his colleagues did not confine themselves to written expressions of support for the war effort. Nernst, always a bit of a self-caricature, at age fifty volunteered as support staff in what was called the Drivers Corps. He drove off in his private car to the front just in time to participate in the first rapid advance on Paris, getting so far that he could see the glow of the city lights at night. When the drive stalled and trench warfare began, he returned to Berlin and devoted himself to developing nonlethal chemical weapons, whose prototypes failed to impress the General Staff. Haber had fewer scruples and focused on developing the truly deadly gas weapons for which the Germans became renowned: chlorine, mustard gas, and phosgene. If the General Staff had believed more strongly in these weapons, the Germans might well have broken through the Allied lines when they were first deployed at Ypres and won the war. Nernst and Planck would both lose sons in the war; Haber would lose his wife, Clara, who committed suicide at least partly out of disgust at her husband’s embrace of deadly invention.1 Remarkably Einstein never spoke out against his colleagues directly and actually defended them, saying that they were “internationally minded as scientists” in comparison to chauvinistic nonscientists.

  While Einstein often mentioned the psychological toll of the war in his letters (“the international catastrophe weighs heavily on me”), he repeatedly demonstrated his preternatural ability to block out the external world and concentrate on his science. The years 1914 and 1915 were devoted to the completion of general relativity, the monumental achievement already discussed. Within months of that exclamation point, he had attacked the quantum problems with renewed vigor. Something big had happened in the atomic world during his cosmic interlude. The 1911 Solvay Congress, which had been of little scientific use to Einstein, had been an eye-opener for a number of the distinguished participants from England and France, where the early quantum theory was barely known. Chief among them was a New Zealander, now transplanted to the physics laboratory at the University of Manchester in England, named Ernest Rutherford. He had been exploring experimentally the structure of the atom, blissfully unaware of the strong evidence from statistical physics that atoms obeyed new rules not explained by classical mechanics and electromagnetic theory. He had already been awarded the Nobel Prize in Chemistry for measuring the elementary unit of charge in the dramatic year of 1908, when Planck’s Nobel nomination in physics was defeated owing to belated comprehension that his quantum of action, h, threatened the foundations of the field. By 1913 Rutherford’s research group had done the decisive experiments supporting the idea of a nuclear atom: in this picture a number of light, negatively charged electrons orbited around a localized, much heavier nucleus with the same number of positive charges. Now one had a well-defined model within which classical physics could crash and burn; that was progress.

  In Rutherford’s lab at the time was a twenty-six-year-old visiting Danish physicist, Niels Bohr. This Bohr was showing distressing signs of preferring theory to experiment, not a popular trait in the laboratory of “Papa” Rutherford, but fortunately his manly vigor compensated for this weakness of character. Rutherford decided he was an acceptable breed of the species: “Bohr is different. He’s a football player.”2

  Bohr in turn greatly admired Rutherford. After enduring an unsuccessful visit to J. J. Thomson in Cambridge before moving to Manchester, he wrote to his brother enthusiastically about the contrast. Rutherford’s lab was “full of characters from all parts of the world working with joy under the energetic and inspiring influence of the ‘great man.’ ” Rutherford himself was “a man you can rely on; he comes regularly and enquires how things are going and talks about the smallest details.” Rutherford communicated to Bohr the extraordinary puzzles posed by the early quantum concepts. As Bohr recalled, “I got a vivid account of the discussions at the first Solvay meeting from Rutherford in 1911, shortly after his return from Brussels.” He immediately set about finding a way to fit Planck’s constant, h, into the Rutherford atom.

  Bohr began his theorizing
at just the right time. For some time the atom had been known to be an electrically neutral object containing negative electrons, which had been discovered by J. J. Thomson in 1897. These electrons appeared to inhabit a region of dimensions one hundredth of a millionth of a centimeter (10−8 cm). The nature of the positive charge, which counterbalanced the electron’s negative charge and made the atom neutral, was not known in the first decade of the twentieth century. Elaborating on a proposal by Lord Kelvin, J. J. Thomson had introduced a “plum pudding” model in which the positive charge was spread out uniformly in a sphere of roughly the same dimensions as the electrons inhabited, that is, 10−8 cm. The electrons were somehow suspended in stationary rings within the positively charged sphere and were the “raisins” in the pudding. Classical physics required that the electrons be stationary (except when they were disturbed by some external perturbation) because, according to Maxwell’s equations, electrons orbiting in the atom would continuously radiate their energy away, a process that was not observed. In contrast, isolated atoms in a gas emitted light only at a few narrow frequencies, specific for each element. Moreover they did not do this continuously but only intermittently or under external disturbance.

  Thomson had not attended the Solvay Congress of 1911, where the necessity of changing fundamental laws at the atomic scale was communicated to Rutherford and others, and when he did attend the second conference, in 1913, he was still defending his classical atom. The distinguished continental attendees, who had been struggling with quantum paradoxes for many years, did not sit still for this. Lorentz interrupted his lecture to state, “The proposed hypothesis gives rise to an … objection of a general … nature. We can take it as established that a model in which everything happens according to the laws of ordinary mechanics will lead to Lord Rayleigh’s formula for the black-body radiation [the ultraviolet catastrophe]. As the model proposed by Sir J. J. Thomson contains nothing which is incompatible with the rules of mechanics, it is highly improbable that we will be able to deduce from it the correct laws of radiation.”