Einstein and the Quantum

by Stone, A. Douglas

  Although in 1921, at the time of these early attacks, Einstein’s scientific colleagues felt that it was unwise of him to engage with this rabble at all, they uniformly defended him. Most striking was a statement by von Laue, Nernst, and Rubens: “It cannot be our task to discuss in detail the unparalleled profound intellectual work which led Einstein to his theory of relativity…. What we do want to emphasize, and what was not touched upon in a single work yesterday [at the antirelativity meeting], is that quite apart from Einstein’s relativistic research, his other work already assures him of an immortal place in the history of science” (italics added). So while the public either swooned or fumed over relativity theory, his Berlin colleagues had not lost sight of the fact that Einstein was the conceptual leader of the new atomic physics. And they had not abandoned the hope that he would yet come up with a true and complete quantum theory.

  Einstein himself, however, seemed for the first time in his life easily distracted from his scientific research. Although he did not feel truly threatened by the anti-Semitic mood of the right wing in 1920, it did appear to rekindle a sense of ethnic identification with his Jewish brethren. In April 1920 he addressed a Jewish group as follows: “there is in me nothing which can be described as ‘Jewish faith.’ But I am happy to belong to the Jewish people.” Not that he had any sympathy for religious observances, as he made clear to a rabbi with whom he had debated: “The [religious Jewish] community is an organization for the exercise of ritualistic forms that are remote from my opinions. I must take it for what it is today and not for what one might perhaps wish to see it transformed into. When I want to drive into town, I do not lay myself down in bed in the hope that it will grow wheels and become an automobile…. [However] I gladly vow … all kinds of efforts in the interest of individual Jews and Jewish communities.”

  In keeping with this pronouncement, less than a year later, despite his professed desire to focus on science, he immediately agreed to an invitation from Chaim Weizmann, the president of the World Zionist Organization, to accompany him to the United States to solicit funding for the planned Hebrew University in Jerusalem. Never mind that the trip’s schedule would require his withdrawal from the first of the revived Solvay Congresses, on “atoms and electrons,” and that among his many talents and interests fund-raising had never previously figured. To Haber (who greatly opposed his participation), he confessed: “I am not needed for my abilities, of course, but only for my name. Its promotional power is anticipated to bring considerable success thanks to our rich fellow clansmen of Dollaria (Einstein’s nickname for the USA).” However, he regarded his participation as a moral duty: “Despite my declared international mentality, I do still always feel obliged to speak up for my persecuted and morally oppressed fellow clansmen, as far as it is within my powers…. The prospect of establishing a Jewish university delights me especially, after recently seeing from countless examples how perfidiously and unkindly fine young Jews are being treated here in the attempt to deprive them of educational opportunities.” In fact, while Einstein created a sensation everywhere he went in America, adding to his legend, the trip was only modestly successful in its monetary goals.

  This trip seemed to spark a wanderlust in Einstein that he had not previously demonstrated. During the next two years, in addition to the trip to the United States, mainly by his own choice, he would visit Holland, Austria, Czechoslovakia, England, France, Italy, Switzerland, Japan, Hong Kong, Singapore, Palestine, Spain, Sweden, and Denmark, not a program conducive to deep contemplation. However, in the summer of 1921, after returning from the United States, Einstein briefly turned his thoughts to the problem of light quanta once again.

  While Einstein had by this time developed his notion of “ghost fields” to explain how particles of light could exhibit the interference effects associated with waves, he did not think that the net result for observations would be exactly as predicted by the classical theory of electromagnetic waves. Thus he sought an experimental test that would directly distinguish his theory, in which all energy was carried by individual light quanta, from the predictions of classical optics. In August of 1921 he thought he had found one, a “very interesting and quite simple experiment about the nature of light emission…. I hope I can carry it out soon.”2

  FIGURE 23.2. Einstein and his second wife, Elsa Einstein, photographed on their trip to the USA in 1921. Library of Congress, courtesy AIP Emilio Segrè Visual Archives.

  The idea was indeed quite simple, but flawed. Einstein assumed that light quanta would not show the Doppler effect when emitted from a moving atom (i.e., its frequency would not be shifted depending on the angle between its motion and the line of sight to the detector), whereas classical radiation was known to show such an effect. Thus he suggested imaging the light from moving atoms through a telescope lens with an inserted prismlike element, to differentially deflect the light of different frequencies. He calculated that the classical theory would give a deflected image and his quantum theory would not. He did not have to do the experiment himself, finding the seasoned professionals Walter Bothe and Hans Geiger quite happy to do these relatively easy measurements. They were completed in December of 1921; no deflection of the image was detected.

  Einstein, again ecstatic, as he had been after his work on quanta in 1916, told Born the latest news. “Thanks to the excellent collaboration of Geiger and Bothe, the experiment on light emission is finished. Result: The emission of light by the moving [atom] is strictly monochromatic, whereas according to the undulatory theory, the color of the elementary emission ought to be different in different directions. Thus it is surely proven that the undulatory field has no real existence…. It is my most powerful scientific experience in years.” However Einstein’s exultation was short-lived. Independently, Ehrenfest and Max von Laue pointed out that Einstein had got the classical prediction wrong; both the classical and the quantum theory predicted no effect. Einstein redid the calculations himself and presented the amended conclusion a couple of months later: “in light of this theoretical result, deeper conclusions cannot be derived from the experiment concerning the nature of the emission process.” He wrote again to Born, with characteristic self-deprecation, “I … committed a monumental blunder (experiment about the emission of light …). But one shouldn’t take it too seriously. Death alone can save one from making blunders.” He was clearly getting frustrated, once again, with the unyielding quantum: “I suppose it is a good thing that I have so much to distract me, else the quantum problem would have long got me into a lunatic asylum…. How miserable the theoretical physicist is in the face of nature.”

  The many distractions associated with his fame were compounded when, in June of 1922, right-wing extremists assassinated Walter Rathenau, the German foreign minister. Rathenau, the first Jew to hold that post, was a personal friend of Einstein’s, and not only did his loss shake Einstein’s equanimity, but in its aftermath multiple threats were received to his own life. He hid out in the country, sheltered by a rich friend, Hermann Anschütz, and even toyed briefly with quitting physics research and working as an engineer, with “a downright normal human existence” and the “welcome chance of practical work.” This fanciful notion vanished in a few days, but he avoided the German physics meeting in Leipzig, bitterly disappointing the twenty-one-year-old Werner Heisenberg, who attended with the hope of meeting him.3 In a letter to Solovine, his longtime friend and “Olympia Academy” alumnus, Einstein recounted: “I am constantly being warned, I have given up my lecture course and am officially absent although I am really here. Anti-semitism is very strong.” He felt it was fortunate that he had “the opportunity of a prolonged absence from Germany,” as he had committed himself to an extended lecturing trip to Japan and points east in October of 1922.

  However, an unexpected wrinkle developed in his plans when he was informed by Svante Arrhenius, who still ruled the Physics Committee for the Nobel Prize, that “it will probably be very desirable for you to come to Stockholm in Dece
mber, and if you are in Japan that will be impossible.” The Nobel committee had finally been moved to award the most famous scientist since Newton its stamp of approval. Characteristically, Einstein was not disposed to dance to the tune of the establishment, particularly for an institution that had passed him over for so long; despite Arrhenius’s hints that Einstein’s absence might put the final vote in doubt, he replied that he was “quite unable to postpone the journey.” So off he went to Japan by ship, on schedule, receiving news of his award somewhere en route on an unknown date, as he failed to even note the event with an entry in his travel diary. Nonetheless, the citation on the award surprised many: “for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.” The Nobel committee had found relativity theory too uncertain and controversial for recognition but instead came to rest on the one work by Einstein that he himself considered “revolutionary.”

  While there was much irony in this development, in fact the citation was carefully crafted to recognize the empirical law of the photoelectric effect, and not the underlying theory. This law had already been confirmed in great detail by the American physicist Robert Millikan by 1916, and by many other experiments subsequently, so it could no longer be doubted. Millikan himself wrung his hands at his own results, saying “I spent ten years of my life testing that 1905 equation of Einstein and, contrary to all my expectations, I was compelled to assert its unambiguous experimental verification in spite of its unreasonableness, since it seemed to violate everything we knew about the interference of light.” The Nobel citation said nothing about quanta of light, a concept that was still rejected by the overwhelming majority of physicists. In fact Bohr, despite his deep admiration for Einstein, could not resist a rather biting joke at Einstein’s expense, saying that if he received a telegram from Einstein confirming the existence of light quanta, he would point out that the telegram itself, transmitted by electromagnetic waves, was proof against them.

  Einstein did not return to Germany until the spring of 1923, and he went to collect his Nobel Prize in the summer. By this time he was involved in a different scientific quest, his famous attempt to unify the gravitational and electromagnetic forces by means of a “unified field theory.” However, he was very hopeful that such a theory would itself point the way to the solution of the quantum problem, even submitting a paper along those lines to the Prussian Academy in December of that year. In 1924, in a radio address, he informed the public, who only wanted to hear about relativity theory, that he was really focused on something else:

  The other great problem that I have been concerned with since about 1900 is that of radiation and the quantum theory. Stimulated by the work of Wien and Planck, I recognized that mechanics and electrodynamics were in irresolvable contradiction with experimental facts, and so I have helped in creating the complex of ideas known by the name of quantum theory, which has been developed so fruitfully particularly by Bohr. I shall probably devote the rest of my life to the fundamental clarification of this problem, however slight the prospects are for attaining the goal may be.

  In fact the goal was now rather close, although it would not take the form Einstein hoped, and he was about to make his final historic contribution to reaching it.

  1 This was often later misquoted as the highest achievement.

  2 It is notable that Einstein, despite having become the paradigm of the pure theorist to the public, was still quite willing to contemplate actually setting up and performing such an experiment himself.

  3 Sommerfeld, with whom Heisenberg was studying, had promised to introduce him to Einstein, who had been Heisenberg’s idol from his high school days. Heisenberg was appalled to find an anti-Semitic leaflet attacking Einstein thrust into his hand as he entered the hall where von Laue was delivering the lecture on Einstein’s behalf.

  CHAPTER 24

  THE INDIAN COMET

  Respected Sir:

  I have ventured to send you the accompanying article for your perusal and opinion. I am anxious to know what you think of it. You will see that I have tried to deduce the coefficient 8πυ2/c3 in Planck’s Law independent of the classical electrodynamics, only assuming that the ultimate elementary region in the phase-space has the content h3.

  This letter to Einstein from an unknown Indian scientist, received in early June, 1924, initiated one of the most extraordinary episodes in the modern history of science, culminating in Einstein’s final historic contribution to the structure of the new quantum theory. At the time of his writing, Satyendra Nath Bose was a thirty-year-old Reader (roughly equivalent to the rank of associate professor) at Dacca University in East Bengal. His previous five research papers had made no impact at all on contemporary research, and he had recently been informed that, due to a funding cutoff to the university, his appointment would not be extended more than a year. Moreover, the paper he was sending to Einstein had already been submitted for publication, and rejected, by the English journal Philosophical Magazine. He had admired Einstein for many years and had even produced a rather undistinguished translation of Einstein’s papers on general relativity into English, for distribution in India. Thus, through some combination of veneration and chutzpah, he hit upon the idea of sending this paper, which related closely to Einstein’s 1916 work on radiation theory, directly to the master, with an astonishing request:

  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 fur Physik. 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 teachings through your writings.

  Yours faithfully, S. N. Bose.

  Einstein by that time, as we have seen, was not just the most famous scientist of his time; he was one of the best-known individuals on the entire planet. He was deluged by letters from strangers, wanting his opinion on everything under the sun, while at the same time struggling to keep up his voluminous scientific correspondence with the large community of physicists with whom he had personal and professional relations. In addition, Einstein spoke very little English and had not been able to deliver his prestigious lectures in England during his visit in 1921 in the native tongue of his audience.1 The a priori probability that S. N. Bose’s paper would end up in the circular file, his work and his name lost to posterity, was extremely high.

  But that is not what happened. Einstein read the paper shortly after its arrival, translated it, and sent it to the German journal Zeitschrift für Physik on July 2, 1924, with his strong endorsement. There it was subsequently published, with a note from Einstein appended. “In my opinion Bose’s derivation of the Planck formula signifies an important advance. The method used also yields the quantum theory of the ideal gas, as I will work out in detail elsewhere.” In fact, shortly thereafter Einstein translated a second paper, which he had received from Bose on the heels of the first one and which he sent on to the journal by July 7, 1924. This one did not elicit such a favorable opinion from the great man, and he published a critical comment along with it, while nonetheless supporting its publication.

  With these magnanimous gestures from the sage, the die was cast. Bose would go on to become one of the most famous names in the history of modern physics. The term “boson” is used for one of the two fundamental categories of elementary particles in modern physics2 because such particles obey novel statistical laws first employed, although not announced, in Bose’s initial paper sent to Einstein. This category includes Einstein’s photons (light quanta) as well as roughly half of the atoms in the periodic table. But Bose’s discovery, like that of Planck twenty-four years earlier, was not as clear-cut as it has been portrayed, and again it would take Einstein to find the radical implications in it.

  S. N. Bose was born into the rising middle class of English-educated Indians in 1894 in Calcutta. He father, an accountant, had a wide range of intellectual inte
rests that he transmitted to his son, who, in addition to his great aptitude for mathematics, became deeply interested in poetry, music, and diverse languages. When he matriculated at the Presidency College in Calcutta in 1909, however, he chose to study science, at least partly because of its potential utility to the future Indian nation, as a wave of nationalism swept through his generation. His cohort was “a particularly brilliant lot—the famous 1909 batch of Presidency College … [which] in all its history has not seen the likes … since.” Bose completed his BSc in 1913 and MSc in 1915, taking first place in both examinations; but there was no obvious avenue for obtaining a doctorate, and the professorial ranks were still reserved for third-rate English academics at that time. Bose therefore went through a period as a striving outsider, not dissimilar to the career of Einstein at the same age.

  He married early (prior to graduation) but, contrary to custom, refused to accept a dowry or other financial support from his wife’s family. Already responsible for a wife and son shortly after he received his MSc, he spent a year eking out a living through private tutoring, while trying to work toward a PhD in mathematics with a well-known professor, Ganesh Prasad. Prasad was noted for his aggressive criticism of prospective students and of their previous teachers, which typically cowed the candidates into silence. But Bose was “notorious for plain speaking.” In an echo of Einstein’s conflicts with authority figures such as Weber, Bose “dared to counter his adverse criticisms” and was summarily dismissed from consideration for PhD work with the comment, “you may have done well in the examination, but that does not mean you are cut [out] for research.” “Disappointed, I came away [and] decided to work on my own,” Bose recalled.

  Like Einstein, he was turned down for low-level teaching jobs before being offered an entry-level lectureship in the new University College of Science in Calcutta, whose founder, Sir Asutosh Mookerjee, began hiring the cream of young Indian scientists, including the future Nobel laureate C. V. Raman. It was at the College of Science that Bose first began to learn about the exciting developments in physics in Europe associated with the names of Planck, Einstein, and Bohr. Here also he and his close friend, the physicist Meghnad Saha, obtained and translated important German works of physics, including Einstein’s papers on relativity theory.