Einstein and the Quantum

by Stone, A. Douglas

  Why, you may ask, would a chemist with a practical and empirical bent like Nernst care deeply about this apparently abstract principle? Because for some years previously it had been realized that knowledge of a system’s low-temperature entropy behavior would allow one to use chemical reaction data over a limited range of temperatures and predict at other temperatures and pressures how much of each product a particular reaction would yield, a fundamental question in all of chemistry. Nernst quickly set out to calculate the “reaction constants” that followed from his principle and showed that they predicted well the results of various experiments. Already in 1910, when he was meeting Einstein for the first time, his approach had been crucially employed by his colleague Fritz Haber to facilitate the development of a chemical technique of immense importance for humanity, the process for removing nitrogen from the air to make ammonia for fertilizer (and explosives).

  Characteristically, Nernst referred to the principle he had discovered as “his theorem,” which is exactly what it wasn’t. A theorem is something logically deduced from other accepted rules or axioms. Nernst’s “theorem” was a hypothesis based on analysis of data; it had no grounding in atomic theory at all, nor could it have had at that time. Systems that obey the equipartition principle of classical mechanics do not obey Nernst’s law; so his conjecture actually contradicted the currently accepted theory. We now know quantum ideas are essential for the validity of this principle. And that is where Einstein comes in.

  Nernst surely realized that his “theorem” was going to require some microscopic underpinning to become a law. And there were absolutely no hints of a microscopic theory that would violate equipartition coming from the leading theorists of the time. Yes, there was that strange business about the radiation law, but it seemed, as Planck would surely have advised him, to relate mainly to matter in interaction with radiation. Thus one can imagine his excitement when he became aware of Einstein’s 1907 paper, explaining how applying Planck ideas to vibrations in solids predicted a violation of equipartition, and just the kind of violation (the freezing out of vibrations) that would justify Nernst’s “theorem.” No wonder that in early March 1910 Nernst made a special trip to Zurich to meet the wunderkind who had provided the first mathematical theory consistent with his historic conjecture.

  Despite Einstein’s rise in status as an associate professor, very few of his colleagues and acquaintances had any idea that a major intellectual figure was among them. His informality with the students and his ever-present sense of humor hardly signaled an august personage; and his dress had not improved greatly from the time he used a runner from his dresser as an impromptu scarf. His first (and only) doctoral student, Hans Tanner, describes his “rather shabby attire, with trousers too short for him and an iron watch chain,” hastening to add that his lecturing style immediately “captured our hearts.” An associate professorship for a man with a family could not have supported much elegance anyway; an older colleague at the time wrote of Einstein, to none other than Arrhenius, “I am most interested in the associate professor at the university, A. Einstein, a still young, totally brilliant chap from whom one can learn a lot…. I believe he has a great future, at present he lives with his wife and children in very modest conditions. He certainly deserves a better fate.”

  The general impression of Einstein’s status changed suddenly and dramatically after Nernst’s visit. George Hevesy, a young assistant at the Zurich Poly at that time, who went on to become a Nobel laureate in chemistry, recalls that Nernst’s visit “made Einstein famous. Einstein in 1909 was unknown in Zurich. Then Nernst came and people in Zurich said ‘that Einstein must be a clever fellow if the great Nernst comes all the way from Berlin to Zurich to talk to him.’ ”

  Very little is known about the details of this visit except that Nernst filled Einstein in on the state-of-the-art measurements of specific heat as a function of temperature being done in his laboratory, and Einstein surely impressed Nernst with his profound understanding of thermodynamics and statistical mechanics, and with his thoughts on how the quantum hypothesis could clear up many issues. Nernst’s reaction is worth quoting at length:

  I visited Prof. Einstein in Zurich. It was for me an extremely stimulating and interesting meeting. I believe that, as regards the development of physics, we can be very happy to have such an original young thinker; a “Boltzmann redivivus [reborn]”; the same certainty and speed of thought; great boldness in theory, which however cannot harm, since the most intimate contact with experiment is preserved. Einstein’s “quantum hypothesis” is probably among the most remarkable thought [constructions] ever; if it is correct then it indicates completely new paths both for the so-called “physics of the ether” and for all molecular theories; if it is false, well, then it will remain for all times “a beautiful memory.”

  The most striking thing about this remarkable quotation is that Nernst, Max Planck’s close colleague and friend, refers to Einstein’s quantum hypothesis without mentioning Planck at all. It is clear to him that in the hands of Einstein, Planck’s ad hoc patch-up of radiation theory has become something very different: a vision of a completely new electromagnetic and molecular theory. In fact, there is no indication that Einstein’s 1907 proclamation of a sweeping quantum revolution in molecular mechanics was noted by anyone until Nernst took it up, apparently in late 1909 or early 1910. Not a single paper had been written relating to the quantum theory as applied to specific heat between early 1907, when Einstein’s work appeared, and February 17, 1910, when Nernst read his first paper on the subject to the Prussian Academy of Sciences, mentioning Einstein’s theory briefly at the end.3 With Nernst leading the charge this changed dramatically; ten such papers appeared in 1911, and over thirty total in the subsequent two years. Moreover it is very likely that, during or shortly after that visit, Nernst conceived the project of bringing Einstein to Berlin; a postcard from Nernst dated July 31, 1910, begins, “I have made inquiries regarding Einstein, but have not yet received any news.”

  As for Einstein, who by now had been struggling fruitlessly for more than two years to explain light quanta by modifying Maxwell’s equations, the visit by Nernst was a great morale boost. A week after Nernst left he wrote to Laub: “For me the theory of quanta is a settled matter. My predictions regarding the specific heats are apparently being brilliantly confirmed. Nernst, who has just been here to see me, and Rubens are busily engaged in the experimental verification, so that we will soon know where we stand.” And three months later he wrote to Sommerfeld with further results: “It seems incontrovertible that energy of a periodical nature, wherever it occurs, always occurs in energy quanta that are multiples of hυ … [whether] as radiation or as oscillation of material [molecular] structures…. It now seems pretty certain that as regards the heat content, the molecules of solid substances behave essentially similar to Planck’s resonators. Nernst found the relationship confirmed in the case of silver and some other substances.”

  But all this support for his heuristic ideas did not for one minute distract him from the underlying challenge: how do wave and particle properties manage to coexist in a full mathematical theory of quantum mechanics or electrodynamics? With characteristic wit he summarized his view in the same letter to Sommerfeld. “The crucial point in the whole question seems to me to be: ‘Can energy quanta and Huygens’ principle [of wave interference] be made compatible with each other?’ The appearances are against it but, as it seems, the Lord knew all the same how to get out of the tight spot.”

  1 The equivalent of roughly 4.5 million 2008 dollars. Diane Barkan, in her biography of Nernst, states that the actual amount Nernst received is unverifiable, but the legend persists.

  2 One consequence his invention did have, ironically, was the rupture of his friendship with Arrhenius. In 1897 in Stockholm Nernst demonstrated his lamp for Arrhenius, who laughed vigorously when it blew all the fuses in the hotel. From this small incident a lifelong feud nucleated, with the consequence that Nernst
received the Nobel Prize only in 1921, after many lesser lights of chemistry had been so recognized.

  3 “The specific heat decreases strongly at low temperatures … corresponding to the requirements of Einstein’s theory [that] it tends to zero” (Nernst, February 17, 1910).

  CHAPTER 18

  LAMENTING THE RUINS

  As for knowing, nobody knows anything. The whole story would be a delight to diabolical Jesuit fathers.

  —ALBERT EINSTEIN, NOVEMBER 1911

  A distinguished white-haired man, impeccably dressed, just over seventy, took the podium to explain his theory. In the small audience of twenty-four, listening attentively, were Einstein, Lorentz, Planck, Nernst, Wien, Rutherford, Madame Curie, Jean Perrin, and H. K. Onnes, all of whom were current or future Nobel laureates, as well as major scientific figures such as Sommerfeld, Rubens, Poincaré, and Jeans. The venue was a small meeting room in the elegant Hotel Metropole in Brussels.

  I decided to take as my starting point the one general concept that could meet the demands of the most scrupulous, philosophical and constructive mind: positive and negative ether, atomically and invariably cubifiable. The interfaces between them form alternating positive and negative atomic planes; there is a universal competition between these two different ethers, although they are essentially the same, because of spacifiable and superficialisable molecules. Spacification and superficialisation are energetically produced, and energy is produced exclusively by molecular contacts. Molecular contact, which has hitherto been neglected, is an essential element in my theory…. I undertook to create the active Universe with the intimate and well-defined mechanism of its own primitive elements.

  Upon his conclusion, none of the assembled dignitaries rose to take issue with either the correctness or the coherence of this eccentric “theory of everything.” On the contrary, Lorentz, the admired chairman of the proceedings, took pains to thank the speaker for “the report he was good enough to send us and … the talk he has just given us explaining its main ideas.” And why had the brilliant men and woman present suspended their otherwise highly developed critical faculties? They were engaging in a time-honored ritual of both art and science: humoring the wealthy patron.

  The speaker was the prosperous Belgian industrialist Ernest Solvay, inventor of an efficient and lucrative process for making soda, now an exponent of scientific progress across all spheres of human activity and a dilettante physical theorist. The occasion of his exposition was the legendary First Solvay Congress of 1911, the beginning of the modern specialized science conference. Monsieur Solvay, enlisted through the political acumen of Nernst, had footed the entire bill for this opulent and exclusive gathering of the crème de la crème of European physics. Fortunately, Solvay’s own “gravito-materialist” theory did not occupy much of the subsequent discussions of atomic theory, which his scientific assistant said he regarded as too “highly specialized.”

  Einstein had arrived in Brussels from a very different place—intellectually, professionally, and geographically—than he had been only nineteen months earlier when he had been so delighted and flattered by Nernst’s visit to Zurich. From the practical point of view, Nernst’s visit marked the beginning of a meteoric rise in Einstein’s stature and conditions, culminating in the invitation to deliver the concluding “report” at the Brussels conference, perhaps the most elite gathering of scientists in history. Einstein’s associate professor position at the University of Zurich was hardly a sinecure; it barely offered him a middle-class living and was not part of any track that would lead him to the position of an Ordinarius, or full professor, who could call his own shots. However, a bare five weeks after Nernst concluded his visit in early March of 1910, Einstein was nominated for a full professor’s position at the German University in Prague, a post he was eager to take, despite his comfort with life in Zurich, because it was a necessary step up the ladder of scientific advancement. During the summer of 1910 the appointment stalled briefly as, for the first time, explicit anti-Semitism seemed to block Einstein’s career; the cognizant ministry in Vienna decided to appoint the second choice of the search committee, an Austrian, Gustav Jaumann, whose role in the history of science is limited to this one cameo appearance. Fortunately for Einstein, in an expression of wounded pride, memorable for its inaccuracy, Professor Jaumann effectively withdrew his candidacy, accusing the university of “chasing after modernity while being blind to real merit.” As a result, by April of 1911, Einstein and family had moved to Prague, where he took up his new position as full professor of theoretical physics.

  FIGURE 18.1. Einstein, the newly minted full professor, in Prague, 1912. ETH-Bibliothek Zurich, Image Archive.

  This was his status when he appeared at the Solvay Congress in October of 1911, but his circumstances were still fluid, with a steady current upward. Even before he left Zurich, he had been contacted by Emil Fischer, the German Nobel laureate in chemistry, with the extraordinary news that an anonymous industrial donor, likely prompted by Nernst, had offered Einstein a gift of fifteen thousand marks “to promote your [scientific] work,” with no strings attached.1 By now Planck had publicly described the theory of relativity as “in boldness [surpassing] anything so far achieved in speculative natural science … [it] can only be compared to … [the revolution] produced by the introduction of the Copernican world system.” It was unlikely that Prague could keep this rising star for long. Only a few months after Einstein’s move there, his close friend Heinrich Zangger, dean of the medical faculty at the University of Zurich and someone whom Einstein admired greatly, began campaigning to bring him back to Zurich by creating a full professor’s position at his alma mater, the Zurich Poly.2 While Einstein was outwardly courteous regarding conditions in Prague, he felt isolated and estranged from the culture, privately confiding that “the air is full of soot, the water life-threatening, the people superficial”; in hindsight he termed the city “semi-barbaric.” Thus when Zangger’s campaign was successful, Einstein immediately accepted the position. He ended up returning to Zurich, with this much-improved status, in July of 1912, barely a year after moving to Prague. His return was made easier by an act of God: the death of his old nemesis, Weber, which he unsentimentally pronounced “a good thing for the Polytechnic.” In the middle of all this professional back-and-forth, Mileva had given birth to his second son, Eduard, in the summer of 1910, notwithstanding which his relationship with his wife continued to deteriorate.

  Throughout all this change, the constant in Einstein’s life was his scientific work, and in particular his focus on what he considered the most important problem of the day, quantum theory. Nernst’s visit to see Einstein in Zurich, and Nernst’s high-profile focus on quantum problems, had finally begun to make the physics community aware of what Einstein had known since 1907: there were really two puzzles of quantum theory. The radiation formula, photoelectric effect, and other similar phenomena suggested that light, conventionally conceived as a wave, came in quantized energy units, hυ, and had particulate properties. At the same time the specific heat theory, now corroborated in its essentials by Nernst’s experiments, pointed strongly to the proposition that molecular mechanics violated Newton’s laws and also involved quantization of energy in units of hυ, at least when the molecular motion was periodic. Since these vibrations could be electrically neutral and thus not interact with light directly, this behavior appeared to be essentially independent of the quantum properties of radiation. Einstein had a major decision to make: which quantum problem would he focus on? He chose the quantum theory of radiation.

  Already in early 1909 Einstein had confided to his idol, Lorentz, that his program was to tinker with Maxwell’s equations in order to generate a theory of light quanta. Lorentz, who undoubtedly had the deepest understanding of electromagnetic theory of his generation, had warned Einstein, “as soon as one makes even the slightest change in Maxwell’s equations, one is faced … with the greatest difficulties.” As he toiled onward through 1909 and 1910, E
instein began to realize that Lorentz was prescient; changing Maxwell’s equations was like touching up the Mona Lisa. Not frivolously had Boltzmann proclaimed of these equations, “was it God that wrote those lines?” The mathematical structure was perfect, and every modification implied a contradiction with the multitude of known electromagnetic phenomena. Einstein was in the midst of these difficult explorations in September of 1909 when he admitted in the conclusion of his Salzburg lecture, “it has not been possible to formulate a mathematical theory of radiation which will do justice both to the undulatory structure and the … quantum structure…. [The] fluctuation properties of radiation [that he had demonstrated in his lecture] … offer few formal clues on which to build a theory.” He boldly prophesied the emergence of a fusion theory of radiation, yet had nothing to show in support but his vague notion of “singularities” attached to an extended field, which he quickly qualified with the statement, “no importance should be attached to such a picture as long as it has not led to an exact theory.”

  In his correspondence throughout the year after Salzburg lecture, Einstein repeatedly alludes to his struggles with radiation theory. On New Year’s Eve of 1909 he writes again to Laub, who was his constant sounding board during this period: “I have not yet arrived at solution to the light quanta question, but I have found quite a few significant things while working at it. I’ll see whether I might not yet succeed in hatching this favorite egg of mine.” In January of 1910 in a letter to Sommerfeld he describes his increasingly radical hypotheses to explain the dual properties of radiation: “maybe the electron is not to be conceived as such a simple structure as we think? There is nothing one would not consider when one is in a predicament.” By July of that year, buoyed by Nernst’s visit, he writes again to Sommerfeld, confident that the two quantum hypotheses (for light and for matter) are correct but allowing that no progress has been made reconciling quanta and waves. He has decided that “[a] crudely materialistic conception of the point structure of radiation … cannot be worked out.” On August 2, to Laub, shortly after being visited by Sommerfeld, he writes: “I have not made any progress regarding the question of the constitution of light. There is something very fundamental at the bottom of it.” Then, again to Laub, in November of 1910, a ray (or wave?) of light: “At the moment I am very hopeful that I will solve the radiation problem, and that I will do so without light quanta. I am awfully curious how the thing will turn out. One would have to give up the energy principle [conservation of energy] in its current form.” Alas, one week later: “The solution of the radiation problem has again come to naught. The devil played a dirty trick on me.”