I believe that we are still far from having satisfactory elementary foundations for electrical and mechanical processes. I have come to this pessimistic view mainly as a result of endless, vain efforts to interpret the second universal constant [h] in Planck’s radiation law in an intuitive way. I even seriously doubt that it will be possible to maintain the general validity of Maxwell’s equations for empty space [italics added].
A year later, in January 1909, Einstein put this radical idea into print in a paper titled, “On the Present Status of the Radiation Problem,” which followed papers of similar focus from Lorentz, Jeans, and Walter Ritz.3 After some preliminaries he again states the fundamental contradiction they were all facing, “There can be no doubt … that our current theoretical views inevitably lead to the law propounded by Mr. Jeans. However we can consider it … equally well established that this formula is not compatible with the facts. Why, after all, do solids emit light only above a fixed, rather sharply defined temperature? Why are ultraviolet rays not swarming everywhere…?” After showing again how quantization of energy leads to Planck’s law, he states, “Though every physicist must rejoice that Mr. Planck disregarded [the requirements of classical statistical mechanics] in such a fortunate manner, it should not be forgotten that the Planck radiation formula is incompatible with the theoretical foundation from which Mr. Planck started out.”4
Einstein then presents a new and subtle argument (which will be described below) for why the Planck formula tells us that light has both particulate and wave properties simultaneously. He concludes, “In my opinion, the last … considerations conclusively show that the constitution of radiation must be different from what we currently believe”; therefore “the fundamental [Maxwell] equation of optics will have to be replaced by an equation in which the [charge of the electron] e … also appears.” After describing some constraints he believes that this new equation must satisfy, he concludes, “I have not yet succeeded in finding a system of equations fulfilling these conditions which would have looked to me suitable for the construction of the elementary electrical quantum and the light quanta. The variety of possibilities does not seem so great, however, for one to shrink from this task.”
Einstein was now focused on finding the “elementary” theory that he expected would underlie both electromagnetic and atomic phenomena, the theory that would put solid walls on the framework of relativity theory, which on its own could go no further in explaining reality at the molecular scale. He communicated his new mindset to Laub in June of 1909: “I am ceaselessly concerned with the constitution of radiation…. This quantum question is so important and difficult that everyone should be working on it.”
1 Sadly, this thesis, which would have provided a window into his thinking at a fascinating moment, has been lost.
2 Much later in his career (after 1925) Einstein consistently worked with collaborators but failed to produce papers of historic significance, with one exception. In 1935 he published with Boris Podolsky and Nathan Rosen a profound work, intended as a critique, pointing out the nonlocal nature of quantum mechanics (“the EPR paradox”). In fact this feature of the theory has been experimentally confirmed and plays a key role in the important and growing field of quantum information physics.
3 Ritz was a promising young Swiss physicist whom the Zurich search committee had actually preferred to Einstein, even after Adler withdrew. Ironically Kleiner had described Ritz, not Einstein, as “an exceptional talent, bordering on genius.” Ritz was denied the position only because he was terminally ill with tuberculosis, which was to claim his life by July of 1909.
4 This frank statement elicited a request from Planck that Einstein make it clear that Planck himself was aware of this problem, which Einstein did in a rather awkward addendum to the paper.
CHAPTER 16
CREATIVE FUSION
“I am very sorry if I have caused you distress by my careless behavior. I answered the congratulatory card your wife sent me on the occasion of my appointment too heartily and thereby reawakened the old affection we had for each other. But this was not done with impure intentions. The behavior of your wife, for whom I have the greatest respect, was totally honorable. It was wrong of my wife—and excusable only on account of extreme jealousy—to behave—without my knowledge—the way she did.” In June of 1909, Einstein sent this apology to someone he had never met, George Meyer, who happened to be the husband of Anna Meyer-Schmid, a woman with whom Einstein had flirted on vacation more than a decade earlier. Anna had read in a newspaper of Einstein’s appointment as professor in Zurich and had sent him a congratulatory postcard. He had responded with a warmth that certainly could have been misconstrued (or indeed correctly construed): “Your postcard made me immeasurably happy. I … cherish the memory of the lovely weeks that I was allowed to spend near you…. [I] am sure that you have become as exquisite and cheerful a woman today as you were a lovely young girl in those days…. If you are ever in Zurich and have time, look me up … it would give me great pleasure.”
Up to this point Einstein’s relationship with his wife had not entered his correspondence in any problematic fashion, and indeed he described her as a dutiful and supportive wife and mother. This was beginning to change. Einstein was becoming well known, if not yet famous beyond the cognoscenti, and as attention and accolades came his way, he began to perceive Maric as a brooding, negative, and jealous figure. The incident just recounted suggests that there are likely two sides to this story. Einstein’s reply to Anna elicited a letter from her that apparently had similar overtones and that somehow came to Maric’s attention. She then wrote directly to Anna’s husband, rather pathetically claiming that Anna’s “inappropriate” letter had outraged Einstein, leading finally to Einstein’s apologetic follow-up with its harsh characterization of his own wife’s behavior. From Mileva’s viewpoint, success had disrupted the harmony of their Bohemian household. “With that kind of fame, he does not have much time left for his wife,” she wrote to a friend; and later, “I am very happy for his success, because he really does deserve it…. I only hope that fame does not exert a detrimental influence on his human side.” In fact Einstein maintained his geniality, modesty, and sense of humor through all his successes, but he did not seem to regard loyalty and attentiveness to a succession of female companions as part of his moral code. Over the next four years Einstein’s relationship with Mileva would deteriorate further, leading ultimately to separation and a drawn-out divorce.
Einstein’s elevation from the patent office to the status of a university professor, a position of enormous respect in Swiss society, was indeed almost unprecedented. A colleague who was present when Einstein submitted his resignation as technical expert second class recounts that his superior refused to believe that he was leaving to become a professor at Zurich, yelling at him roughly, “That’s not true, Herr Einstein. I just don’t believe it. It’s a very poor joke!” But despite his new prestige, Einstein hardly became a typical Herr Professor of the Weber variety. He lectured quite informally, encouraging his students to interrupt and ask questions, and routinely invited them to further discussions at the Terasse, a café nearby, or even at his home (where he would brew the coffee himself). His students very much appreciated this style, which, despite a certain degree of disorganization, showed his personal concern for them. And by this point he had become quite a good teacher, although he was very surprised at how much time this took from his own research. By November of 1909 he was already confiding in Besso that “my lectures keep me very busy so that my actual free time is less than in Bern.” This tension between the personal pedagogical relationships, which he enjoyed, and his overriding drive to confront the mysteries at the frontiers of science ultimately would lead him to escape from mandatory teaching when the opportunity presented itself. He never found anything as satisfying as sitting at his desk with a pad of paper serving as window into the universe. And in 1909 nothing was more puzzling and obscure in that window than the “shape
” of radiation and quanta.
His January 1909 paper on the current status of the radiation problem, responding as it did to that of Lorentz and others, gave Einstein a natural opening to initiate a scientific correspondence with the man he most admired. At the end of March 1909 he wrote to Lorentz:
I am sending you a short paper on radiation theory, which is the trifling result of years of reflection. I have not been able to work my way through to a real understanding of the matter. But I am sending you the paper all the same, and even ask you to take a quick look at it, for the following reason. The paper contains several arguments from which it seems to me to follow that not only molecular mechanics, but also Maxwell-Lorentz’s electrodynamics cannot be brought into agreement with the radiation formula…. I cherish the hope that you can find the right way.
A couple of weeks later he followed up with an almost obsequious note praising the “beauty” of Lorentz’s derivation of the Jeans law in his Rome lecture and saying that reading it was “a real event.” Given Einstein’s unshakable insistence that the Jeans law was the only possible outcome of classical reasoning (stated repeatedly since 1905 and reiterated in his most recent paper), one has to wonder if for once he was engaging in a bit of flattery. At any rate he was rewarded a month later with a lengthy reply from Lorentz, with such detailed scientific arguments that Einstein opined “it is a pity” that this “clear and beautiful exposition … will not be read by all of those who are working in this matter.”
Lorentz begins by pointing out that the Planck energy quantization rule, εquant = hυ, makes no sense when it is applied to electrons instead of molecules. Molecules at that point were known to be combinations of atoms bound together, which naturally vibrate when they interact with light; in contrast, electrons in solids are often moving freely as in a gas, and “their existence [free electrons] in metals can hardly be denied.” Because of this free, nonperiodic motion, “there can be no question of a definite frequency υ, and thus an energy element hυ.” Thus the quantum of action, h, is not a property of matter in general, but more plausibly one should “[ascribe] to the ether, and not to [matter,] the property that energy can be taken up and given off only in definite quanta.”
Note that Lorentz continues to speak of electromagnetic fields as sustained by the ether, the notion Einstein hoped to banish with relativity theory; and he even puts in a mild dig at Einstein and the relativists: “If one regards h as a constant of the ether, one then deprives this medium of part of its simplicity, and directly opposes the views of those physicists who want to deny to ether almost all ‘substantiality.’ ” He then zeros in on the notion of “pointlike” energy packets of light, Einstein’s light quanta. Interference of light waves is observed to occur over millions of oscillations, corresponding to light moving a distance of almost a meter—thus he concludes that this is the minimum length of the hypothetical quanta. By a similar argument relating to the focusing of light through a telescope objective, he argues that their width would also have to be macroscopic. “The individuality of each single light quantum would be out of the question,” he concludes, wrapping up with the meager consolation, “it is a real pity that the light quantum hypothesis encounters such serious difficulties, [as it] is very pretty, and many of the applications that you and Stark have made of it are very enticing.”
Finally, Lorentz throws cold water on Einstein’s suggestion that perhaps a modification of Maxwell’s equations will explain all these conundrums: “as soon as one makes even the slightest change in Maxwell’s equations, one is faced, I believe, with the greatest difficulties.” Having rejected all of Einstein’s new ideas in the most supportive and gentle tone possible, he finishes with, “permit me to say how glad I am that the problems of radiation theory have given me a chance to enter into a personal relationship with you, after having admired your papers for such a long time.”
FIGURE 16.1. Einstein with Hendrik Lorentz circa 1918. Museum Boerhaave Leiden.
Einstein seems to have been so pleased to be noticed by the great man that he was hardly fazed by Lorentz’s dismissal of his ideas. Shortly after receiving the reply, he wrote to Laub in starstruck tones: “I am presently carrying on an extremely interesting correspondence with H. A. Lorentz on the radiation problem. I admire this man like no other; I might say, I love him.” But this love would not deter him at all from his project, which was to change Maxwell’s equations so as to encompass light quanta in some form. In the same letter he continues, “My work on light quanta is proceeding at a slow pace. I believe I am on the right track…. But I haven’t yet gotten far.”
On May 23, 1909, he wrote back to Lorentz an almost equally long and technical letter explaining his program. He is of course “delighted” with Lorentz’s detailed letter, which should be read by the whole community; but he then points out that Lorentz’s argument that electrons lack a definite frequency of motion is moot. Since we don’t know yet the new basic laws of molecular mechanics and electromagnetism, there can be no contradiction with Planck’s law, only “the difficulty of generalizing Planck’s approach.” Einstein has correctly perceived that quantum theory is going to be a general mechanical theory, one implication of which is εquant = hυ for Planck’s oscillators, but that some different relation will apply to free electrons. He then goes on to describe the general sort of theory of light quanta that he hopes to develop. In this theory light is neither a particle nor a wave; instead it consists of pointlike objects that carry an extended field along with them, and this field is essentially the conventional electromagnetic field. The pointlike objects are “singularities” in the field, where it becomes infinite, similar to the manner in which the electric field becomes infinite near a single-point electric charge. Every time light is absorbed, one of these pointlike objects disappears and deposits energy hυ, where υ is the frequency of the light field. We see here the contrast between the flexible thinking of Einstein and the more rigid views of the aging master, Lorentz, who is wedded to the old categories of physics. While in mathematical detail Einstein’s conception is not very close to our modern theory, it is the first, albeit groping, attempt to introduce mathematical objects into physics that are simultaneously particulate and wavelike, a foundation stone in the conceptual structure of modern quantum theory.
Einstein concludes his reply to Lorentz with, “I consider it a great blessing to be able to enter into a closer relationship with you.” Here the surviving correspondence with Lorentz from this period ends.
Einstein’s exhilaration in the exchange with Lorentz appears to be that of a chess master playing at such a high level that he was delighted to have finally found an opponent who could “give him a game,” someone against whom he could test his mettle. But Lorentz could not shake Einstein’s conviction that wave and particle properties of light coexist and that a new electrical and mechanical theory would provide a synthesis of these old categories. At this time Einstein was the only scientist on the planet to perceive this need. Of the few who understood both Planck’s derivation of the radiation law and Einstein’s 1905 work, almost all rejected the notion that the blackbody law implied some form of light quantum. Lorentz and Planck, the two most knowledgeable actors, now agreed that “energy elements … play a certain role in the laws of thermal radiation” but also that the notion of physically localized quanta should be rejected.
Johannes Stark, the one established physicist to champion the idea of light quanta at the time, seems to have regarded quanta and wave theory as irreconcilable. Stark, a talented experimenter who would win the Nobel Prize in 1919, was a difficult man who tried to compete in theory beyond his level of competence and became embroiled in disputes with others about the validity of his theories and about scientific priority.1 However, in April of 1907 it was he who had offered Einstein his first paid academic job, as an assistant in his lab, which Einstein declined for financial reasons (it paid much less than the patent job). And it was Stark who invited Einstein to do the important review
article on relativity theory in which the principle of equivalence was first announced. Ironically, this first reputable supporter of Einstein’s quantum ideas would become, many years later, a leader, with Philip Lenard, of the Nazi movement against “Jewish physics.” All this was in the distant future in July of 1909, when Einstein wrote to his ally, Stark, relating that Planck “stubbornly opposes material (localized) quanta.” “You cannot imagine,” he continues, “how hard I have tried to contrive a satisfactory mathematical formulation of the quantum theory. But I have not succeeded thus far.” Despite his frustration, he is “[looking] forward to making [Stark’s] acquaintance in Salzburg.”
In fact, at that time, Albert Einstein, the paradigm-shattering conjurer of modern physics, still had not met a single one of the leading physicists of Europe, not Planck, nor Lorentz, nor Sommerfeld, nor Wien (all of whom had corresponded with him). That was about to change. Once a year, since 1822, the physicists of the German-speaking countries assembled in a different city at a major convention of more than 1,300 scientists and physicians, the Deutsche Gesellschaft der Naturforscher und Arzte. In 1908 the assembly had convened in Cologne, and Einstein had planned to attend, but exhaustion prevented him from using his meager vacation time from the patent office for this trip. He had been a star in absentia; it was at that meeting that the mathematician Minkowski had added four-dimensional frills to Einstein’s relativity theory and announced the “union” of space and time into a single space-time continuum. But finally, in 1909, with the meeting to be held in Salzburg, Einstein had been invited (probably by Planck) to give a plenary lecture; the new messiah would finally be seen and heard by the congregation and make the acquaintance of the elder prophets. Wolfgang Pauli, who would lead the next generation of quantum theorists, termed this event “one of the turning points in the evolution of theoretical physics.”
Einstein and the Quantum Page 15