Einstein and the Quantum (20 page)

Einstein's friend Laub, to whom he announced his appointment, had previously come to visit Einstein and work with him while he was still in Bern, shortly after sending his 1908 letter terming Einstein's situation a “bad joke.” He thus became the first scientist to actually coauthor a paper with Einstein (prior to this Einstein had been the sole author of every one of his works). In fact, although Einstein would collaborate intermittently through his career and he greatly enjoyed discussing physics with colleagues, none of his greatest papers were to have coauthors,
²
and his collaboration with Laub was no exception. They produced together two undistinguished papers on relativity theory, and soon after Laub departed in May of 1908, Einstein set relativity theory aside and devoted himself solely to radiation/quantum theory. During the summer and fall of 1908, while Lorentz was still vacillating between the Rayleigh-Jeans and Planck laws, and the kingpins were wrangling over Nobel prizes in Stockholm, Einstein had digested the profound implications of quantization of energy and was trying to make sense of light quanta.

Already, in January of 1908, Einstein had indicated that his principal concern was not relativity theory but understanding the quantum theory, which he now had shown comprised both radiation (through light quanta) and atomic mechanics (through the quantum law of specific heat). At that time he replied to an inquiry from Arnold Sommerfeld, the other great German theorist of the time (along with Planck). Sommerfeld had succeeded to Boltzmann's chair in theoretical physics in Munich in 1905. He was Prussian through and through, with a large mustache and a bearing that gave the “
impression of a colonel
of the Hussars,” accentuated by a dueling scar on his face acquired as a member of the drinking and fencing society (the
Burschenschaft
) during his student days. Not only was his appearance
intimidating; so also was his intellect, reflecting a mathematical facility rare even among theoretical physicists. His initial reaction to Einstein's work hints at some resistance to a new Jewish “prophet”; in a letter to Lorentz, Sommerfeld wrote: “
we are now all longing
for you to comment on that whole complex of Einstein's treatises. Works of genius though they are, this unconstruable and unvisualizable dogmatism seems to me to contain something almost unhealthy … perhaps it reflects … the abstract-conceptual character of the Semite.” This initial bias dissipated rapidly, however, and soon he would speak of Einstein with great respect and make major contributions to both relativity and quantum theory.

In his January letter replying to Sommerfeld, Einstein seems a bit embarrassed by a previous complimentary letter from him (which is lost) and begins thus: “
Your letter made me uncommonly happy
…. Thanks to my having hit upon the fortunate idea of introducing the relativity principle into physics, you (and others) enormously overestimate my scientific abilities … let me assure you that if I were in Munich … I would sit in on your lectures in order to perfect my knowledge of mathematical physics.” Then Einstein gets to the point. In response to a query from Sommerfeld, he states that relativity theory does not at all provide a definitive theory of electrons: “a physical theory can be satisfactory only when it builds up its structures from
elementary
foundations.” Relativity theory, he says, is like thermodynamics
before
Boltzmann explained what entropy means at the atomic level.

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,
ε
_quant
=
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.”