Einstein and the Quantum (21 page)

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
ε
_quant
=
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.”

When Einstein stepped to the podium on the afternoon of September 21 there were over a hundred colleagues in attendance, including Planck, who chaired the session, Wien, Rubens (the blackbody experimenter), and Sommerfeld, as well as younger physicists who would become friendly with Einstein, such as Max von Laue, Max Born, Fritz Reiche, and Paul Epstein. Planck apparently expected him to review the now–accepted relativity theory, but he had chosen a title consonant with his current interests, “On the Development of Our Views concerning the Nature and Constitution of Radiation.” He begins his lecture in familiar territory: “
Once it has been recognized
that light exhibits the phenomenon of interference … it seemed hardly doubtful … that light is to be conceived as wave motion.” This wave motion
seems to require an ether in which to propagate, he notes, quoting an authoritative text that designates the existence of the ether as a “near certainty” (we have seen that both Lorentz and Planck are still using the ether concept). But Einstein is having none of it: “However, today we must regard the ether hypothesis as an obsolete standpoint.”

Having rudely dismissed the central dogma of electromagnetic theory for forty years, he says it is “undeniable” that certain properties of light suggest a particulate nature. Then, the bombshell:

It is therefore my opinion that the next stage
in the development of theoretical physics will bring us a theory of light that can be understood as a kind of fusion of the wave and emission [particle] theories of light. To give reasons for this opinion and to show that a profound change in our views on the nature and constitution of light is imperative is the purpose of the following remarks.

These remarks are prescient; exactly such a “fusion” theory of light would arise, but it would take almost sixteen years for its earliest forms to emerge, and no other physicist would share Einstein's vision of the future of physics for almost as long.

Having already nailed his revolutionary thesis to the church door, Einstein proceeds with the sermon. He briefly reviews how relativity theory has made the ether superfluous and has suggested that light is an independent entity, not a disturbance in a medium. However, he makes it clear that relativity theory does not itself require light quanta. “
Regarding our conception of the structure of light
… the theory of relativity does not change anything. It is nevertheless my opinion … that we are at the threshold of highly significant developments…. What I shall say is … the result of considerations that have not yet been sufficiently checked by others. If I nonetheless present these considerations, this should not be attributed to excessive confidence in my views but rather to the hope that I may induce one or another among you to concern himself with the problem in question.”

He then goes on to review the many processes, such as the photoelectric effect, that seem to depend on the frequency of light and not
on its intensity, an elaboration of the same considerations that began in his 1905 paper. This leads him to Planck's derivation of the black-body law and the mysterious “energy element,” where he again minces no words: “
to accept Planck's theory
means plainly to reject the foundations of our [classical] radiation theory.” But Planck's theory, he points out, has just been verified yet again by the measurements of Rutherford and Geiger on the value of the elementary charge (the event on which Arrhenius had based his Nobel nomination of Planck a year earlier). Since we cannot reject the Planck law, we must interpret it through quanta of light.

In a Socratic flourish, Einstein then puts on the brakes. “
Isn't it conceivable
that Planck's formula is correct, but that nevertheless a derivation of it can be given that is not based on an assumption as horrendous-looking…?” His answer to the imagined conservative (who could well have been Planck himself) is a resounding negative. He has a trick up his sleeve, an argument that for the first time does not tend to prove that light is a particle or to prove that light is a wave. He has an argument to prove it is both.

His argument is based on another of his ingenious thought experiments. He imagines a cavity that contains a perfect gas at temperature
T
and, necessarily, thermal radiation, distributed in frequency according to Planck's law, in equilibrium with that gas (i.e., having the same temperature). In this blackbody cavity is suspended a perfectly reflecting mirror on a rail that can thus move freely in the direction perpendicular to its surface. This mirror is in contact with the gas, and it will suffer collisions with gas molecules at irregular intervals, causing it to move randomly to the left or right.
²
But the mirror also experiences another force, which is due to the pressure of the thermal radiation reflecting off each of its surfaces. This force of radiation pressure is not a quantum effect and had been known since the time of Maxwell; it is responsible for the tail on comets (as hypothesized by none other than
Arrhenius). In the context of Einstein's mirror experiment it has an interesting property: “
The forces of pressure exerted
on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the [front surface] than on the back surface. The backward-acting force of pressure … is thus larger than the force of pressure acting on the back surface,” leading the plate to experience “radiation friction” opposing its motion.