Einstein and the Quantum (22 page)

But this cannot be the only effect of the radiation, because if it were, the mirror would be continually taking energy out of the gas through the molecules' collisions with the mirror and effectively transferring it to radiation, hence heating up the radiation, something we know from experience does not occur. The resolution of this paradox is that the radiation, besides it average tendency to slow down the plate, has the same kind of irregular fluctuations in its interaction with the plate as do the gas molecules, transferring back to the plate as much energy as it is receiving on average. It is easiest to imagine this force as arising from the random arrival of unequal numbers of light quanta on each side of the plate, just as the force due to the gas arises from collisions with unequal numbers of molecules on either side. It looks like another argument for light quanta is about to emerge. But this is not where Einstein is heading. Assuming that the Planck law is correct, Einstein can calculate the fluctuating force of radiation, and to the surprise of the crowd
³
he obtains
two
contributions to the force. The first is indeed just what one would expect from “molecules” of light with energy
hυ
(and momentum
hυ
/
c
, where
c
is the speed of light) hitting each side of the mirror randomly. But the second term is precisely what Maxwell would have expected, fluctuations in radiation pressure arising from complicated
interference
between light
waves
moving in both directions.
⁴
There you have it: the magician has removed the screen to show that the lady he has just sawed in half is in fact whole again. Wavelike
and particle-like effects
coexist in the same formula
, a formula that follows simply from the existence of equilibrium between matter and radiation, and the undeniable validity of Planck's radiation law.

Einstein concludes by sketching his “singularity” picture for a new theory of radiation, while admitting “
it has not yet been possible
to formulate a mathematical theory of radiation that would do justice to the undulatory structure and … quantum structure [of radiation]…. All I wanted is briefly to indicate … that the two structural properties (undulatory and quantum) simultaneously displayed by radiation … should not be considered as mutually exclusive.”

Planck, as chairman, rose to moderate the discussion of Einstein's paper. One can imagine a hush of expectation: how would the great man respond to this radical proposal concerning the nature of light, from the physicist whose work on relativity Planck had promoted and lauded so widely. A hint emerges as Planck thanks the audience for “
listening with greatest interest
… even where opposition may have emerged.” He continues, “Most of what the lecturer has been saying will not meet with any disagreement. I too emphasize the necessity of introducing certain quanta … the question is where to look for those quanta. According to … Mr. Einstein, it would be necessary to conceive … [of] light waves themselves as atomistically constituted, and hence to give up Maxwell's equations. This seems to me a step which in my opinion is not yet necessary…. I think that first of all one should attempt to transfer the whole problem of the quantum theory to the area of the interaction between matter and radiation.” The voice of conservative reason has been heard; we are not ready for photons, and certainly not for wave-particle duality.

Much later a young physicist who was in the audience, Paul Epstein, was questioned as to the persuasiveness of Einstein's Salzburg lecture. “
It had no [great effect]
,” Epstein replied. “You see the chairman of the meeting was Planck, and he immediately said that it was very interesting but he did not quite agree with it. And the only man who seconded it was Johannes Stark. You see, it was much too far advanced.”

 

¹
A year later Einstein gave a blunt analysis of one such squabble in a letter to Laub: “
The quarrel between Stark and Sommerfeld
is unedifying. Stark has once again produced unadulterated rubbish … nothing sensible ever comes out of a quarrel.”

²
This random momentum should correspond to an average kinetic energy of motion
kT
/2 due to the equipartition theorem; the mirror is assumed macroscopic so that the quantum effects, which violate equipartition, can be neglected.

³
Fritz Reiche, a young physicist in the audience, recalls: “I was very much impressed by the second term in the fluctuation formula…. I remember of course that people were opposed and tried to find another reason.”

⁴
Einstein interprets this term as due to Maxwell waves but doesn't derive it from Maxwell's equations; shortly afterward Lorentz himself filled in this step.

CHAPTER 17

THE IMPORTANCE OF BEING NERNST

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].”

—WALTHER NERNST, MARCH 1910

Although in Salzburg it was clear to observers such as Max Born that “
Einstein's achievement received its seal
[of approval] before the assembled world of scientists,” the achievement most recognized was his theory of relativity, which by then had been well confirmed by the fast-electron experiments of Alfred Bucherer in Bonn. As just noted, Einstein's quantum hypotheses were regarded by all the leaders present in Salzburg as perhaps inventive, but certainly rash and premature. This impression was possibly facilitated by Einstein's decision not to mention in his lecture his lesser-known work on the specific heat of solids. This work, showing that Planck's distribution law of thermal radiation could also be applied to electrically neutral vibrations of atoms, clearly indicated the necessity of a non-Newtonian atomic mechanics, as opposed to treating Planck's “energy element” as some anomaly associated only with the interaction of radiation and matter, as Planck had suggested. But there was one leader, not present at Salzburg, who
was
keenly aware of Einstein's work on specific heat, and to whom it was a very big deal. His name was Walther Nernst.

Nernst was a physical chemist, like Arrhenius, and indeed the two met in their twenties while Arrhenius was studying in Germany in 1886 and became fast friends, as well as boisterous drinking companions. Arrhenius pronounced Nernst's work on heat conduction “
the best that any laboratory practitioner
has done in a long time” and got him invited to work with his patron, Ostwald, in Leipzig. Like Arrhenius, Nernst was not much to look at. He was short of stature with a “
fishlike mouth
” and had a distinctive, high-pitched voice that was often employed in claiming priority for some idea or other, which he typically insisted had already appeared in his famous textbook on physical chemistry. When, in the early 1900s, Nernst became well known in Berlin society, a joke circulated about a superman whose brain God had created but whose body had been left to lesser craftsmen. The disappointing result was then brought to life by the Devil for amusement; you can guess the name of this golem.

Nernst himself had a distinctive form of sarcastic humor, which he expressed with a completely deadpan delivery. For example, surrounded by avid hikers including Planck, who climbed mountains well into his seventies, he would opine that he too had climbed a mountain once in his youth, and that would suffice for a lifetime. He was indeed a talented scientist; Einstein praised “
his truly amazing scientific instinct
combined both with a sovereign knowledge of an enormous volume of factual materials … and with a rare mastery of the experimental methods and tricks in which he excelled.” Despite what Einstein called his “childlike vanity,” he was, according to Nernst trainee Robert Millikan, “in the main, popular in the laboratory, despite the fact that in the academic world he nearly always had a quarrel on with somebody.” Millikan recounts that in 1912 he wrote a review chapter for Nernst's famous textbook, dealing with the determination of the electric charge,
e
(the topic on which Millikan would eventually do Nobel-winning research). Nernst initially accepted the draft, but after Jean Perrin, a well-known French physicist and eventual Nobel laureate himself, annoyed Nernst at a conference, he demanded that Millikan expunge every mention of the man's name from the chapter. Perrin's offense was speaking too long in the lecture before Nernst was scheduled to speak, hence
depriving Nernst of some of his allotted time. Such a combination of determination, charisma, and pettiness was Walther Nernst.

These qualities conspired to make Nernst one of the most successful scientific “operators” of the twentieth century, a person capable of convincing officials in government and industry of the importance of scientific work in general, and of his own contributions in particular. Soon these attributes would have a great influence on Einstein's career and on the development of quantum theory. Nernst's political savvy showed itself early in his career. At age twenty-four, in 1888, he developed an idea, originally due to the chemist van ‘t Hoff, into an important relation now known as the Nernst equation, which allows the useful energy of a chemical reaction to be estimated from electrochemical measurements, and he quickly parlayed this into an academic position at Göttingen. By 1895 he had procured a full professorship and his own physical chemistry institute there, obtained under the threat of leaving for a position in Munich. Around that time he began working on one of the key technological problems of the era: cheap, durable electric lighting. In fact electric lighting provided a primary motivation for the momentous research program on blackbody radiation by Rubens, Kurlbaum, and others that was reaching fruition at almost the same time.

By 1897 Nernst had developed and patented the “Nernst lamp,” based on a heated cerium oxide glass rod, which was superior in a number of ways to the incandescent metal filament bulb pioneered by Edison and others. Understanding that the development of the market for lighting was unpredictable, Nernst refused to accept royalties for his invention, which was licensed by the German firm AEG, instead insisting on a large lump sum payment up front. As perhaps Nernst had foreseen, his lamp shone brightly for a few years, magnificently lighting the German pavilion at the Paris Exhibition of 1900 and selling over four million units in the next decade, but eventually losing out to the less-expensive tungsten filament technology perfected by a former Nernst student, the chemist Irving Langmuir. Long before this denouement Nernst had visited Edison in American in 1898, and after being subjected to a lecture on the irrelevance of academic work
by the aging inventor, he shouted into Edison's ear trumpet, “
How much did you get
for your light-bulb patent?” Upon Edison's reply that he got nothing, Nernst bellowed, “I got a million marks
¹
for mine! The trouble with you Edison is that you are not a good businessman!”

Because of his negotiating acumen, the commercial failure of his lamp was of little consequence;
²
Nernst was now a wealthy man and a figure to be reckoned with in German society. In 1905 he accepted a professorship at the center of German science, the University of Berlin, where he became a close associate of Planck, whose earlier thermodynamic work had put the Nernst equation on a more sound theoretical footing. His distinguished colleague in Berlin, the organic chemist Emil Fischer, who already had receive the Nobel Prize in 1902, described him approvingly as “
versatile, many-faceted
, full of curiosity and enterprise.” His students referred to him jokingly as the
Kommerzienrat
, German for a successful businessman (in contrast to the usual
Geheimrat
, denoting a distinguished scholar). Even before moving, he had been decorated by the emperor and appointed privy councillor, and upon his arrival he was immediately admitted to the prestigious Prussian Academy of Sciences.

Around this time he made the most important scientific discovery of his life, a principle that is now known as the Third Law of thermodynamics. This principle, in modern terms, is expressed by the statement that the entropy of any system tends to zero as its temperature tends to absolute zero. Unlike the other two laws of thermodynamics, which don't require quantum effects to make sense, this law is all about quantum “freezing.” According to Boltzmann, a system's entropy depends on the number of its accessible states at a given temperature.
We already have seen from Einstein's work on vibrations in solids that when a solid gets very cold the atoms cannot vibrate, because they don't have enough thermal energy to reach even the first excited quantum level, which is
hυ
higher in energy than the lowest (ground) state. In other words the system tends toward a single, unique ground state, and the entropy, by definition, is zero. Nernst's law says this always happens for any system, no matter how complicated.

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).