Einstein and the Quantum (18 page)

Arrhenius, like all his contemporaries, was blissfully unaware of the looming crisis in atomic physics, uncovered by the work of the young Einstein, who was now becoming known—not for challenging the Newtonian paradigm of continuous motion but instead for dismissing another Newtonian axiom, the concept of absolute time. While Einstein had quickly moved to the terra incognita of the nascent quantum theory,
assuming
that atoms existed and trying to figure out their laws of motion and their interactions with radiation, Arrhenius was still fighting the last war, the war to prove that atoms were real. The ensuing episode illustrated just how oblivious the scientific community was to the gathering storm.

Had Arrhenius known the story of the checkered career of the German/Swiss Jew, who was still not recognized formally by the conservative professoriate of Switzerland in 1908, he likely would have recognized a kindred spirit. Arrhenius grew up near Uppsala, Sweden, where his father was a surveyor for the University of Uppsala, the oldest and among the most prestigious of the Nordic universities. A science and math prodigy, he had matriculated at the university at age seventeen, and received his degree in two years, before moving on to graduate studies in physics. However, in a striking parallel to Einstein, he alienated the senior members of the faculty, Tobias Thalen (physics) and Per Theodor Cleve (chemistry), and left after three years to complete his doctorate at the new Physical Institute of the Academy of Sciences in Stockholm. Unfortunately for Arrhenius the new institute was not yet allowed to grant PhDs on its own. Thus when, in 1884, he produced a monumental 150-page work on the conductivity of electrolytic solutions, explaining, for example, the high conductivity of salt in water by its dissociation into ions, it was received with great skepticism by a committee consisting mainly of faculty whom he had spurned at Uppsala. In the end the thesis was approved with the lowest possible passing grade,
non sine laude approbatur
, (“accepted, not without praise”). Forty years later Arrhenius would recount bitterly that Cleve and Thalen even refused to offer him the customary congratulations after the doctoral ceremony, saying that they had decided to “
sacrifice him
.” Although this work and its extensions would
eventually earn him the Nobel Prize, the grade it had received was so poor that he was at least nominally disqualified from pursuing an academic career in Sweden at the time.

Here, however, his story diverges from that of Einstein, for he boldly sent the devalued thesis to the leading lights of European chemistry and physics, Clausius (inventor of the concept of entropy), van ‘t Hoff in Amsterdam (who would be the first Nobel Laureate in Chemistry), and Ostwald in Riga (the ninth Nobel chemistry laureate). One of these men, Ostwald, immediately recognized its innovativeness, to the extent that he even traveled personally to Uppsala to offer Arrhenius a job at his own institution.
¹
Arrhenius did not cut a particularly impressive figure, according to Ostwald: “
[Arrhenius] is somewhat corpulent
with a red face and a short mustache, short hair; he reminds me more of a student of agriculture than a theoretical chemist with unusual ideas.” But a brilliant chemist he was, and eventually Arrhenius did move to Europe and trained with Ostwald, van ‘t Hoff, and even with Boltzmann before returning to Sweden to become the unquestioned leader of Swedish physical chemistry, and the person who defined the international scope of the Nobel prizes at their inception.

A decade later, at the turn of the century, there was still a major movement in chemistry and physics that regarded atoms as somewhat suspect heuristic entities, a movement led by Arrhenius's former mentor, Wilhelm Ostwald. This school of thought was known as “energetics” and also had adherents in the Swedish physics community, which maintained an attitude of distrust toward theory in general and of “
pronounced hostility toward atomism
and toward atomic theory” in particular. Arrhenius had decided to put this movement to final rest and make 1908 the Nobel Year of the Atom. Max Planck would receive the physics prize for the manner in which his radiation law had led to an accurate determination of Avogadro's number and
the elementary unit of atomic charge,
e
. The chemistry prize would be awarded to the British physicist Ernest Rutherford, who had shown that atoms disintegrated (i.e., emitted doubly ionized helium atoms, known as alpha particles) during radioactive decay. In a very recent experiment with Geiger, Rutherford had deduced a value of the elementary charge from alpha particles in excellent agreement with that calculated by Planck using his radiation law, tying the two prizes neatly together.

The fact that Rutherford considered himself a physicist and would be very surprised to know that he had been reclassified a chemist
²
did not deter Arrhenius from his plan. Arrhenius had nominated Rutherford for
both
the physics and chemistry prizes that year, but it is likely that he had planned all along to support Planck in the Physics Committee, of which he was a member. By the time of the crucial meeting on September 18, 1908, he knew that the Chemistry Committee (based on an internal report he had apparently ghostwritten) was committed to awarding the prize to Rutherford. Planck and Wien had been jointly nominated in physics for the theory of heat radiation by Ivar Fredholm, a Swedish mathematician and mathematical physicist, and Arrhenius swung his support to this nomination, but with the intention of splitting the ticket and engineering a prize for Planck alone.

Why did Arrhenius think that Planck alone should be recognized? Because at that time Arrhenius was not interested in the physical principles behind the law of thermal radiation
³
so much as in its connection to the fundamental constants in molecular chemistry. This is an aspect of Planck's work of 1900 that is barely mentioned in modern times, but at that time it overshadowed his radical quantum hypothesis.
Planck's radiation law depended on the two newly discovered physical constants that he introduced,
h
, the “quantum of action” (Planck's constant), and
k
, Boltzmann's constant (the constant associated with entropy through the equation
S
=
k
log
W
and thermal energy through the equipartition relation
E
_mol
=
kT
.) From a careful fit of blackbody radiation data one can extract quite precise values for both
h
and
k
, and Planck did so immediately after deriving his radiation law in 1900. The constant
h
appeared to him completely enigmatic and was not put to any immediate use, but the constant
k
, which only later became known as Boltzmann's constant,
⁴
was instantly recognized as providing a theoretical microscope for studying the atom.

In his December 1900 magnum opus Planck states, “
To conclude, I may point to
an important consequence of this theory which at the same time makes possible a further test of its reliability.” He goes on to show by straightforward steps that the Boltzmann constant satisfies the simple relationship
k
=
R
/
N
_a
, where
R
is the constant in the ideal gas law
PV
=
RT
for a mole of gas, and
N
_a
is Avogadro's number (which has struck fear into so many beginning chemistry students), the number of atoms contained in a mole of any gas. This number was imperfectly known in 1900, whereas
R
was very well known. Hence by extracting
k
very precisely from the radiation law, Avogadro's number could be determined to unprecedented precision. Planck found the value
N
_a
= 6.175 × 10
²³
, which is within 2.5 percent of the currently accepted value 6.022 × 10
²³
. Using the same information, he could determine the mass of a hydrogen atom, again with high accuracy. Finally, in a coup that must have impressed the physical chemist, he used considerations from electrolytic chemistry, Arrhenius's own field, to find the elementary charge on a proton, obtaining a value within 2.5 percent of the modern value. In contrast the best-known value of
e
, the charge on an electron, measured by J. J. Thomson from electron studies, was off by 35 percent! Planck concluded his 1900 analysis with the confident declaration, “
If the theory is at all correct
, all of these
relations should not be approximately, but absolutely valid. The accuracy of the calculations … is thus much better than all determinations up to now.”

Planck had always been fascinated by fundamental constants as expressions of the absolute and eternal in physics. Even before his work of 1900 he had realized that the radiation law involved two distinct and new fundamental constants. Fundamental constants allow one to define what are called
absolute units
, units of measurement relating to the basic laws of physics. For example, the speed of light,
c
, provides a natural unit of velocity, because no signal can travel faster than
c
and all relativistic phenomena become more and more important as this speed is approached. In the famous twin paradox of special relativity, your identical twin ages more and more slowly compared with you as her relative velocity approaches
c
. Planck pointed out that his two newly discovered constants, when combined with the speed of light and the gravitational constant, would allow fundamental units to be defined for
all
physical quantities (length, time, temperature, etc.). Transported by this revelation, the staid professor allowed his inner geek to emerge in print, rhapsodizing that these units would be valid for “all times and civilizations … even extraterrestrial ones.” Later, when Planck became embroiled in a philosophical debate with the Viennese philosopher-scientist Ernst Mach, Mach would lampoon his exuberance over fundamental units: “
concern for a physics
valid for all times and all peoples, including Martians, seems to me very premature and even almost comic.”

Nonetheless in 1900 it was these fundamental constants, which had emerged from his radiation law, that most excited Planck, and not his unexamined introduction of discontinuity into the laws of physics. To his disappointment, the rest of the physics community did not immediately appreciate even this aspect of his breakthrough. He later recounted:

I could derive some satisfaction
from these results. But matters were viewed quite differently by other physicists. Such a calculation of an elementary electrical [charge] from measurements of thermal radiation was
not even given serious consideration in some quarters. But I did not allow myself to become disturbed by such a lack of confidence in my constant
k
. Nevertheless, I only became completely certain on learning that Ernest Rutherford had obtained a [very similar] value by counting alpha particles.

This spectacular agreement between completely disparate physical phenomena, all pointing to a single consistent atomic picture of the world, had convinced Arrhenius that Planck alone should be recognized with the physics Nobel Prize in 1908. It was the connection to fundamental constants that distinguished Planck's work from Wien's in Arrhenius's mind, and in his report to the Nobel Physics Committee he barely mentioned Planck's derivation of the radiation law and completely omitted any mention of “quanta of energy.” Planck's use of the constant
k
, he said, had “
made it extremely plausible
that the view that matter consists of molecules and atoms is correct…. No doubt this is the most important offspring of Planck's magnificent work.”

Arrhenius's enthusiasm did not sweep through the conservative Physics Committee unchallenged. Among its members was the distinguished experimentalist Knut Angström, who had actually done experiments on heat radiation and was aware of the experimental prehistory leading up to Planck's “act of desperation.” With much justice he wrote, “
it is very far from being
that the theoretical works have guided the experimental ones, but rather that one could justly make a completely contrary statement.” However, there was a small problem with his argument that an experimenter should receive or share the prize: none had been nominated that year. Angström and the other skeptics on the Physics Committee were reluctantly convinced by Arrhenius to join the Planck bandwagon.

And so the modest, upright Planck (who had himself nominated Rutherford for the physics prize that year) might have received this honor, not because of a deep appreciation of the true significance of his work, elucidated by Einstein from 1905 to 1907, but rather because of a general
ignorance
of its full implications. After the Physics Section of the Swedish Academy had approved Planck as the awardee, rumors of the result quickly traveled around the continent, apparently
reaching Planck himself, who stated to the press, “
[if true] I presume
that I owe this honor principally to my works in the area of heat radiation.” But the full Swedish Academy would still have to approve the recommendation of the Physics Committee, and in the interim between these votes something had changed the mood in Stockholm. The most famous theoretical physicist of his generation, the man Einstein admired the most, had finally spoken publicly on the Planck law, and his opinion would derail Arrhenius's well-laid plans.

Hendrik Antoon Lorentz was born on July 18, 1853, in Arnhem, the Netherlands, to an unexceptional middle-class family. His extraordinary brilliance was recognized early, and by the age of twenty-four he was appointed to the newly created Chair of Theoretical Physics at the University of Leiden. He devoted his early years to the application and extension of Maxwell's theory of radiation. In particular, while J. J. Thomson is credited with “discovering the electron” in 1897, Lorentz
deduced
its existence a year earlier, in 1896, from his analysis of light emitted from a gas in the presence of a magnetic field—the “Zeeman effect,” discovered by his former student and assistant Pieter Zeeman. He shared the Nobel Prize in Physics with Zeeman in 1902 for this work (the first theorist to be so honored) and went on to develop an elegant theory of the interaction of electrons with light, published in 1904. In related work, Lorentz came to the very edge of the special theory of relativity, coming up short only by his unwillingness to interpret relativistic effects as arising from the relative nature of time, as did Einstein in 1905. In fact Lorentz was troubled by Einstein's approach, complaining, “
Einstein simply postulates
what we have deduced with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field.” Despite these misgivings, within a few years Lorentz became Einstein's close confidant and scientific father figure, supporting and providing constructive criticism for all his major research.