Einstein and the Quantum (25 page)

Einstein, at least temporarily, had put up a metaphorical sign over the door to the atom: this way lies madness. He admitted as much with a joke he told to a friend and colleague, Philipp Frank, whom he had met during his year in Prague. Frank had quickly been captivated by Einstein's wit and whimsy: “
his sense of humor
was readily apparent … when someone said something funny … the laughter that welled up from the very depth of his being was one of his characteristics which immediately attracted one's attention.” As Frank tells the story, “about that time Einstein began to be much troubled by the paradoxes arising from the dual nature of light
⁶
[wave and particle]…. his state of mind over this problem can be described by this [the following] incident.” Einstein's office in Prague looked over a park, whose patrons had odd characteristics: only women appeared in the morning, only men in the afternoon, sometimes alone and talking to themselves, other times in groups engaged in vehement discussions. The explanation for these patterns turned out to be that the park belonged to the mental asylum of Bohemia, whose less violent patients were allowed its use. Einstein led Frank to his window, and then remarked playfully, “
there are the madmen
who do not occupy themselves with the quantum theory.”

 

¹
The letter from Fischer mentioned only Einstein's “
great theoretical papers in the area of thermodynamics
” and not relativity theory, indicating the input of Nernst.

²
The Zurich Polytechnic had just been raised to the status of a technical university capable of granting doctorates and renamed ETH Zurich.

³
In Newtonian physics the momentum of an object is its mass times its velocity (
p
=
m
v), and would be zero for a massless object.

⁴
The correspondence was actually initiated by a job feeler from Julius's University of Utrecht, which Einstein ultimately received and turned down in favor of ETH Zurich.

⁵
Einsteinian synecdoche: Planck's constant,
h
, stands for the entire quantum conundrum.

⁶
Frank was of course wrong here; Einstein had been concerned about this paradox for at least four years prior to moving to Prague.

CHAPTER 19

A COSMIC INTERLUDE

Scientific endeavors are quite extraordinary
; often nothing is more important than seeing where it is not advisable to expend time and effort…. an instinct must be developed for what is just barely attainable upon the exertion of the utmost effort. [My recent] magnetic experiment, for example, could have been done by any old lout. But general relativity is of another kind. Having actually arrived at this goal gives me the greatest satisfaction of my life, even though up to now not a single colleague in the field has recognized the depth and necessity of this path.

—ALBERT EINSTEIN, MAY 31, 1915

Having decided that a true quantum theory was not yet attainable in 1911, even with his utmost exertion, Einstein devoted himself for the next four years primarily to his new theory of gravity, which arose as a natural generalization of his special theory of relativity and is hence termed the general relativity theory. The inspiration for his first work in this area, the special theory, had come from the properties of electromagnetic waves, arising from Maxwell's equations. Gravity played no role at all in his thinking, and in fact prior to 1907, in contrast to his well-documented interest in atoms, there is no evidence Einstein was particularly interested in gravitational phenomena. Gravitational effects were of primary interest in astronomy, as it is only on the celestial scale that gravitational forces dominate over electromagnetic and nuclear forces. However, Einstein was nothing if not dogged in pursuit of conceptual clarity. Upon enunciation of the principle of relativity, the statement that the laws of physics should
appear the same to all observers in uniform relative motion, he quickly noted that “
the question arises whether this statement
should not also be extended to non-uniform [i.e., accelerated] motion.” When in accelerated motion, you feel forces not present in uniform motion. For example, when you go from zero to sixty in four seconds, you are pressed back in your seat; you cannot say you are standing still and the world around you is accelerating backward, because people outside your car are not pushed forward. The conclusion that you are “really accelerating” and they are not seems unavoidable. Thus it appears that one can at least define absolute acceleration, if not absolute velocity.

However, in 1907, Einstein got the idea that pointed the way to a theory in which
all
motion, even that involving acceleration, is relative—a general theory of relativity. The hint to his idea is contained in a phrase used by the zero-to-sixty crowd: “pulling
g
s.” The force you feel pushing you back in your seat feels sort of like gravity; in fact, if your acceleration were constant and exactly the same as that due to gravity at the earth's surface (9.8 meters per second squared, denoted by the letter
g
), you would “weigh” exactly the same with respect to a scale placed in the back of your seat as you do with a scale standing upright. Einstein surmised that the inertial force experienced during acceleration is completely indistinguishable from the force of gravity. It followed that a general theory of relativity, with no special, privileged states of motion, could perhaps be achieved if it were also combined with a new theory of gravitation. He sketched the earliest, most primitive outline of such a theory in 1907 but did nothing more on it until 1911, as he began to relinquish his single-minded focus on quantum theory and the nature of radiation. For the next four years almost all his original research papers were on the theory of gravitation, and his few works pertaining to atoms and/or quantum phenomena were not of a groundbreaking nature. His final success did not come until November of 1915, six months after his premature declaration of success (quoted above).

This episode in his scientific life was a departure from his earlier modus operandi. Contrary to some depictions, Einstein had been very interested in and aware of experiments in all his previous work; in fact, during this very same year, 1915, he had published his only
experimental paper, an attempt to determine the origin of atomic magnetism in collaboration with Lorentz's son-in-law, Wander J. de Haas.
¹
Moreover, ever since his student days he had not been much excited about higher mathematics, which he dismissed as needless erudition. He wanted to explain nature, not impress his fellow physicists with his mathematical prowess. General relativity changed his outlook. He quickly realized that he would need more sophisticated mathematical tools than previously, and his theory building was not motivated by any puzzling experiments or even community consensus about fundamental questions, but rather by his own conviction that a consistent framework for physical laws must exist in which all motion is relative. The fact that at the end of a herculean struggle he ended up with a beautiful mathematical construction, which also predicted and explained a few observable astronomical phenomena, created a paradigm of supreme theoretical insight for all who followed.

Nothing quite like this had transpired before in natural science. As early as 1919 J. J. Thomson, the British Nobel laureate. pronounced it “
one of the highest achievements
of human thought.” Quantum pioneers and Nobel laureates Paul Dirac and Max Born went one step further: Dirac called general relativity “
probably the greatest scientific discovery
ever made,” and Born pronounced it “
the greatest feat of human thinking
about nature.” Einstein himself was transported by his breakthrough: “
The theory is of incomparable beauty
,” he told his friend Zangger; to Besso he wrote, “
my boldest dreams
have now come true.” The die was cast; henceforth this achievement would overshadow everything he had done or would do in theoretical physics, not just to the public, who went crazy over curved space and bent light rays when news of the theory's confirmation emerged in 1919, but eventually to Einstein himself. His autobiographical notes, written at his seventieth birthday, present a view of his scientific career in which all his earlier work was the prelude to general relativity and all his subsequent work flowed from it. His quantum mania is barely mentioned.

But this is the perspective of a man who knows how the story will turn out: he knows it will end with an atomic theory he cannot fully accept. The Einstein of 1915 was still in hot pursuit of the new “fusion theory,” as he himself had dubbed it, in which light would be both a particle and a wave, and Newtonian mechanics would be replaced by a theory of particle motion that naturally incorporated quantum discontinuity. In February of 1916 he wrote to Sommerfeld, waxing poetic about Sommerfeld's recent theory of atomic spectral lines, which he said had “
enchanted me
. A revelation!” even calling it, a few months later, “
among my finest experiences
in physics.” By the end of May 1916, six months after completing general relativity, he already was presenting new work on an application of quantum theory to physical chemistry, a proof that any chemical reaction that requires the input of light to proceed, absorbs energy in the amount of
hυ
per molecular reaction. By early July of 1916 his next great quantum breakthrough had materialized. He published an initial report that month and was polishing it for a more definitive presentation on August 11, 1916, when he wrote to Besso: “
A brilliant idea has dawned
on me about radiation absorption and emission; it will interest you.” That idea would be the foundation of the modern quantum theory of radiation, the first chapter in every modern textbook on the subject.

The Einstein who wrote those lines was living a very different life from the expatriate professor in Prague who in 1911 had temporarily left quantum theory to the lunatics and raised his intellectual gaze from the atom to the cosmos. Recall that in July of 1912 the newly eminent physicist A. Einstein, father of two young boys and husband of one increasingly unhappy spouse, had returned to Zurich as a full professor of theoretical physics at the Poly, now upgraded in status to the Swiss Federal Institute of Technology (ETH). The Einstein family loved Zurich and had many close friends there, but a variety of forces were conspiring to attract Professor Einstein to a different equilibrium state.

Already, two years before this, the formidable Nernst had begun pulling the levers that would pry Einstein out of Switzerland and into Germany. In this effort he had gained by 1912 a powerful ally in his colleague Fritz Haber, the assimilated German-Jewish chemist who was responsible for the development of the ammonia extraction process,
a process that would be critical to Germany's military strength and, ultimately, to the agricultural revolution of the twentieth century. In April of 1912, even before returning to take up the post at Zurich, Einstein had visited Berlin and spoken with Nernst, Planck, Haber, Rubens, and Warburg; and job possibilities were already being floated. As an intellectual center of the new quantum physics, Berlin outshone not only Zurich but any place else on the planet as well, and this clearly interested Einstein. However, with his famous intellectual independence, he hardly needed to move yet again simply to improve his scientific neighbors. But then two new factors entered the equation.

On that very first trip to Berlin in April of 1912 he renewed his acquaintance with a female cousin, Elsa Einstein, whom he remembered fondly from childhood visits. Elsa, a divorcée, three years his senior with two daughters from her marriage, was Albert's cousin through both her father's and mother's family; but, by the customs of the time, this would not have hindered at all an amorous relationship between the two. Later Elsa would claim that she had fallen in love with Albert when she knew him as a boy because of his beautiful violin playing. She was as comfortable and familiar to Einstein as Mileva had been different and intriguing. Born in the Einstein ancestral home of Hechingen,
²
she shared his Swabian dialect and prized the Swabian value of gemütlichkeit, which narrowly refers to a cozy domestic environment but more generally denotes warmth, good humor, and acceptance. While contemporaries judged her prettier than Mileva, she was not a beauty, but shared Einstein's stocky build and curly hair to the extent that later in life people commented on how much they looked alike. Einstein was drawn to her, it seems, as someone who would understand his needs and take care of him, which in fact is exactly what transpired.

How Elsa and Albert reconnected on that first visit to Berlin in April 1912 is not known in detail, but their reunion had an immediate effect on both. Within days of his return Elsa wrote to Einstein at his work address (to avoid Mileva's surveillance). While Elsa's letters from
the time have not survived, Albert's were lovingly preserved by Elsa, who clearly saw the prospect of a rewarding future life with him. In his reply to her first letter he wrote, “
I can't even begin to tell
you how fond I have become of you during these few days…. I am in seventh heaven when I think of our trip to Wannsee [the forest near Berlin].” In this very first letter he seems already to have fixed his mind on a future romantic relationship, continuing quite boldly, “I have to have someone to love, otherwise life is miserable. And this someone is you; you cannot do anything about it, as I am not asking you for permission.” And, finally, he warns her not to assume that he is unmanly because he defers to Mileva in public: “Let me categorically assure you that I consider myself a full-fledged male. Perhaps I will sometime have the opportunity to prove it to you.”

During the same visit to Berlin at which he kindled the relationship with Elsa, Einstein was courted for a position in the Physikalisch-Technische Reichsanstalt, the laboratory at which many of the fundamental studies on blackbody radiation had been done. However, this position did not materialize and in any case would not have held much attraction for Einstein. In fact he had told Elsa in that first letter that “
the chances of my getting a call
to Berlin are, unfortunately, rather slight.” And, perhaps for this reason, Einstein rapidly backtracked on his overture to Elsa, saying just three weeks later, “
it will not be good
for the two of us as well as for others if we form a closer attachment.” However, his judgment on his prospects in Berlin was overly pessimistic; by July of the next year (1913) Walther Nernst and Max Planck had traveled to Zurich to make him an offer he could not refuse.