Einstein and the Quantum (33 page)

The many distractions associated with his fame were compounded when, in June of 1922, right-wing extremists assassinated Walter Rathenau, the German foreign minister. Rathenau, the first Jew to
hold that post, was a personal friend of Einstein's, and not only did his loss shake Einstein's equanimity, but in its aftermath multiple threats were received to his own life. He hid out in the country, sheltered by a rich friend, Hermann Anschütz, and even toyed briefly with quitting physics research and working as an engineer, with “
a downright normal human existence
” and the “welcome chance of practical work.” This fanciful notion vanished in a few days, but he avoided the German physics meeting in Leipzig, bitterly disappointing the twenty-one-year-old Werner Heisenberg, who attended with the hope of meeting him.
³
In a letter to Solovine, his longtime friend and “Olympia Academy” alumnus, Einstein recounted: “
I am constantly being warned
, I have given up my lecture course and am officially absent although I am really here. Anti-semitism is very strong.” He felt it was fortunate that he had “
the opportunity of a prolonged absence
from Germany,” as he had committed himself to an extended lecturing trip to Japan and points east in October of 1922.

However, an unexpected wrinkle developed in his plans when he was informed by Svante Arrhenius, who still ruled the Physics Committee for the Nobel Prize, that “
it will probably be very desirable
for you to come to Stockholm in December, and if you are in Japan that will be impossible.” The Nobel committee had finally been moved to award the most famous scientist since Newton its stamp of approval. Characteristically, Einstein was not disposed to dance to the tune of the establishment, particularly for an institution that had passed him over for so long; despite Arrhenius's hints that Einstein's absence might put the final vote in doubt, he replied that he was “
quite unable to postpone
the journey.” So off he went to Japan by ship, on schedule, receiving news of his award somewhere en route on an unknown date, as he failed to even note the event with an entry in his travel diary. Nonetheless, the citation on the award surprised many:
“for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.” The Nobel committee had found relativity theory too uncertain and controversial for recognition but instead came to rest on the one work by Einstein that he himself considered “revolutionary.”

While there was much irony in this development, in fact the citation was carefully crafted to recognize the
empirical
law of the photoelectric effect, and not the underlying theory. This law had already been confirmed in great detail by the American physicist Robert Millikan by 1916, and by many other experiments subsequently, so it could no longer be doubted. Millikan himself wrung his hands at his own results, saying “
I spent ten years
of my life testing that 1905 equation of Einstein and, contrary to all my expectations, I was compelled to assert its unambiguous experimental verification in spite of its unreasonableness, since it seemed to violate everything we knew about the interference of light.” The Nobel citation said nothing about quanta of light, a concept that was still rejected by the overwhelming majority of physicists. In fact Bohr, despite his deep admiration for Einstein, could not resist a rather biting joke at Einstein's expense, saying that if he received a telegram from Einstein confirming the existence of light quanta, he would point out that the telegram itself, transmitted by electromagnetic waves, was proof against them.

Einstein did not return to Germany until the spring of 1923, and he went to collect his Nobel Prize in the summer. By this time he was involved in a different scientific quest, his famous attempt to unify the gravitational and electromagnetic forces by means of a “unified field theory.” However, he was very hopeful that such a theory would itself point the way to the solution of the quantum problem, even submitting a paper along those lines to the Prussian Academy in December of that year. In 1924, in a radio address, he informed the public, who only wanted to hear about relativity theory, that he was really focused on something else:

The other great problem
that I have been concerned with since about 1900 is that of radiation and the quantum theory. Stimulated by the work of
Wien and Planck, I recognized that mechanics and electrodynamics were in irresolvable contradiction with experimental facts, and so I have helped in creating the complex of ideas known by the name of quantum theory, which has been developed so fruitfully particularly by Bohr. I shall probably devote the rest of my life to the fundamental clarification of this problem, however slight the prospects are for attaining the goal may be.

In fact the goal was now rather close, although it would not take the form Einstein hoped, and he was about to make his final historic contribution to reaching it.

 

¹
This was often later misquoted as
the
highest achievement.

²
It is notable that Einstein, despite having become the paradigm of the pure theorist to the public, was still quite willing to contemplate actually setting up and performing such an experiment himself.

³
Sommerfeld, with whom Heisenberg was studying, had promised to introduce him to Einstein, who had been Heisenberg's idol from his high school days. Heisenberg was appalled to find an anti-Semitic leaflet attacking Einstein thrust into his hand as he entered the hall where von Laue was delivering the lecture on Einstein's behalf.

CHAPTER 24

THE INDIAN COMET

Respected Sir:

I have ventured
to send you the accompanying article for your perusal and opinion. I am anxious to know what you think of it. You will see that I have tried to deduce the coefficient 8
πυ
²
/
c
³
in Planck's Law independent of the classical electrodynamics, only assuming that the ultimate elementary region in the phase-space has the content
h
³
.

This letter to Einstein from an unknown Indian scientist, received in early June, 1924, initiated one of the most extraordinary episodes in the modern history of science, culminating in Einstein's final historic contribution to the structure of the new quantum theory. At the time of his writing, Satyendra Nath Bose was a thirty-year-old Reader (roughly equivalent to the rank of associate professor) at Dacca University in East Bengal. His previous five research papers had made no impact at all on contemporary research, and he had recently been informed that, due to a funding cutoff to the university, his appointment would not be extended more than a year. Moreover, the paper he was sending to Einstein had already been submitted for publication, and rejected, by the English journal
Philosophical Magazine
. He had admired Einstein for many years and had even produced a rather undistinguished translation of Einstein's papers on general relativity into English, for distribution in India. Thus, through some combination of veneration and chutzpah, he hit upon the idea of sending this paper, which related closely to Einstein's 1916 work on radiation theory, directly to the master, with an astonishing request:

I do not know sufficient German
to translate the paper. If you think the paper worth publication, I shall be grateful if you arrange for its publication in Zeitschrift fur Physik. Though a complete stranger to you, I do not feel any hesitation in making such a request. Because we are all your pupils though profiting only by your teachings through your writings.

Yours faithfully, S. N. Bose.

Einstein by that time, as we have seen, was not just the most famous scientist of his time; he was one of the best-known individuals on the entire planet. He was deluged by letters from strangers, wanting his opinion on everything under the sun, while at the same time struggling to keep up his voluminous scientific correspondence with the large community of physicists with whom he had personal and professional relations. In addition, Einstein spoke very little English and had not been able to deliver his prestigious lectures in England during his visit in 1921 in the native tongue of his audience.
¹
The a priori probability that S. N. Bose's paper would end up in the circular file, his work and his name lost to posterity, was extremely high.

But that is not what happened. Einstein read the paper shortly after its arrival, translated it, and sent it to the German journal
Zeitschrift für Physik
on July 2, 1924, with his strong endorsement. There it was subsequently published, with a note from Einstein appended. “
In my opinion Bose's derivation
of the Planck formula signifies an important advance. The method used also yields the quantum theory of the ideal gas, as I will work out in detail elsewhere.” In fact, shortly thereafter Einstein translated a
second
paper, which he had received from Bose on the heels of the first one and which he sent on to the journal by July 7, 1924. This one did not elicit such a favorable opinion from the great man, and he published a critical comment along with it, while nonetheless supporting its publication.

With these magnanimous gestures from the sage, the die was cast. Bose would go on to become one of the most famous names in the history of modern physics. The term “boson” is used for one of the two fundamental categories of elementary particles in modern physics
²
because such particles obey novel statistical laws first employed, although not announced, in Bose's initial paper sent to Einstein. This category includes Einstein's photons (light quanta) as well as roughly half of the atoms in the periodic table. But Bose's discovery, like that of Planck twenty-four years earlier, was not as clear-cut as it has been portrayed, and again it would take Einstein to find the radical implications in it.

S. N. Bose was born into the rising middle class of English-educated Indians in 1894 in Calcutta. He father, an accountant, had a wide range of intellectual interests that he transmitted to his son, who, in addition to his great aptitude for mathematics, became deeply interested in poetry, music, and diverse languages. When he matriculated at the Presidency College in Calcutta in 1909, however, he chose to study science, at least partly because of its potential utility to the future Indian nation, as a wave of nationalism swept through his generation. His cohort was “
a particularly brilliant lot
—the famous 1909 batch of Presidency College … [which] in all its history has not seen the likes … since.” Bose completed his BSc in 1913 and MSc in 1915, taking first place in both examinations; but there was no obvious avenue for obtaining a doctorate, and the professorial ranks were still reserved for third-rate English academics at that time. Bose therefore went through a period as a striving outsider, not dissimilar to the career of Einstein at the same age.

He married early (prior to graduation) but, contrary to custom, refused to accept a dowry or other financial support from his wife's family. Already responsible for a wife and son shortly after he received his MSc, he spent a year eking out a living through private tutoring, while trying to work toward a PhD in mathematics with a well-known
professor, Ganesh Prasad. Prasad was noted for his aggressive criticism of prospective students and of their previous teachers, which typically cowed the candidates into silence. But Bose was “
notorious for plain speaking
.” In an echo of Einstein's conflicts with authority figures such as Weber, Bose “dared to counter his adverse criticisms” and was summarily dismissed from consideration for PhD work with the comment, “
you may have done well in the examination
, but that does not mean you are cut [out] for research.” “
Disappointed, I came away
[and] decided to work on my own,” Bose recalled.

Like Einstein, he was turned down for low-level teaching jobs before being offered an entry-level lectureship in the new University College of Science in Calcutta, whose founder, Sir Asutosh Mookerjee, began hiring the cream of young Indian scientists, including the future Nobel laureate C. V. Raman. It was at the College of Science that Bose first began to learn about the exciting developments in physics in Europe associated with the names of Planck, Einstein, and Bohr. Here also he and his close friend, the physicist Meghnad Saha, obtained and translated important German works of physics, including Einstein's papers on relativity theory.

In 1921 Bose accepted a faculty position at the new University of Dacca, in East Bengal, recently established by an ambitious vice-chancellor, P. J. Hartog. At Dacca he “
spent many sleepless nights
” trying to understand the Planck law, while at the same time teaching it to his students. He felt an obligation to present something to them that he himself found clear and consistent: “
As a teacher
who had to make these things clear to his students I was aware of the conflicts involved…. I wanted to know how to grapple with the difficulty in my own way….
I wanted to know
.” In late 1923 he hit upon his new approach to deriving the law and sent off a manuscript to the
Philosophical Magazine
, where he had previously published papers on quantum theory, only to receive the reply, in the spring of 1924, that the referee's decision had been negative. It was at this point that Bose took the bold step of sending the paper to Einstein, a strategy so speculative that its success appeared to violate the very principle of maximum entropy employed in the paper itself!

It was remarkable, but nonetheless true, that Planck's blackbody formula remained somewhat mysterious a full twenty-four years after Planck's initial derivation. It was not that anyone doubted any longer the validity of the formula, but the tortured reasoning Planck had used to derive it left physicists unsatisfied for decades. That is why Bose's paper, titled “Planck's Law and the Quantum Hypothesis.” was of interest to Einstein and others. As we saw earlier, Planck had been reluctant to treat radiation directly with statistical mechanics, and instead, using classical reasoning, he related the mean energy of radiation at a given frequency to the mean energy of idealized vibrating molecules (“resonators”). He then calculated the entropy of these resonators by introducing into the counting of states his quantized energy “trick.” A key factor in totaling up the number of allowed states in Planck's method, which was not appreciated for quite some time, was that one could treat the units of energy belonging to each resonator as indistinguishable quantities (i.e., if resonator one had seven units of energy
hυ
and resonator two had nine units, one didn't have to ask
which
units they were). In 1912 Peter Debye, an outstanding young theorist and future Nobel laureate, rederived the Planck law, not by counting resonator states, but by counting states of classical electromagnetic waves that could fit in the blackbody cavity and then ascribing to them the same average energy that Planck had assigned to each resonator. The counting of the number of allowable
waves
in the cavity led to the factor in the Planck radiation formula, 8
πυ
²
/
c
³
, to which Bose alludes in his letter to Einstein. This factor was very easy to find from classical wave physics but very hard to find from quantum principles, hence Bose's emphasis on having found a quantum route to it.