In a previous post we examined how the Einsteinian hypothesis that light was made up of quanta of light went from being a mere hypothesis to a fact, especially after Arthur H. Compton’s experiments on the scattering of X-rays. However, the question of how to derive Planck’s formula for black body radiation without the use of Maxwell’s electrodynamics remained unresolved. The theoretical derivation of Planck’s formula that would avoid the use of electromagnetism was still elusive to all physicists at the beginning of the 20th century, including Einstein and Planck. That changed on 2 July 1924. On that day, an article entitled “Planck’s law and the light quanta hypothesis” (Gesetz und Lichtquantenhypothese), signed by an unknown Satyendra Nath Bose from Dhaka, but with a special recommendation from Einstein (who was the translator), arrived in the editorial office of the prestigious German journal Zeitschrift für Physik:
In my opinion, Bose’s deduction of Planck’s formula is an important advance. The method used also provides the quantum theory of the ideal gas as I will develop in detail elsewhere.
But, who was this S.N. Bose?
Satyendra Nath Bose was born in Calcutta on 1 January 1894 into a well-to-do family (his father held a senior position in the Executive Engineering Department of East Indian Railways). In 1909 he started his studies at Presidency Collegue, Calcutta, a very prestigious institution in India where notable personalities had studied since its opening in 1817. There he had superb teachers who introduced him to the main problems of physics at the time. Together with his friend and College fellow Meghnad Saha (later to become a respected astrophysicist) he translated into English a number of important papers on relativity, which were not available in India at the time (and which they published in a monograph in 1922). Bose also published several research papers, some in collaboration with Saha. In 1921 he went to the University of Dhaka, now the capital of present-day Bangladesh, as a lecturer. There he had to teach, among other things, experimental physics. Although he did not publish anything between 1921 and 1924, given his lack of time, what he did was to seriously study the “masters”, as he used to refer to the leading scientists of the time, such as Einstein, Lorentz, Sommerfeld, Planck, among others. From this need to study and understand the ideas of the “greats” in order to transmit them to his students, Bose developed the following motto, which he used to motivate his students:
Never accept an idea if you are not satisfied with its consistency and the logical structure on which the concepts are based. Study the “masters”. These are the ones who have made significant contributions to the subject. Others with less authority cleverly sidestep the difficult points.
Bose applied this motto not only to the way he gave his lectures, but also to his general approach. It was probably this way of thinking and acting that made him famous in the world of physics, because he solved the problem that none of the “masters” could solve: to deduce Planck’s law without using classical electrodynamics. Bose himself told this several years later, in 1970, to the historian of science Jedish Mehra:
I knew Einstein’s derivation of Planck’s formula and that he had never been satisfied with his deduction of it and kept coming back to it. Planck’s conditions contradicted classical ideas. Planck was also aware of the difficulties but was never able to solve them. He had relations obtained from Maxwell’s electromagnetic theory and others in which discontinuities arose. He wanted to reconcile his theory with classical theory. […] As a teacher who had to make these things clear to students I was aware of the conflicts involved and had thought about them. I wanted to know how to deal with the difficulties in my own way. It was not any teacher who asked me to solve this little problem. I wanted to know and this led me to apply statistics.
The miracle unfolded as follows. His friend Saha visited him in Dhaka in March 1924, and Bose told him of his intention to test Planck’s formula without using the classical theory, and thus rid it of its intrinsic contradictions. Saha then brought to his attention certain papers of 1923 published by Pauli, on the one hand, and Einstein and Ehrenfest, on the other. After the discussion with Saha, Bose devoted himself to an in-depth study of the aforementioned works, as well as other no less important works by Debye, Compton (of whom we have already spoken here), among others. In June 1924, Bose had already prepared a paper (it seems that he sent a first version to the Philosophical Magazine, but it was rejected) and it was then that he decided to send it to Einstein because he understood that, in a way, what he had done was a simple continuation of Einstein’s work. The paper was accompanied by the following letter dated 4 June 1924 (and which probably reached its destination a few weeks later):
Respected Sir:
I venture to send you an enclosed article for your knowledge and opinion. I am anxious to know what you think of it. You will see that I have tried to derive the coefficient \(8\pi\nu^2/c^3\) from Planck’s law, independently of classical electrodynamics, assuming only that the ultimate elementary regions of phase space have the content \(h^3\). I don’t know enough German to translate the article. If you think it deserves to be published I would be grateful if you would arrange for its publication in the Zeitschrift für Physik. Although I am a complete stranger to you, I feel no hesitation in making such a request. For we are all your disciples, having benefited from your teachings through your writings. I do not know whether you remember that someone from Calcutta asked you for permission to translate your articles on relativity into English. You accepted the request. The book has since been translated. I was the one who translated your article on general relativity.
Yours
S.N. Bose
That Einstein, surely the world’s most renowned scientist (remember that in 1919 the General Theory of Relativity was “experimentally” confirmed, which made him famous, and in 1921 he was awarded the Nobel Prize) and one of the most famous personalities of the time, had the deference to read an article in English (a language he did not master very well), and that he took the trouble to translate it into German and add to it the note mentioned above (and which undoubtedly ensured its publication) says a lot not only about the relevance of Bose’s result, but also about Einstein’s integrity (at least as a scientist), for, as A. Douglas Stone remarks in his “Einstein and the Quantum: The Quest of the Valiant Swabian”
He [Einstein] was overwhelmed with letters from strangers, wanting his opinion on all sorts of things, while at the same time trying to maintain his voluminous scientific correspondence with the large community of physicists with whom he had personal and professional relations. […] The a priori probability that S.N. Bose’s article would end up in the wastepaper basket, and his work and name lost to posterity, was extremely high.
Bose opened his article by mentioning the different ways of obtaining Planck’s formula with a special mention of the “very elegant way” proposed by Einstein in 1916, and then went on to state:
“In all cases, it seems to me that the demonstrations have not been sufficiently justified from a logical point of view. In contrast to these, the quantum hypothesis of light combined with statistical mechanics (as formulated to meet the needs of quantum theory) seems sufficient for a derivation of the law independently of classical theory. A brief sketch of the method follows”.
From that point on, the article is quite technical. Bose’s basic idea was to consider that light (electromagnetic radiation in general) was made up of independent particles, the quanta of light or photons (as we call them today), and then to discuss in how many different ways these quanta of light could be distributed in a certain number of cells, following Bolzmann’s (and even Planck’s) original ideas of statistical physics. After a series of calculations Bose arrived at the famous Planck formula that we have already discussed in several previous posts.
Einstein, on reading Bose’s article, was surely impressed, for in record time (remember that Bose’s letter to Einstein was dated 4 June, and on 2 July the Zeitschrift für Physik received Bose’s article with Einstein’s recommendation that it be published), he translated it and sent it, as suggested by the unknown Indian professor, to the Zeitschrift für Physik, where it was published in August of the same year [the English and German versions of Bose’s paper can be found in his complete works, which can be downloaded here]. The reason Einstein did so was surely the discovery (probably to his astonishment) that Planck’s formula for black body radiation could indeed be deduced without using any of the classical theories as Planck, or he himself, had unsuccessfully tried to do.
Furthermore, Einstein, as promised in his note at the end of Bose’s article, used the idea proposed by Bose to develop the quantum theory of the ideal gas, which he published the same year (Quantentheorie des einatomigen idealen Gases, Sit.ber Preuss. Akad. Wiss. 1924), which was one of Einstein’s last relevant contributions to science and which undoubtedly proved the relevance of Bose’s ideas.
Apart from translating Bose’s work and ensuring its publication, Einstein sent Bose a postcard (the English translation of which can be found in Einstein’s complete works) dated 2 July 1924 in which he wrote:
I have translated your paper and submitted it to the Zeitschrift für Physik for printing. It constitutes an important advance and I liked it very much. I think, however, that your objections to my paper are not correct. For Wien’s displacement law does not presuppose the use of wave theory, and Bohr’s correspondence principle is not used at all. Nevertheless, that does not matter. You were the first to derive the factor quantum theoretically, even if not entirely strictly due to the polarisation factor 2. It is a fine advance.
With friendly greetings, yours, A. Einstein
That postcard would change Bose’s life. First of all, Bose’s teaching contract at the University of Dhaka was due to expire in a year, and it was far from certain that it would be extended. Moreover, at the beginning of 1924, Bose had applied for a two-year leave of absence to extend his studies outside India, but by the end of June he had not yet received a reply. Bose himself recounts what happened in an interview given to Mehra years later:
“They were going to discuss it [the permit] in the Senate Council [of the University]. Einstein’s postcard was a great help to me. I sent it to the Council. As soon as they showed it to Hartog [the Vice-Chancellor], all the problems were solved. As a student, Hartog had spent some time at the University of Paris and knew what that experience could mean to a young man. That little thing [Einstein’s postcard] gave me a kind of passport to study leave. I was given leave for two years on fairly generous terms. I received a good grant. They also gave an allowance for my family, otherwise I wouldn’t have been able to travel abroad. They also reimbursed my travel expenses. That was very generous. I also got a visa from the German consulate just by showing them Einstein’s card – they didn’t even require me to pay the visa fee!”
That “little thing” allowed Bose to spend a year in France working with Langevine and also in Maurice le Broglie’s laboratory (considered the best physics laboratory in France), and of course to travel to Germany where he was finally able to meet Einstein. Bose’s admiration for Einstein can be summed up in the following opinion written by Bose shortly after Einstein’s death in 1955:
“During the upheavals between the two world wars, Einstein suffered greatly. In 1933 he was forced to leave Berlin and was robbed of all his possessions… His indomitable will never submitted to tyranny and his love of man often induced him to speak unpleasant truths that were sometimes misunderstood. His name would remain indissolubly linked with all the bold achievements of the physical science of this age, and the story of his life was a dazzling example of what can be achieved by pure thought”.
The long-awaited meeting between Bose and Einstein took place at the end of 1925. This is how Bose remembered it 45 years later:
“The meeting was most interesting. He wanted to know how I had managed to prove Planck’s law in that way. Then he challenged me. He wanted to know if my hypothesis, that particular statistic, really brought something new about the interaction of quanta and if I could develop the details.”
In that order it is curious that Bose never boasted of having solved a problem that had defeated the most famous physicists of his time. This is what he told Mehra in 1970:
“I had no idea that what I had done was really new. I thought maybe it was the way of looking at things. I wasn’t an expert in statistics to the extent that I knew whether what I was doing was really something different from what Boltzmann would have done, something different from Boltzmann’s statistics. […] In a way, that was the same question that Einstein asked me when we met: how had I arrived at this method of deducing Planck’s formula? Well, I recognised the contradictions in Planck’s and Einstein’s attempts, and I applied the statistics in my own way, but I didn’t think it was different from Boltzmann’s statistics”.
Although Bose, for various reasons, never managed to solve the problems suggested by Einstein, his stay in Germany was very profitable for him because, as he himself says, thanks to Einstein’s support all doors were opened and he was able to meet many of the great German scientists of the time. In fact, he had several conversations with Einstein on various topical subjects (in particular on Hilbert’s well-known paper on the theory of general relativity published in 1924, or Heisenberg’s famous 1925 paper laying the foundations of quantum mechanics).
In 1926, at the end of his stay in Berlin, Bose received a letter from his friends in Dhaka advising him to apply for a professorship in Dhaka and, since he did not have a PhD, suggesting that he ask Einstein for a letter of recommendation. Einstein was surprised, as he felt that Bose’s scientific merits were more than sufficient for such a position, but he agreed and wrote the letter. However, the seat was offered to Debendra Mohan Bose (who was not related to our Satyendra Nath Bose) but he declined and it was finally given to (Satyendra) Bose, who became Professor at the University of Dhaka and Head of the Department of Physics in 1927.
On his return to Dhaka, Bose was immersed in the daily routine of teaching, supervising students and administration (paperwork). Perhaps this is why he never again focused on a specific research problem, but jumped from one to another. Bose himself confessed this to Mehra:
“On my return to India I wrote some articles. I did some more on statistics and then again on the theory of relativity, a kind of a mixture, a potpourri. They were not so important. I wasn’t really in science any more. I had been like a comet, a comet that came once and never came back.“
Satyendra Nath Bose died at the age of 80 in Calcutta. He received many honours during his lifetime and his mark on physics will remain forever thanks not only to his “small” contribution in 1924 that was such a surprise to Einstein and laid the foundations of what is now called Bose-Einstein statistics, but also to the work of many physicists motivated by it, which led to the discovery of a new state of matter: the Bose-Einstein condensate (synthesised for the first time in 1995).
Whatever else one may think about Bose’s life and work, the best summary of it can be found in the concluding paragraph of the biography written by Mehra in 1975:
S.N. Bose had the opportunity to make an important discovery and write a four-page paper about it, and that discovery had far-reaching consequences in modern physics. This is often more than enough for one man in the History of Science.
Learn more:
Jagdish Mehra, Satyendra Nath Bose, 1 January 1894 – 4 February 1974, Biographical Memoirs of Fellows of the Royal Society, 21, 1971
Luis Navarro Veguillas, Satyendranath Bose: Un cometa fugaz. Arbor, CLIII (1996), pp. 45-65.
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