The untold story of Satyendra Nath Bose and Albert Einstein statistics Research Paper

While presenting a lecture at the University of Dhaka on the theory of radiation and the ultraviolet catastrophe, Bose intended to show his students that the contemporary theory was inadequate, because it predicted results not in accordance with experimental results. In the process of describing this discrepancy, Bose for the first time took the position that the Maxwell–Boltzmann distribution would not be true for microscopic particles, where fluctuations due to Heisenberg's uncertainty principle will be significant. Thus he stressed the probability of finding particles in the phase space, each state having volume h3, and discarding the distinct position and momentum of the particles. Bose adapted this lecture into a short article called "Planck's Law and the Hypothesis of Light Quanta" and sent it to Albert Einstein with the following letter.

While presenting a lecture at the University of Dhaka on the theory of radiation and the ultraviolet catastrophe, Bose intended to show his students that the contemporary theory was inadequate, because it predicted results not in accordance with experimental results.

In the process of describing this discrepancy, Bose for the first time took the position that the Maxwell–Boltzmann distribution would not be true for microscopic particles, where fluctuations due to Heisenberg's uncertainty principle will be significant.

Thus he stressed the probability of finding particles in the phase space, each state having volume h3, and discarding the distinct position and momentum of the particles.

Bose adapted this lecture into a short article called "Planck's Law and the Hypothesis of Light Quanta" and sent it to Albert Einstein with the following letter:

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 8π ν2/c3 in Planck's Law independent of classical electrodynamics, only assuming that the ultimate elementary region in the phase-space has the content h3. I do not know sufficient German to translate the paper. If you think the paper is worth publication I shall be grateful if you arrange for its publication in Zeitschrift für 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. I do not know whether you still remember that somebody from Calcutta asked your permission to translate your papers on Relativity in English. You acceded to the request. The book has since been published. I was the one who translated your paper on Generalised Relativity.

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 8π ν2/c3 in Planck's Law independent of classical electrodynamics, only assuming that the ultimate elementary region in the phase-space has the content h3.

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 für 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.

I do not know whether you still remember that somebody from Calcutta asked your permission to translate your papers on Relativity in English. You acceded to the request. The book has since been published. I was the one who translated your paper on Generalised Relativity.

Einstein agreed with him, translated Bose's papers "Planck's Law and Hypothesis of Light Quanta" into German, and had it published in Zeitschrift für Physik under Bose's name, in 1924.    

Possible outcomes of flipping two coins Two heads Two tails One of each (1) There are three outcomes. What is the probability of producing two heads? Outcome probabilities   Coin 1 Head Tail Coin 2 Head HH HT Tail TH TT

(2) Since the coins are distinct, there are two outcomes which produce a head and a tail. The probability of two heads is one-quarter.

The reason Bose's interpretation produced accurate results was that since photons are indistinguishable from each other, one cannot treat any two photons having equal energy as being two distinct identifiable photons. By analogy if, in an alternate universe, coins were to behave like photons and other bosons, the probability of producing two heads would indeed be one-third (tail-head = head-tail).

Bose's interpretation is now called Bose-Einstein statistics. This result derived by Bose laid the foundation of quantum statistics, and especially the revolutionary new philosophical conception of the indistinguishability of particles, as acknowledged by Einstein and Dirac.

When Einstein met Bose face-to-face, he asked him whether he had been aware that he had invented a new type of statistics, and he very candidly said that no, he wasn't that familiar with Boltzmann's statistics and didn't realize that he was doing the calculations differently. He was equally candid with anyone who asked.    

Bose–Einstein condensate

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Zweig Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose–Einstein condensate. Left: just before the appearance of a Bose–Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate. Einstein also did not at first realize how radical Bose's departure was, and in his first paper after Bose, he was guided, like Bose, by the fact that the new method gave the right answer.

But after Einstein's second paper using Bose's method in which Einstein predicted the Bose-Einstein condensate (pictured left), he started to realize just how radical it was, and he compared it to wave/particle duality, saying that some particles didn't behave exactly like particles. Bose had already submitted his article to the British Journal Philosophical Magazine, which rejected it before he sent it to Einstein.

It is not known why it was rejected. Einstein adopted the idea and extended it to atoms. This led to the prediction of the existence of phenomena which became known as Bose–Einstein condensate, a dense collection of bosons (which are particles with integer spin, named after Bose), which was demonstrated to exist by experiment in 1995.