Satyendra Nath Bose - Bose–Einstein Statistics

Bose–Einstein Statistics

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 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 paper "Planck's Law and Hypothesis of Light Quanta" into German, and saw to it that it was published in Zeitschrift für Physik under Bose's name, in 1924.

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, as acknowledged by Einstein and Dirac.

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.

Although several Nobel Prizes were awarded for research related to the concepts of the boson, Bose–Einstein statistics and Bose–Einstein condensate—the latest being the 2001 Nobel Prize in Physics given for advancing the theory of Bose–Einstein condensates—Bose himself was not awarded the Nobel Prize.

In his book, The Scientific Edge, the noted physicist Jayant Narlikar observed:

S. N. Bose’s work on particle statistics (c. 1922), which clarified the behaviour of photons (the particles of light in an enclosure) and opened the door to new ideas on statistics of Microsystems that obey the rules of quantum theory, was one of the top ten achievements of 20th century Indian science and could be considered in the Nobel Prize class.

However, when asked about the omission, Bose himself said:

I have got all the recognition I deserve.