Wikimedia Commons 40 OPTICS & PHOTONICS NEWS APRIL 2013 Satyendra Nath Bose and Bose-Einstein Statistics Barry R. Masters Satyendra Nath Bose is an often overlooked hero in the field of particle physics and quantum statistics. ver since researchers found evidence for the existence of the Higgs boson in 2012, the particle has made frequent appearances in scientific and E mainstream media. Many people recognize Peter Higgs—one half of the particle’s namesake, but fewer realize that the “boson” half of the moniker refers to Indian physicist Satyendra Nath Bose. Although not as well known as his contemporaries, S.N. Bose was arguably one of the most important scientists of the 20th century. His revolutionary way of viewing photon behavior and photon statistics—later known as Bose statistics—changed the field in a dramatic way. Albert Einstein played an integral role in publishing his work and also extended Bose’s new statistics to atoms and predicted the Bose- Einstein condensate (BEC). Wikimedia Commons APRIL 2013 OPTICS & PHOTONICS NEWS 41 1047-6938/13/04/40/8-$15.00 ©OSA In 1918, Bose and Meghnad Saha published a joint paper on the kinetic theory of gases in the prestigious English journal, Philosophical Magazine. Several years ago, with the support of an the lectures and laboratory demonstrations of OSA Fellow Travel Award (OPN, May 2004), his physics teacher Jagadish Chandra Bose, who I lectured in the various Indian Institutes of developed novel instruments to produce and Technology and the two Bose Institutes in detect millimeter waves. On his final examina- Calcutta, one of which was named after S.N. tions, Bose achieved the highest ranking among Bose (the second was named after Jagadish the B.Sc. students and repeated this feat on his Chandra Bose). The trip inspired me to take a M.Sc. examinations. closer look at his work and his life. This article In 1914, at the age of 20 and while still an honors the seminal work of Bose, his statistics M.Sc. student, Bose married Ushabati Ghosh, and the BEC. the 11-year-old daughter of a prominent physician in Calcutta. Of their nine children, Early life and education two died in infancy; the surviving children Bose was born on 1 January 1894 in Calcutta, consisted of five daughters and two sons. the capital of British India. At the age of five, he enrolled in the Normal School in North Early professional life Calcutta and completed his final years of pri- In 1917, Bose became a lecturer in physics and mary education at the Hindu School in Cal- applied mathematics at the University College cutta. When he was eight, Bose demonstrated of Science, Calcutta University. In 1918, Bose extraordinary intellect and mathematical and Meghnad Saha published a joint paper on talent. He attributed to his upbringing his the kinetic theory of gases in the prestigious urbane, liberal and open-minded character; English journal, Philosophical Magazine. his deep curiosity and love of the arts; and Subsequently they translated Einstein’s his perfectionism. papers into English so that Indian students Following his studies at the Hindu School, who did not know German could read them. Bose studied at the Presidency College in This work, The Principle of Relativity, which Calcutta from 1909 to 1915. Although he contained papers by Einstein and Hermann suffered from weak vision, he loved to read; Minkowski, was published in 1919 by Cal- his favorite poets were Tagore and Tennyson. cutta University. His motivation to study science was similar to Bose worked at the University of Dhaka in that of many of his fellow students: The process East Bengal from its founding in 1921 to 1924. of science could facilitate the advancement of His initial post was as a reader (pre-profes- development and prosperity in his country. sorial position) in the physics department. “We wanted to put scientific knowledge to use He taught courses on thermodynamics and through technology for the benefit of the people electromagnetic theory to the M.Sc. students. or to contribute to science by intensive study,” For Bose, Dhaka was isolated from the Euro- Bose said. pean centers and thus many of the modern Presidency College was the best place to developments in relativity theory and quantum study science in Calcutta, and the competition theory. But his colleague saved him from seclu- to get in was intense; about 2,000 applicants sion. Debendra Mohan Bose returned from competed for 32 slots. Bose overcame the odds his doctoral studies in Germany in 1919 and and earned himself a spot. He was impressed gave Bose a wonderful gift: Max Planck’s book with his science teachers and especially with Thermodynamik und Wärmestrahlung. 42 OPTICS & PHOTONICS NEWS APRIL 2013 Bose’s 1924 publications Statistical Mechanics Bose read Planck’s papers on the distribution of Prior to Bose’s Statistics energy in blackbody radiation in order to teach this material to his class. He was disturbed by 1877 Planck’s derivation of the law with its ad hoc Ludwig Boltzmann develops a method of assumptions. In 1924, Saha stayed with Bose calculating probability by counting states in Dhaka and pointed out the 1923 papers of and applied it to an ideal gas at equilibrium; he found the equilibrium state, which is the Wolfgang Pauli, Einstein and Paul Ehrenfest most probable state, is given by the Maxwell- Boltzmann and their relation to Einstein’s 1917 paper. Boltzmann distribution. This led him to develop Bose statistics—a new method to count states of indistinguishable 1900 particles—and applied it to his derivation of Max Planck builds upon Boltzmann’s prior Planck’s radiation law. work that related entropy and probability Bose wrote two papers in which he inde- and develops the Boltzmann principle or pendently derived and further developed the equation: S = klnW, where S is entropy, k is Boltzmann’s constant, and W is the probability previous work of Planck: “Planck’s law and the of a distribution of elements into cells. Planck light-quantum hypothesis,” and “Thermal equi- published his law of blackbody radiation based Planck librium in the radiation fi eld in the presence of on Maxwell’s classical electromagnetic theory and the ad hoc assumption that the energy « of the oscillators or matter.” He considered the papers as a single resonators was quantized. Some years later, Planck accepted that unit and submitted them to the Philosophical it was not possible to derive his law only from Maxwell’s electro- Magazine. He did not receive a reply from the magnetic theory and Maxwell-Boltzmann statistics. prestigious English journal; therefore, on 4 June 1924, he sent the fi rst paper to Einstein, along 1905 with a letter: Albert Einstein analyzes the energy fluc- “If you think the paper worth publication, tuations of radiation that obeyed Wien’s law and concludes that the radiation consists I shall be grateful if you arrange for its of particles of discrete light-quanta with publication in Zeitschrift für Physik. energy, « = hn, where h is Planck’s constant Though a complete stranger to you, I do and n is the frequency of the oscillator. Einstein not feel any hesitation in making such a request. Because we are all your pupils 1910 though profi ting only by your teachings Peter Debye publishes his derivation of through your writings.” Planck’s law; instead of following Planck, who The two had corresponded before, when used the classical relation between energy density of the blackbody radiation and the av- Bose had asked Einstein if he could translate erage energy of a resonator, Debye calculates his paper on generalized relatively into English. the probability of a given state of the radiation (Einstein acceded.) Bose’s fi rst paper stated that, using the state without invoking resonators. Debye in the thermal equilibrium of massless par- ticles (photons), the number of particles are not conserved due to the absorption and emission 1911, 1914 of photons. These particles could be described From a historical perspective, the little- known work of Ladislas in a new way—with Bose statistics, which Natanson is significant. used the counting of cells in one-particle phase He shows that both Planck space instead of the previous method of totaling and Debye have made the the number of standing waves in a cavity in tacit assumption of the in- distinguishability of quanta Onnes order to obtain the number of states. in their derivations. Both Only one year before, Arthur Compton Paul Ehrenfest and Kamerlingh Onnes had published his seminal paper on the reach the same conclusion. Ehrenfest Compton effect. Bose interpreted Z, the Wikimedia commons APRIL 2013 OPTICS & PHOTONICS NEWS 43 S.N. Bose number of states in the frequency interval logical fl aws. He stated that Einstein’s 1917 viewing a between n and n + dn as the number of cells derivation used “Wien’s law based on classical photo of Albert Einstein that contain a given number of photons with theory and the Bohr correspondence principle, (1953). frequency n, and not the number of particles, which assumes that the quantum theory agrees AIP Emilio Segre as was previously done by Boltzmann. with the classical theory in certain limiting Visual Archives, Gift of cases.” Bose went on to say that “a new form of Kameshwar Wali and On 14 June, he sent Einstein his second Etienne Eisenmann paper: statistical mechanics is required to be compat- ible with quantum theory; these logical fl aws “I hope my fi rst paper has reached your can be solved by using statistical mechanics hands. The result to which I have arrived without any assumption of mechanism of seems rather important (to me at any rate).