# Bose, Satyendranath

# BOSE, SATYENDRANATH

(*b*. Calcutta. India. I January 1894; *d.* Calcutta, 4 February 1974)

*physics.*

Bose was the son of Surendranath Bose, an accountant in the executive engineering department of the East India Railways, who later was a founder of the Indian Chemical and Pharmaceutical Works. His mother was Amodini Raichaudhuri. The family were members of the Kayastha caste. Bose began his primary education in the local English-language schools. The upsurge of Bengali nationalism that followed Lord Curzon’s decision to divide the province of Bengal into two administrative units, however, convinced his father to send him to a Bengali-language secondary school in 1907. Two years later Bose enrolled as an undergraduate in Presidency College, Calcutta, where his teachers included Jagadischandra Bose in physics and mathematics, and Prafullachandra Ray in chemistry. Meghnad Saha, Jranchandra Ghosh, and Jnanendranath Mukherjee were among his classmates. He received the M.Sc. in mathematics in 1915, ranking first in his class.

Sir Asutosh Mookerjee, vice-chancellor of Calcutta University, had inaugurated the University College of Science in 1914. This institution, funded largely through the endowments of Sir Taraknath Palit and Dr. Rashbehari Ghose, was the first college in India to offer advanced studies in science. In 1915 Bose and Saha, among others, suggested that Mookerjee build upon the existing postgraduate chemistry curriculum at the college by instituting courses in mathematics and physics. Mookerjee agreed to their request and also obtained for them stipendiary scholarships and funds for procuring scientific journals and laboratory apparatus. When the physics department was organized in 1917. they were appointed lecturers. A year later Chandrasekhara V. Raman. then a civil servant in the Indian Finance Department, joined the department as Palit Professor of Physics.

Bose left Calcutta in 1921 to become Reader in Physics at the newly established University of Dacca in East Bengal. In July 1924 he sent a short manuscript entitled “Plancks Gesetz und Lichtquantenhypothese” to Albert Einstein for criticism and possible publication. Einstein himself translated the paper into German and had it published in the *Zeitschrift für Physik* later that year. He added a note that stated: “In my opinion Boses 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.”

Einstein’s enthusiastic endorsement of his work enabled Bose to obtain a two-year paid study leave from Dacca University. which he spent in France and Germany. During his year in France he was guided in his studies by Paul Langevin and was in close contact with Maurice and Louis de Brogue. Late in 1925 he had a brief but reportedly cordial meeting in Berlin with Einstein, and in the early summer of 1926 he heard Max Born’s lectures at Göttingen on the new matrix mechanics of Werner Heisenberg. Later that summer Bose returned to Dacca as professor and head of the physics department. He held these posts until 1945, when he returned to Calcutta University as Khaira professor of physics and. from 1952 to 1956. as dean of the Faculty of Sciences. Following his retirement from Calcutta, he served for three years as vice-chancellor of Visva-Bharati University, an institution in West Bengal that had been established by Rabindranath Tagore. He relinquished that position in 1959 upon his appointment as a national professor by the government of India. Bose was president of the National Institute of Sciences of India in 1949- 1950, and from 1952 to 1958 served in the upper house of the Indian parliament. He was awarded the Padma Vibhushan by the government of India in 9154 and was elected fellow of the Royal Society in 1958. Bose married Ushabala Ghosh in 1914. and was the father of two sons and five daughters.

Bose’s twenty-six original scientific papers. published between 1918 and 1956, include contributions to statistical mechanics, the electromagnetic properties of the ionosphere, the theories of X-ray crystallography and thermoluminescence, and unified field theory. Two of his first four papers were investigations of the equation of state for gases. written with Saha. In 1919 the Calcutta University Press published a two-volume editions of Einstein’s collected papers on the special and on the general theories of relativity, translated into English by Saha and Bose, respectively. Bose’s first paper on quantum theory (1920) demonstrated that the empirical formulas for the line spectra of’ the alkali atoms are derivable from the Bohr-Sommerfeld quantization rules, and included the assumption that the effective potential in which the valence electrons of these atoms move can be expressed as the superposition of potentials due to a point charge and an electric dipole.

Bose is known outside India primarily for his first paper in the *Zeitschrift für Pkysik* (1924) in which he succeeded in deriving the Planck blackbody radiation law without reference to classical electrodynamics. Einstein’s generalization of Bose’s method led to the first of two systems of quantum statistical mechanics, known as the Bose-Einstein statistics. Paul Dirac later coined the term “boson” for particles that obey these statistics.

Planck’s radiation law, derived in 1900, relates the electromagnetic energy density in equilibrium with a blackbody. or ideal radiator, at an absolute temperature. *T*, to the radiation frequency, *v*. Using modern notation:

where *V* is the volume of the radiator. *c* the speed of light, *k* the Boltzmann constant, and Ii Planck’s constant. Planck based his derivation on a model in which the radiation emitted and absorbed by the blackbody is in equilibrium with a set of charged oscillators. He took the laws of classical electrodynamics as valid but assumed in addition that each oscillator could emit and absorb only in quanta proportional to its frequency of oscillation. That is, E = *nhv*, where n is any integer.

Planck regarded his quantum hypothesis as an ad hoc assumption to be grafted onto the inviolable body of classical electrodynamics. In contrast, Einstein. in his “photoelectric effect” paper of 1905, used general thermodynamic arguments to show that electromagnetic radiation could be regarded as having an atomic or quantum structure. Thus, he argued in effect that electromagnetic radiation in equilibrium with matter could be regarded as a gas similar in some respects to an ordinary gas the quanta of which are atoms or molecules. The zero-rest-mass quanta of the electromagnetic field are now called photons, a term introduced in 1926.

Bose’s 1924 paper showed that the Planck law was completely consistent with Einstein’s quantum gas model. His derivation followed a general procedure introduced by Boltzmann for determining the equilibrium energy distribution of the microscopic entities that constitute a macrosystem. The procedure begins by enumerating all the possible, distinguishable microstates of the entities, where each such state is defined by a set of coordinates and momenta. That is, each possible state of a single entity is specified by a point in six-dimensional phase space the axes of which correspond to the three spatial coordinates and the three components of momentum. Each possible state of the system is specified by a distribution of such phase points. Bose’s innovation was to assume that two or more such distributions that differ only in the permutation of phase points within a subregion of phase space of volume h^{3} (where *h* is Planck’s constant) are to be regarded as identical. Thus, in effect he asserted that two truly identical photons cannot be distinguished even in principle. This method of counting has the effect of enhancing the populations of lower-energy photon states at the expense of those of higher energy, and leads to the correct Planck distribution law.

The assumption that the region *h*^{3} sets a limit on the distinguishability of two photons appears to have been completely ad hoc and was arrived at, according to Bose’s later recollection, in the course of preparing a lecture on the Planck law for a postgraduate physics class at Dacca. It can easily he shown to be consistent with the uncertainty principle of Werner Heisenberg, announced in 1927, and. more fundamentally, with either the matrix mechanics of Heisenberg (1925) or the wave mechanics of Schrodinger. In July 1924 Einstein had already generalized Bose’s results to particles of nonzero rest mass the total number of which is conserved: and in January 1925 he showed that such a gas would, under conditions of extreme temperature and pressure, exhibit marked deviations in behavior from that of a classical ideal Maxwell-Boltzmann gas. The latter paper also showed that Bose’s assumption is consistent with the relationship between the wavelength and momentum of a particle, λ *h/p*, which Louis de Broglie had hypothesized in 1923. Thus, by generalizing Bose’s theory, Einstein completed the formulation of the first of two types of quantum statistics. In 1926 Enrico Fermi derived a second System of quantum statistics, now called the Fermi-Dirac statistics, in which it is assumed that each subvolume *h*^{3} in phase space can be occupied by no more than one point, consistent with the exclusion principle enunciated by Wolfgang Pauli in 1925.

Bose’s first paper in *Zeitschrift für Physik* was followed by another that was also translated by Einstein and published during 1924. In it Bose provided a general statistical treatment of emission and absorption processes for electromagnetic radiation in equilibrium with matter. This paper was accompanied by a note by Einstein expressing serious doubts about the method. In January 1925 Bose wrote to Einstein from Paris that he was working on a paper he felt would remove these doubts. But it seems never to have been completed.

Bose’s next published scientific contribution consisted of two papers on mathematical statistics (1936). Two works on the electromagnetic properties of the ionosphere were published in 1937 and 1938, respectively. A paper on the mathematical properties of the Lorentz group appeared in 1939. Two more mathematical works, one on the inhomogeneous Klein-Gordon equation and one on an integral equation for the hydrogen atom. were published in 1941. Most of his published theoretical work between 1943 and 1950 was on X-ray crystallography and thermoluminescence, both areas in which experimental groups were active at Dacca. Bose’s last six scientific papers, published between 1953 and 1955, were on unified field theory, a topic on which he and Einstein exchanged at least one letter in 1953.

Bose is reputed to have been a devoted and inspiring teacher. His ability to deliver polished lectures without notes was legendary and considered phenomenal even in India, where professors take considerable pride in that accomplishment. This skill was aided by a remarkable memory which he developed as a schoolboy, partly because of his exceedingly weak vision.

Born and educated in an era when Rabindranath Tagore was presiding over the Bengali cultural renaissance, Bose remained devoted to that movement throughout his life. In 1948 he founded the Bangiya Bijnam Parishad, or Science Association of Bengali, as a means of popularizing science in his native language. Like Tagore, he loved poetry. which he read and quoted not only in Bengali and Sanskrit, but also in English and French, both of which he spoke fluently.

## BIBLIOGRAPHY

I. Original Works. Bose’s papers include “On the Influence of the Finite Volume of Molecules on the Equation of Slate,” in *Pilosophical Magazine.* 6th ser.. **36** (1918). 199–202. written with M.N. Saha; “On the Equation of State/’ ibid., 39 (1920), 456. written with M. N. Saha; “On the Deduction of Rydberg’s Law From the Quantum Theory of Spectral Emission” *ibid,***40** (1920). 6 19–627; “Plancks Gesetz und Lichtquanten-hypothese” in *Zeitschnft fur Physik,***26** (1924). 178–181; “Warmegleichgewicht im Strahlungsfeld bei Anwesenheit von Materie” *ibid.,***27** (1924). 384–390: “Anomalous Dielectric Constant of Artificial Ionosphere” in *Science and Culture,***3** (1937), 335–351. written with S. R. Khastgir; “On the Total Reflection of Electromagnetic Waves in the Ionosphere” in *Indian Journal of Physics,***12** (1938). 121–144; “On an Integral Equation Associated With the Equation for Hydrogen Atom“in *Bulletin of the Calcutta Mathematical Society,***37** (1945), 51–61; and “Solution d’une équation tensorielle intervenant dans la théorie du champ unitaire” in *Bulletin de la Société mathématique di France,***83** (1955). 81–88.

Five letters from Bose to Einstein (1924- 1926) and a copy of a 1953 letter from Einstein to Bose are among the Einstein papers at the Institute for Advanced Study. Princeton. New Jersey.

II. Secondary Literture. See William A. Blan-pied. “Natvendrana!h Bose: Co-Founder of Quantum Statistics.” *in American Journal of Physics,***40** (1972). 1212- 1220: Nirendranath Roy. “Professor Satyendranath Bose” in A. K. Datta and Asima Chatterjee, eds.. *Satyendranath Bose 70th Birthday Commemoration Volume*(Calcutta. 1964). 6–12; and Jagadish Sharma. “Satyendra Nath Bose” in *Physics Today.***27** . no. 4 (Apr. 1974). 129–131.

William A. Blanpied

# Satyendranath Bose

# Satyendranath Bose

Satyendranath Bose (1894-1974) was a major figure in the development of quantum statistics and theoretical physics. Albert Einstein built upon his ideas to develop a system of quantum mechanics that became known as Bose-Einstein statistics. Bosons, sub atomic particles of finite mass studied in quantum physics, were named after him.

Satyendranath was born in Calcutta, India, on January 1, 1894, to Surendranath Bose and Amodini Raichaudhuri. As the only son and eldest of seven children, Bose was raised comfortably as a member of the Kayastha caste. His father, an accountant in the executive engineering department of the East India Railways, later was a founder of the Indian Chemical and Pharmaceutical Works. His mother had little formal education but was able to manage a large family. His primary education began in the local English language school established by the British during the colonial period in India. When the British decided to divide the province of Bengal into two administrative units in 1907, his father transferred Bose to a Bengali-languagesecondary school. There he was encouraged in his interest in science by his headmaster and his mathematics teacher.

After graduation from secondary school, Bose completed a Master of Science degree in mathematics at Presidency College in Calcutta in 1915, ranking first in his class. An early influence was his physics teacher Jagadischandra Bose (no relation). Because Indians were not allowed to enter administrative government service, Bose continued to study physics on his own despite a lack of current textbooks and laboratory materials. Two years later Bose became a lecturer in physics at the University of Calcutta in the college of science that had been established in 1914. This was the first college in India that offered advanced degrees in science. Bose helped establish the physics department and saw that it was properly equipped and had current textbooks. After reading a book by J. Willard Gibbs concerning phase space and Boltzmann statistics, Bose developed a special interest in statistical mechanics. In 1914, Bose married Ushabala Ghosh. The union eventually produced two sons and five daughters.

During the years he taught at the University of Calcutta, Bose worked with Meghnad Saha. In 1919, the two men coauthored one of the first anthologies in English of Einstein's scientific papers on relativity. The next year, Bose published his first paper on quantum statistics in the *Philosophical Magazine.*

## Created Ground Breaking Theory for Quantum Statistics

Bose became a reader in physics at the newly created University of Dacca in East Bengal in 1921. He turned his attention to the statistics of photons, a quantum of electromagnetic energy that has no charge or mass but carries energy, such as light and x-rays, in both wave and particle form. By now he had studied Planck's theory of heat radiation. He became interested in Plank's radiation formula, the expression that gives the distribution of energy in the radiation from a black body. Bose commented in an interview with American physicist William A. Blanpied in the *American Journal of Physics,* that he had "spent many sleepless nights" contemplating Planck's law. Finally, while teaching a class, he thought of a new theory for quantum mathematics. By 1923, he had written *Planck's Law and the Hypothesis of Light Quanta,* but was unable to get it published. Bose was able to substantiate Einstein's proposal that electromagnetic radiation had an atomic structure made up of a measurable, or quantum, amount of electromagnetic energy. Even Einstein had been unable to prove his own theory.

The subject of Bose's paper was how to derive Planck's black body radiation law, in which the black body is a theoretical ideal body that absorbs all radiation and reflects none. Planck's equation describes the spectral energy distribution from such a body. Einstein's 1905 paper questioned Planck's assumption that his law could be applied ad hoc to classical electrodynamics (a discipline concerned with the inter-relatedness of electric and other currents and magnets). In Einstein's thermodynamic approach, the quantum structure of electromagnetic radiation could be viewed the same as an ordinary gas and its atomic structure. Without reference to classical electrodynamics, Bose used a phase space approach that treated radiation as an ideal gas in order to show that Einstein's model was consistent with Planck's law. This ultimately pointed the way for future developments in electrodynamics. Because his background was in mathematics, Bose failed to see the far-reaching ramifications his work had in the field of physics, especially in the areas of electrodynamics and quantum gasses. As a result, he did not gain the prestige that Einstein and Planck did.

## Bose and Einstein

Though his paper was only four pages long, it had far reaching consequences. In fact, it was his single greatest contribution to science. Isolated in India and unable to get his paper published, Bose turned to Albert Einstein and asked him to examine his work and see if he could help. Though he had never met Bose, Einstein was impressed. The paper was translated it into German and Einstein used his considerable clout to get it published in *Zeitschrift fur Physik* in 1924. Einstein stated in the journal, "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." This paper and support from Einstein established Bose's place in the world of physics. It enabled him to get a two-year paid leave of absence from Dacca University in order to study in France, where he met Langevin, Madame Curie, and the de Broglies and in Germany where he heard talks by Max Born about the new quantum mechanics. In 1925, Bose was able to meet briefly with Einstein. He had hoped to work closely with Einstein, but that never materialized. Einstein continued to build upon Bose's work and developed the foundation for the Bose-Einstein statistics. This approach to quantum physics was the first of two approaches to determine the distribution of certain subatomic particles among the various possible energy values. Depending on the approach used, the particles that adhere to these mathematical laws are known as bosons—named after Bose—or fermions, named after Enrico Fermi.

## Revered Scientific Leader in India

Bose returned to Dacca in 1926 as professor and head of the physics department. He devoted himself to teaching and was named Khaira professor of physics at Calcutta University in 1945. His students considered him an inspiring teacher and his ability to deliver lectures without notes was legendary. This was a skill he developed as a young man because of his poor vision. Bose became the dean of the Faculty of Sciences from 1952 to 1956. He left Calcutta to become vice-chancellor of Visva-Bharati University in West Bengal, and served in this position for three years. Bose was president of the National Institute of Sciences of India in 1949-1950. He also founded the Science Association of Bengali in 1948. This organization was dedicated to popularizing science in his native language.

## Indian Nationalist

Throughout his life, Bose was an ardent nationalist. He supported the independence of India from Great Britain. When given the opportunity, Bose served in the upper house of the Indian parliament from 1952 to 1958. He received the *Padma Vibhushan,* or national professor of India award from the government of India in 1958. That same year, he was elected fellow of the British Royal Society. Between 1918 and 1956, Bose published only twenty-six original scientific papers, most of which dealt with mathematical statistics, electromagnetic properties of the ionosphere, x-ray crystallography, thermoluminescence, and the unified field theory. He loved poetry, which he could read and recite fluently in Bengali, English, French, and Sanskrit. He was a member of the Bengali cultural renaissance, presided over by Rabindranath Tagore, all of his adult life. Bose died in Calcutta, on February 4, 1974, at the age of eighty. Jagadish Sharma, who studied physics under him, commented in *Physics Today* that his rise to "the highest echelons of science" must be viewed in the context of an India that was ruled by Great Britain and that offered few opportunities in science for the native Indian.

## Further Reading

*Dictionary of National Biography,* 1971-1980, Oxford University Press, 1986.

*Dictionary of Scientific Biography,* Volume XV, Supplement I, Charles Scribner's Sons, 1978.

*Notable Twentieth-Century Scientists,* edited by Emily J. McMurray, Gale Research Inc., 1995.

*The New York Times Biographical Service,* Arno Press, 1974. □

# Bose, Satyendranath

**Bose, Satyendranath** (1894–1974) Indian physicist and mathematician who contributed to the theory of quantum mechanics and statistical mechanics. Bose made the initial advances to describe the statistical properties of certain elementary particles (now called bosons). These particles all have the property that any number of them can occupy the same quantum state: that is they do not obey Enrico Fermi's exclusion principle. Bose's work was developed by Einstein and the statistics that such particles obey are called *Bose-Einstein statistics*.

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