Daily Archives: October 19, 2026

Authors: Y C Kamala

Abstract: In 1924 Satyendra Nath Bose, then at the University of Dacca, derived Planck’s radiation law without appeal to classical electrodynamics. He divided the phase space of light quanta into cells of volume h³ and counted the ways in which quanta could be distributed among them. Einstein translated the paper and extended its method to material particles, and the result became Bose–Einstein statistics. This paper re-reads Bose’s derivation as an exercise in combinatorics. It shows that Bose’s own counting, in terms of the numbers of cells that contain a given number of quanta, is exactly equivalent to the “stars and bars” count of indistinguishable objects in distinguishable boxes, and it proves the equivalence with a generating function. Exact enumerations confirm the equivalence for small systems and show how sharply it departs from the count for distinguishable quanta. Numerical maximisation of Bose’s weight recovers the geometric distribution of quanta per cell that yields Planck’s law, and exact finite-system calculations show the convergence of the single-cell distribution and of the fluctuations to their thermodynamic limits, including Einstein’s fluctuation formula with its particle and wave terms. The paper relates Bose’s counting to Planck’s combinatorial argument of 1900, to Natanson’s analysis of 1911 and to the Ehrenfest–Kamerlingh Onnes derivation of 1915, and argues that the novelty of Bose’s work lay less in a new formula than in a new choice of the objects to be counted.

DOI: https://doi.org/10.5281/zenodo.23473406

Published by: vikaspatanker

Authors: Y C Kamala

Abstract: The century between the Battle of Plassey (1757) and the founding of the universities of Calcutta, Bombay and Madras (1857) is usually treated as a prehistory of modern science in India, a period of surveys and collections before the age of the laboratory. This paper argues that these years laid down institutional foundations that shaped how physics would later be taught and practised in the subcontinent. Drawing on published educational records and the historiography of colonial science, it examines three clusters of institutions: the state’s instruments of measurement and communication (the observatory, the Great Trigonometrical Survey and the electric telegraph); the policy debates that decided whether, in what language and for whom natural philosophy would be taught; and the colleges and translation bodies through which Indian students first met mechanics, optics and higher mathematics. The analysis shows that the physical sciences entered colonial India chiefly as practice in the service of the state, in the form of precision measurement, geodesy, meteorology and telegraphy, while formal teaching of natural philosophy remained thin, uneven and dependent on Indian initiative. The examining universities of 1857 consolidated this pattern by rewarding the reproduction of knowledge rather than its creation. The paper concludes that the later struggle to build research-led physics in India was, in large part, a struggle against the institutional settlement of this first colonial century

DOI: https://doi.org/10.5281/zenodo.23472477

Published by: vikaspatanker