Planck’s Radiation Law, The Light Quantum, and Indistinguishability in the Teaching of Quantum Statistics

Abstract

Peter M. Enders* and Zhumanazar R. Aibekuly

Planck’s 1900 introduction of the “energy elements”, i.e., electromagnetic radiation quanta of energy hν each, for founding his radiation law marks the origin of quantum theory and is discussed in all courses on this subject. Surprisingly, the question whether Planck really implied quantisation is debated among historians of physics. We present a simplified account of that debate which also sheds light on the issue of indistinguishability and Einstein’s light quantum hypothesis. Here, the relevance of the notion ‘(in)distinguishability’ is often overemphasized. It has to be treated together with ‘equality’, ‘identity’, and ‘interchangeability’, where the latter one is the decisive notion in this context. As a result, the difference between Planck’s and Einstein’s concepts of ‘light particles’ becomes more easily to grasp. For that and many other reasons, we believe that the teaching of quantum physics benefits from including the material presented here, and that beyond the demand of historical completeness.

Nevertheless, for the sake of our readers’ convenience, we almost completely reprint Planck’s former students Hettner’s remembering of Planck’s way to his radiation law, together with its translation into English. It seems that Planck has not really done the calculations described in his December 1900 lecture. For this, following Becker, we show how to overcome the difficulties over there, and we sketch his simplifying approach in his subsequent 1901 article. Strangely enough, in his 1906/07 lectures on the theory of heat radiation, Planck deviates from those calculations and obtains a non-extensive entropy. This, too, is most easily analyzed using Bach’s three-level scheme ‘configuration. occupation. occupancy’ for the counting combinatorics involved. Boltzmann’s 1877, Planck’s 1900, Einstein’s 1905, Bose’s 1924, and other treatments are systematized using that scheme.

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