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arXiv:1703.05635 · European Journal of Physics

Planck’s radiation law, the light quantum, and the prehistory of indistinguishability in the teaching of quantum mechanics

O. Passon, Johannes Grebe-Ellis

Published Mar 15, 2017• 35 citations
arXivHTMLPDF

Abstract

Abstract Planck’s law for black-body radiation marks the origin of quantum theory and is discussed in all introductory (or advanced) courses on this subject. However, the question whether Planck really implied quantisation is debated among historians of physics. We present a simplified account of this debate which also sheds light on the issue of indistinguishability and Einstein’s light quantum hypothesis. We suggest that the teaching of quantum mechanics could benefit from including this material beyond the question of historical accuracy.

DOI
10.1088/1361-6404/aa6134

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Abstract Planck’s law for black-body radiation marks the origin of quantum theory and is discussed in all introductory (or advanced) courses on this subject. However, the question whether Planck really implied quantisation is debated among historians of physics. We present a simplified account of this debate which also sheds light on the issue of indistinguishability and Einstein’s light quantum hypothesis. We suggest that the teaching of quantum mechanics could benefit from including this material beyond the question of historical accuracy.
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
Abstract With the failure of classical physics to explain the experimentally observed black body radiation spectrum, the photoelectric effect and the existence of narrow spectral lines in the light emitted by excited atoms, physicists were forced to reach out for new ideas. Following Planck’s initial “drastic hypothesis” of light “quanta”, Einstein led the way in exploring some of the myriad implications of this idea. In particular, the study of fluctuations led to a new understanding of the interaction of electromagnetic radiation with atoms. Einstein invented the photon by showing, through fluctuation studies, that light emitted by atoms must be in the form of plane waves. These ideas led to the first notions regarding the quantization of matter and its dynamics.
This chapter presents the basic physical ideas that underpin the quantum theory. Historians place the beginnings of the quantum theory at 1900. That year Max Planck published his famous formula for the distribution of energy as a function of frequency in black-body radiation. Curiously, although radiation theory gave birth to quantum mechanics, the interaction of matter and electromagnetic radiation is a rather advanced topic in quantum mechanics and it took almost fifty years for an acceptable formulation to be achieved. One reason for this is that photons are quanta of the electromagnetic field, and the quantum theory of fields requires a relativistic treatment to be entirely successful. The corpuscular nature of light was only half of the input that gave birth to quantum mechanics. The other half concerns matter. Given that the discreteness of photons manifests itself during the emission and absorption process, it is not surprising to find that quantum oddities afflict the behaviour of material particles too.
Abstract There are two rather different phenomena that furthered the development of quantum theory: blackbody radiation and atomic spectra. In fact quantum theory began in 1900 with Planck’s radiation law and his introduction of the quantum of action h (Episode 7). His derivation of the law was by no means stringent. He assumed the existence of many resonators (atoms or molecules) of different but fixed frequencies ν, which could emit or absorb radiation only in quanta of energy E = hν. Einstein, in his light-quantum hypothesis of 1905, postulated that the energy quantization is a property of the radiation field itself and not due to the material resonators. He found a similarity between a cavity filled with radiation consisting of quanta and a vessel filled with gas consisting of atoms. However, he could not obtain Planck’s law but only Wien’s (Episode 10).
This article analyzes the scientific problems that arose at the end of the 19th and beginning of the 20th centuries due to the limitations of classical physics, particularly the issues of measuring the speed of light and the radiation of a blackbody. This article highlights the concept of quantization proposed by M. Planck and its significance in resolving these problems. The formation of quantum mechanics, its main concepts, its role in describing the laws of motion of micro-objects, and its connection with classical mechanics are discussed in detail in this section. Furthermore, this article examines the fundamental concepts of quantum mechanics: discreteness, wave-particle duality, and the significance of Planck’s constant. This article also addresses the challenges of teaching quantum mechanics and ways to overcome them, including the effectiveness of using the case study method.