In order to show how formal analogies between different physical systems play an important conceptual work in physics, this paper analyzes the evolution of Einstein’s thoughts on the structure of radiation from the point of view of the formal analogies he used as “lenses” to “see” through the “black box” of Planck’s blackbody radiation law. A comparison is also made with his 1925 paper on the quantum gas where he used the same formal methods. Changes of formal points of view are most of the time taken for granted or passed over in silence in studies on the mathematization of physics as if they had no special significance. Revisiting Einstein’s classic papers on the nature of light and matter from the angle of the various theoretical tools he used, namely entropy and energy fluctuation calculations, helps explain why he was in a unique position to make visible the particle structure of radiation and the dual (particle and wave) nature of light and matter. Finally, this case study calls attention to the more general question of the surprising creative power of formal analogies and their frequent use in theoretical physics. This aspect of intellectual creation can be useful in the teaching of physics.
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Prepared for the special issue of Science and Education, on the relations between physics and mathematics, this paper is a revised English translation of a previous paper published in French in Gingras (2011).
For a detailed survey of the use of models in different disciplines see Morgan and Morrison (1999).
See for example Hesse (1966, 8–10), where models are discussed in terms of positive and negative analogies. See also W. H. Leatherdale (1974, 1). The confusion between models and analogies is often due to the fact that most authors concentrate on the special cases of analogical models. For a recent analysis, see Bailer-Jones (2009).
For convenience we use modern notations.
Einstein’s reflections on those foundations led to his 1906 paper “On the Theory of Light Production and Light Absorption” in which he clarified Planck’s derivation, concluding that “Mr Planck introduced into physics a new hypothetical element: the hypothesis of light quanta”, thus confirming that his own views on the quantum of light and those of Planck were not incompatible as he first thought in 1905; see Einstein (1989, 192, 196).
We are not discussing here the logical necessity of the analogy used by Einstein but the historical fact of its particular use in his argumentation for the particle structure of radiation. For a logical analysis see Dorling (1971).
For details on this question, see Pais (1982, 68–70).
Though it is not the place to develop that argument here, I think the acceptance of the idea of “duality” between particle and wave is closely linked to the Copenhagen interpretation of Quantum mechanics and its underlying operationalist philosophy in which the ontology is defined by measuring instrument. Though always marginal, some major physicists always opposed the idea of “wave-particle duality” as absurd; see for example Landé (1965).
Dorling (1971) writes that the use of arguments by analogy “seemed quite uncharacteristic of Einstein” and that it does not occur “in any of his other major writings”. As this paper shows, this is far from being the case.
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Gingras, Y. The Creative Power of Formal Analogies in Physics: The Case of Albert Einstein. Sci & Educ 24, 529–541 (2015). https://doi.org/10.1007/s11191-014-9739-1
- Formal Analogy
- Dual Nature
- Light Quantum
- Energy Fluctuation
- Black Hole Evaporation