The development of attitudes to the wave-particle duality of light and quantum theory, 1900–1920

References

• The main exceptions here are Stuewer Roger H. The Compton effect—turning point in physics New York 1975 and especially Martin J. Klein, ‘Einstein and the wave-particle duality’, Nat. philosopher, 3 (1964), 1–49 and ‘The first phase of the Bohr-Einstein dialogue’. Hist. stud. phys. sci., 2 (1970), (1–39). See also Bruce R. Wheaton, ‘On the nature of X and gamma rays: attitudes toward localisation of energy in the “new radiations”, 1896–1922’ (Ph.D. dissertation, Princeton, in preparation). For discussions bearing less directly on the problem see the studies cited below and the general works: Max Jammer, The conceptual development of quantum mechanics (1966, New York); Armin Hermann, The genesis of quantum theory (1899–1913) (1971, Cambridge, Mass.); Leon Rosenfeld, ‘La premi`ere phase de l'evolution de la théorie des quanta’, Osiris, 2 (1936), 149–196; and Thomas S. Kuhn, Black-body theory and the quantum discontinuity (1978, London).
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• For the background to Planck's law see Hiebert Erwin N. The concept of thermodynamics in the scientific thought of Mach and Planck Ernst-Mach-Institut Freiburg 1968 Stephen Brush, ‘The development of the kinetic theory of gases VIII—randomness and irreversibility’, Arch. hist. ex. sci., 12 (1972), 1–88 (also ch. 14 of his The kind of motion we call heat (1976, Amsterdam)); and Hans Kangro, The early history of Planck's radiation law (1976, London). For its reception see Kuhn (footnote 1) and Elizabeth Garber, ‘Some reactions to Planck's law, 1900–1914’, Stud. hist. phil. sci., 7 (1976), 89–126. My account of the origins and derivation of Planck's law draws heavily on Martin J. Klein, ‘The beginnings of quantum theory’, in C. Weiner (ed.), History of twentieth century physics (1977, New York). I have, however, departed from the tone and emphasis of this account in some respects.
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• See Kangro Klein Brush Hiebert The concept of thermodynamics in the scientific thought of Mach and Planck Ernst-Mach-Institut Freiburg 1968 Neither Kangro nor Klein seem to do justice to the extraordinary naivety of Planck's arguments against Boltzmann, which must have taxed the latter's patience to the utmost.
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• Planck , M. 1900 . Über eine Verbesserung der Wienschen Spektralgleichung . Verhandl. Deut. Phys. Ges. , 2 : 202 – 204 .
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• This story has been well told by Klein The beginnings of quantum theory History of twentieth century physics Weiner C. New York 1977 7ff 7ff who does not however emphasize the point that the experimenters, Rubens and Kurlbaum, originally fitted their results to the formula of Lummer and Jahnke (see Klein, p. 9). This was one important reason why Planck should have felt that ‘a theoretical derivation [of his law] had to be found at any cost, no matter how high’, when he had not previously felt this to be necessary for the then experimentally established law of Wien. Planck's ‘derivation’ was really little more than a statement of the entropy formula corresponding to the result required. This may have been an achievement in Planck's entropy-oriented eyes—though even this is doubtful, in the light of his attitude to his own law—but it can hardly be seen objectively as such. So far as Planck's ignoring the equipartition law is concerned, the only explanation offered has been by Hermann (footnote 1), who suggests that he might not have known of it. It was however very well known, and must have been so to Planck who, as Hiebert (footnote 3) has shown, was thoroughly familiar with the writings of Maxwell and Boltzmann, on whose statistical mechanics the law was founded. Since it would have been introduced at the very point at which Planck had to abandon his derivation and resort to the mere statement of the result required, one can only deduce that he must have consciously rejected it; but why then did he not profit from the situation at Boltzmann's expense by pointing out that it led to an impossible result, to infinite radiation? The answer to this seems to lie in the fact that Planck had already recognised that his own theory, with its hypothesis of natural radiation, would itself be subject to any criticism of this kind that he might make against Boltzmann. See below, and, for the development of this aspect of Planck's thought, Hiebert and Brush (footnote 3).
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• Planck apparently did not know of Rayleigh's law—more strictly, with the correct constant factor, the Rayleigh-Jeans law—at this stage: see Klein The beginnings of quantum theory History of twentieth century physics Weiner C. New York 1977
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• See references in Hiebert Erwin N. The concept of thermodynamics in the scientific thought of Mach and Planck Ernst-Mach-Institut Freiburg 1968
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• This attitude is explicit in Planck's paper Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum Ann. d. Phys. 1901 4 553 563
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• Rosenfeld . 1936 . La premi`ere phase de l'evolution de la théorie des quanta . Osiris , 2 : 149 – 196 . and Klein (footnote 3) consider it probable that Planck reached this formula by working backwards; but Planck did show an awareness that it applied to identical energy elements, and this suggests that he may have taken it from a text on mathematical probability theory, perhaps trying several and selecting the one (for the distribution of identical balls over distinguishable urns) that gave the required answer: the reverse derivation, involving the reverse application of Stirling's formula; is not easy.
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• See Garber Some reactions to Planck's law, 1900–1914 Stud. hist. phil. sci. 1976 7 89 126 and Kuhn (footnote 1).
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• Larmor J. Rep. Brit. Assn. Adv. Sci. 1902 546 546 in See also his article ‘Radiation’, Enc. Brit., (10th ed., 1902) vol. 32, 120–128, where Planck's law is discussed but its implications are not.
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• Faraday-tubes were three dimensional versions of Faraday's lines of electric force, and had been used as a model by Thomson since 1893, Notes on recent researches in electricity and magnetism London 1893 They became the subject of a considerable body of research in Britain in the 1920s, featuring in Whittaker's atomic model and appearing, quantised and in four dimensions, as his calamoids (see H. S. Allen, The quantum and its interpretation (1928, London)). The fundamentally wave nature of light was stressed by Thomson throughout.
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• Both Millikan's change of heart and de Broglie's report of his results came at the third Solvay Congress of April 1921 (Institut International de Physique Solvay Atomes et electrons Paris 1921
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• See, for example, Jammer The conceptual development of quantum mechanics New York 1966 and Klein (footnote 86).
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• While working in the context of the light-quantum hypothesis, Einstein assumed that there should be a component of stimulated emission, as in the classical theory. While it was natural for an incoming wave to stimulate the emission of another wave of the same frequency, the same could be true of light-quanta only if one assumed quanta of the same frequency to be mutually dependent. The assumption of stimulated emission gave light-quanta a quasi-wave-like behaviour, and the assumption that the radiation should tend to infinity with temperature ensured that this aspect of the classical theory was wholly retained. The importance of the latter assumption was noticed apparently first by Eddington in On the derivation of Planck's law from Einstein's equation Phil. mag. 1925 50 6 803 808
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• Eddington , A.S. 1920 . Space, time and gravitation 182 – 182 . Cambridge Pauli's views are not stated explicitly in extant correspondence until Pauli to Eddington, 20 September 1923, but they may be inferred from Weyl to Pauli, 9 December 1919 and Einstein to Born, 27 January 1920. The Pauli letters are printed in his Briefwechsel (ed. A. Hermann et alii), volume 1 to be published by Springer, 1979, letters no. 45, 2. The Einstein letter is in The Born-Einstein letters (1971, New York), letter no. 13. See Hendry ibid.
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