Experimenting theory: The proofs of kirchhoff's radiation law before and after planck

Historical Studies in the Physical and Biological Sciences

Volumn 33, Issue 2, 2003, Pages 299-335

  Schirrmacher, Arne ^a  

^a DEUTSCHES MUSEUM   (Germany)

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[No Author keywords available]

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EID: 4344603677     PISSN: 08909997     EISSN: None     Source Type: Journal    
DOI: 10.1525/hsps.2003.33.2.299     Document Type: Review

References (170)

1. David Hilbert, "Vortrag Münster," HP, 586, 5f (manuscript for a lecture delivered at the 84th meeting of the Vereinigung Deutscher Naturforscher und Ärzte in Münster on 18 Sep 1912).
2. Georg Simon Ohm, Die galvanische Kette, mathematisch bearbeitet (Berlin 1827). In Ohm's notation S=A/L where S denotes the electric current, L is a measure for the resistance ("reduced length"), and A the sum of all "tensions."
3. Gustav Kirchhoff, "Ueber den Zusammenhang von Emission und Absorption von Licht und Wärme," Akademie der Wissenschaften, Monatsberichte (Berlin, 1860), 783-787, 784, 786, reprinted in Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und das Spektrum der chemischen Elemente und weitere ergänzende Arbeiten aus den Jahren 1859-1862 (Osnabrück, 1972), ed. Hans Kangro.
4. Gustav Kirchhoff, "Ueber den Zusammenhang von Emission und Absorption von Licht und Wärme," Akademie der Wissenschaften, Monatsberichte (Berlin, 1860), 783-787, 784, 786, reprinted in Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und das Spektrum der chemischen Elemente und weitere ergänzende Arbeiten aus den Jahren 1859-1862 (Osnabrück, 1972), ed. Hans Kangro.
5. Christa Jungnickel and Russell McCormmach, Intellectual mastery of nature. Theoretical physics from Ohm to Einstein. Vol. 1. The torch of mathematics, 1800-1870 (Chicago, 1986), 53.
6. Criticism of the physicists' lack of logic and rigor has been raised repeatedly; cf. Arthur Jaffe and Frank M. Quinn, "'Theoretical mathematics': Towards a cultural synthesis of mathematics and theoretical physics," Bulletin (New Series), American Mathematical Society, 29 (1993), 1-13, which uses "experimental mathematics" to designate physicists' non-rigorous mathematics.
7. Cf. John Ackermann, "Review article: The new experimentalism," British journal of philosophy of science, 40 (1989), 185-190; Michael Heidelberger and Friedrich Steinle, Experimental essays - Versuche zum Experiment (Baden-Baden, 1998); and Christoph Meinel, ed., Instrument - Experiment: Historische Studien (Bassum, 1999), esp. Klaus Hentschel, "Historiographische Anmerkungen zum Verhältnis von Experiment, Instrumentation und Theorie," ibid., 13-51.
8. Cf. John Ackermann, "Review article: The new experimentalism," British journal of philosophy of science, 40 (1989), 185-190; Michael Heidelberger and Friedrich Steinle, Experimental essays - Versuche zum Experiment (Baden-Baden, 1998); and Christoph Meinel, ed., Instrument - Experiment: Historische Studien (Bassum, 1999), esp. Klaus Hentschel, "Historiographische Anmerkungen zum Verhältnis von Experiment, Instrumentation und Theorie," ibid., 13-51.
9. Cf. John Ackermann, "Review article: The new experimentalism," British journal of philosophy of science, 40 (1989), 185-190; Michael Heidelberger and Friedrich Steinle, Experimental essays - Versuche zum Experiment (Baden-Baden, 1998); and Christoph Meinel, ed., Instrument - Experiment: Historische Studien (Bassum, 1999), esp. Klaus Hentschel, "Historiographische Anmerkungen zum Verhältnis von Experiment, Instrumentation und Theorie," ibid., 13-51.
10. Cf. John Ackermann, "Review article: The new experimentalism," British journal of philosophy of science, 40 (1989), 185-190; Michael Heidelberger and Friedrich Steinle, Experimental essays - Versuche zum Experiment (Baden-Baden, 1998); and Christoph Meinel, ed., Instrument - Experiment: Historische Studien (Bassum, 1999), esp. Klaus Hentschel, "Historiographische Anmerkungen zum Verhältnis von Experiment, Instrumentation und Theorie," ibid., 13-51.
11. This paper is a history of justifications rather than a history of discoveries. For the latter see Edmund T. Whittaker, A history of the theories of aether and electricity. Vol. 1. The classical theories (New York, 1951), chapt. 12; Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970); and "Kirchhoff und die spektralanalytische Forschung," in Kirchhoff, Untersuchungen (ref. 3), l-54; Hans-Georg Schöpf, Von Kirchhoff bis Planck. Theorie der Wärmestrahlung in historisch-kritischer Darstellung (Berlin, 1978); Eisui Uematsu, "The role of Kirchhoff's 1859 work in the history of radiation theory" [in Japanese], Kagakusi kenkyu: Journal of history of science of Japan, 25 (1986), 14-19.
12. This paper is a history of justifications rather than a history of discoveries. For the latter see Edmund T. Whittaker, A history of the theories of aether and electricity. Vol. 1. The classical theories (New York, 1951), chapt. 12; Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970); and "Kirchhoff und die spektralanalytische Forschung," in Kirchhoff, Untersuchungen (ref. 3), l-54; Hans-Georg Schöpf, Von Kirchhoff bis Planck. Theorie der Wärmestrahlung in historisch-kritischer Darstellung (Berlin, 1978); Eisui Uematsu, "The role of Kirchhoff's 1859 work in the history of radiation theory" [in Japanese], Kagakusi kenkyu: Journal of history of science of Japan, 25 (1986), 14-19.
13. This paper is a history of justifications rather than a history of discoveries. For the latter see Edmund T. Whittaker, A history of the theories of aether and electricity. Vol. 1. The classical theories (New York, 1951), chapt. 12; Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970); and "Kirchhoff und die spektralanalytische Forschung," in Kirchhoff, Untersuchungen (ref. 3), l-54; Hans-Georg Schöpf, Von Kirchhoff bis Planck. Theorie der Wärmestrahlung in historisch-kritischer Darstellung (Berlin, 1978); Eisui Uematsu, "The role of Kirchhoff's 1859 work in the history of radiation theory" [in Japanese], Kagakusi kenkyu: Journal of history of science of Japan, 25 (1986), 14-19.
14. This paper is a history of justifications rather than a history of discoveries. For the latter see Edmund T. Whittaker, A history of the theories of aether and electricity. Vol. 1. The classical theories (New York, 1951), chapt. 12; Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970); and "Kirchhoff und die spektralanalytische Forschung," in Kirchhoff, Untersuchungen (ref. 3), l-54; Hans-Georg Schöpf, Von Kirchhoff bis Planck. Theorie der Wärmestrahlung in historisch-kritischer Darstellung (Berlin, 1978); Eisui Uematsu, "The role of Kirchhoff's 1859 work in the history of radiation theory" [in Japanese], Kagakusi kenkyu: Journal of history of science of Japan, 25 (1986), 14-19.
15. This paper is a history of justifications rather than a history of discoveries. For the latter see Edmund T. Whittaker, A history of the theories of aether and electricity. Vol. 1. The classical theories (New York, 1951), chapt. 12; Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970); and "Kirchhoff und die spektralanalytische Forschung," in Kirchhoff, Untersuchungen (ref. 3), l-54; Hans-Georg Schöpf, Von Kirchhoff bis Planck. Theorie der Wärmestrahlung in historisch-kritischer Darstellung (Berlin, 1978); Eisui Uematsu, "The role of Kirchhoff's 1859 work in the history of radiation theory" [in Japanese], Kagakusi kenkyu: Journal of history of science of Japan, 25 (1986), 14-19.
16. Jungnickel and McCormmack (ref. 4), 299, 301.
17. Aimé Cotton, "The present status of Kirchhoff's law," Astrophysical journal, 9 (1899), 237-268; Heinrich Kayser, Handbuch der Spectroscopie. Vol. 2 (Leipzig 1902). Aimé Auguste Cotton (1869-1951) completed his thesis on "Recherches sur l'absoption et la dispersion de la lumiére par les milieux doués du pouvoir rotaire" in 1896 at the Ecole Normale in Paris. On Kayser's see Matthias Dörries, "Heinrich Kayser as philologist of physics," HSPS, 26:1 (1995), 1-33, on 27-31.
18. Aimé Cotton, "The present status of Kirchhoff's law," Astrophysical journal, 9 (1899), 237-268; Heinrich Kayser, Handbuch der Spectroscopie. Vol. 2 (Leipzig 1902). Aimé Auguste Cotton (1869-1951) completed his thesis on "Recherches sur l'absoption et la dispersion de la lumiére par les milieux doués du pouvoir rotaire" in 1896 at the Ecole Normale in Paris. On Kayser's see Matthias Dörries, "Heinrich Kayser as philologist of physics," HSPS, 26:1 (1995), 1-33, on 27-31.
19. Aimé Cotton, "The present status of Kirchhoff's law," Astrophysical journal, 9 (1899), 237-268; Heinrich Kayser, Handbuch der Spectroscopie. Vol. 2 (Leipzig 1902). Aimé Auguste Cotton (1869-1951) completed his thesis on "Recherches sur l'absoption et la dispersion de la lumiére par les milieux doués du pouvoir rotaire" in 1896 at the Ecole Normale in Paris. On Kayser's see Matthias Dörries, "Heinrich Kayser as philologist of physics," HSPS, 26:1 (1995), 1-33, on 27-31.
20. Gustav Kirchhoff, "Ueber das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsverm̈gen der Körper für Wärme und Licht," Annalen der Physik, 109 (1860) 275-301, on 276.
21. Kirchhoff, "Zusammenhang" (ref. 3).
22. Gustav Kirchhoff, "Ueber die Fraunhoferschen Linien," Monatsberichte, Akademie der Wissenschaften, Berlin, 1860, 662-665.
23. Kirchhoff, "Zusammenhang" (ref. 3), 784.
24. Ibid., 786f. Kirchhoff did not recognize that his law, which supposed thermal equilibrium, could hardly be used for non-equilibrium phenomena like burning gases. In 1903 Ernst Pringsheim spoke of the need to deprive Kirchhoff's law of the "nimbus" of being the theoretical foundation of spectral analysis; "Über die Strahlungsgesetze," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 391-417, on 394.
25. Ibid., 786f. Kirchhoff did not recognize that his law, which supposed thermal equilibrium, could hardly be used for non-equilibrium phenomena like burning gases. In 1903 Ernst Pringsheim spoke of the need to deprive Kirchhoff's law of the "nimbus" of being the theoretical foundation of spectral analysis; "Über die Strahlungsgesetze," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 391-417, on 394.
26. Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und die Spektren der chemischen Elemente (2nd edn., Berlin, 1962), appendix, "Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht," 22-39; also in Gesammelte Abhandlungen. Vol 1 (Leipzig, 1882) 571-598, English trans. in D.B. Brace, ed., The laws of radiation and absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen (New York, 1901), 75-97. The version of 1862 omits the final paragraph on the supposed validity of the law for fluorescent bodies.
27. Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und die Spektren der chemischen Elemente (2nd edn., Berlin, 1962), appendix, "Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht," 22-39; also in Gesammelte Abhandlungen. Vol 1 (Leipzig, 1882) 571-598, English trans. in D.B. Brace, ed., The laws of radiation and absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen (New York, 1901), 75-97. The version of 1862 omits the final paragraph on the supposed validity of the law for fluorescent bodies.
28. Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und die Spektren der chemischen Elemente (2nd edn., Berlin, 1962), appendix, "Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht," 22-39; also in Gesammelte Abhandlungen. Vol 1 (Leipzig, 1882) 571-598, English trans. in D.B. Brace, ed., The laws of radiation and absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen (New York, 1901), 75-97. The version of 1862 omits the final paragraph on the supposed validity of the law for fluorescent bodies.
29. Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und die Spektren der chemischen Elemente (2nd edn., Berlin, 1962), appendix, "Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht," 22-39; also in Gesammelte Abhandlungen. Vol 1 (Leipzig, 1882) 571-598, English trans. in D.B. Brace, ed., The laws of radiation and absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen (New York, 1901), 75-97. The version of 1862 omits the final paragraph on the supposed validity of the law for fluorescent bodies.
30. Note that Kirchhoff's one-wavelength plate is now, by itself, a perfect mirror for all radiation with a wavelength different from the specified one.
31. Kirchhoff (ref. 15), 26; cited in Brace (ref. 15), 79f.
32. Kirchhoff (ref. 15), 26; cited in Brace (ref. 15), 79f.
33. Kirchhoff (ref. 10), 279.
34. Kirchhoff (ref. 15), 23 (76).
35. Gustav Kirchhoff, "Zur Geschichte der Spektral-Analyse und der Analyse der Sonnenatmosphäre," Annalen der Physik, 194 (1862), 94-111, a justification against priority claims by Balfour Stewart and others; Daniel M. Siegel, "Balfour Stewart and Gustav Robert Kirchhoff: Two independent approaches to 'Kirchhoff's radiation law,'" Isis, 67 (1976), 565-600; Kangro (ref. 3), 24-26. Stewart plays no role in what follows since his formulation did not lead to a universal function.
36. Gustav Kirchhoff, "Zur Geschichte der Spektral-Analyse und der Analyse der Sonnenatmosphäre," Annalen der Physik, 194 (1862), 94-111, a justification against priority claims by Balfour Stewart and others; Daniel M. Siegel, "Balfour Stewart and Gustav Robert Kirchhoff: Two independent approaches to 'Kirchhoff's radiation law,'" Isis, 67 (1976), 565-600; Kangro (ref. 3), 24-26. Stewart plays no role in what follows since his formulation did not lead to a universal function.
37. Gustav Kirchhoff, "Zur Geschichte der Spektral-Analyse und der Analyse der Sonnenatmosphäre," Annalen der Physik, 194 (1862), 94-111, a justification against priority claims by Balfour Stewart and others; Daniel M. Siegel, "Balfour Stewart and Gustav Robert Kirchhoff: Two independent approaches to 'Kirchhoff's radiation law,'" Isis, 67 (1976), 565-600; Kangro (ref. 3), 24-26. Stewart plays no role in what follows since his formulation did not lead to a universal function.
38. Kayser (ref. 9), 26; Ernst Pringsheim, "Herleitung des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 360-364.
39. Kayser (ref. 9), 26; Ernst Pringsheim, "Herleitung des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 360-364.
40. Wilhelm Wien, "Temperatur und Entropie der Strahlung," Annalen der Physik und Chemie, 52 (1894) 132-165, on 163. Owing to the Doppler effect, a plate that could completely reflect, absorb, and let penetrate certain wavelength ranges would lead to contradictory results when moved. Apparently referring to Kirchhoff's second proof, Wien concluded that one can only require that certain wavelengths be reflected, etc., to a high degree but not fully.
41. Cotton (ref. 9), 267.
42. Kayser (ref. 9), 27.
43. Wilhelm Wien, "Theorie der Strahlung," Encyklopädie der mathematische Wissenschaften. Vol. 5 (Leipzig, 1909), 282-357, on 285.
44. Woldemar Voigt, "Über die Proportionalität von Emissions- und Absorptionsvermögen," Annalen der Physik, 67 (1899), 366-387, on 366.
45. Balfour Stewart, "Reply to some remarks by G. Kirchhoff in his paper 'On the history of spectrum analysis,'" Philosophical magazine, 25 (1863), 354-360, on 359, cited after Siegel (ref. 20), 589.
46. Kirchhoff (ref. 15), 25-27 (English transl., 79-81).
47. Brace (ref. 15), 32; Hermann von Helmholtz, Handbuch der physiologischen Optik. Vol. 1 (Leipzig, 1856), 169.
48. Brace (ref. 15), 32; Hermann von Helmholtz, Handbuch der physiologischen Optik. Vol. 1 (Leipzig, 1856), 169.
49. Frederic de la Provostaye, "Considération théorique sur la chaleur rayonnante," Annales de chimie et physique, 67 (1863), 5-51.
50. Kayser (ref. 9), 26-27.
51. Ibid., 30f. Kayser estimated that these dependencies were negligible.
52. Paul Drude, Lehrbuch der Optik (Leipzig, 1900), 454-457.
53. Hermann von Helmholtz, Vorlesungen über theoretische Physik. Vol. 6. Vorlesungen über Theorie der Wäerme (Leipzig, 1903).
54. Helmholtz also presented two different proofs, the first of which, in Vorlesungen (ibid.), 162-164, resembles Stewart's argument. As it only applies to radiation absorbed and emitted perpendicular to the surface, the statement is of limited generality. Kayser (ref. 9), 8-12.
55. Helmholtz also presented two different proofs, the first of which, in Vorlesungen (ibid.), 162-164, resembles Stewart's argument. As it only applies to radiation absorbed and emitted perpendicular to the surface, the statement is of limited generality. Kayser (ref. 9), 8-12.
56. Helmholtz (ref. 34), 165f.
57. He claims that the same ratio of emissive and absorptive power "that applies to the total radiation must also apply for each single kind of radiation separately," which would imply constancy with respect to the wavelength. Helmholtz (ref. 34), 166.
58. Woldemar Voigt, "Phänomenologische und atomistische Betrachtungsweise," Emil Warburg, ed., Physik, Kultur der Gegenwart, Ser. 3, 3:1, ed. Emil Warburg (Leipzig, 1915), 714-731, on 715f, Olivier Darrigol, Electrodynamics from Ampére to Einstein (Oxford, 2000), 43-49.
59. Woldemar Voigt, "Phänomenologische und atomistische Betrachtungsweise," Emil Warburg, ed., Physik, Kultur der Gegenwart, Ser. 3, 3:1, ed. Emil Warburg (Leipzig, 1915), 714-731, on 715f, Olivier Darrigol, Electrodynamics from Ampére to Einstein (Oxford, 2000), 43-49.
60. Quotations of Voigt, Helmholtz, and Boltzmann from Klaus Hentschel, "Gustav Robert Kirchhoff und Robert Wilhelm Bunsen," Karl von Meyenn, ed., Die großen Physiker, 1 (Munich, 1997), 416-430, on 416.
61. Ludwig Boltzmann, "Gustav Robert Kirchhoff," in his Populäre Schriften (Leipzig, 1905), 53-75, on 73.
62. Gustav Kirchhoff, Vorlesungen über mathematische Physik, Vierter Band. Vol. 4. Theorie der Wärme (Leipzig, 1894).
63. Friedrich Pockels, "Gustav Robert Kirchhoff," Fritz Schöll, ed., Heidelberger Professoren aus dem 19. Jahrhundert (Heidelberg, 1903), 2, 243-263, on 256f.
64. Hentschel (ref. 39), 430.
65. Gustav Kirchhoff, Abhandlungen über Emission und Absorption (Ostwald's Klassiker der Exacten Wissenschaften, Nr. 100), ed. Max Planck (Leipzig, 1898), 37-41.
66. Wien (ref. 25), 285.
67. Franz Richarz, "Bemerkungen zur Theorie des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 5-8, on 8.
68. Franz Richarz, "Nochmalige Bemerkung zur Theorie des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 359-360.
69. Ernst Pringsheim, "Kirchhoff's Gesetz und die Strahlung der Gase," Annalen der Physik, 45 (1892), 428-459, on 428f.
70. Woldemar Voigt, Thermodynamik. Vol. 2 (Leipzig, 1904), §117 (radiation "occurs" in a cavity), §125 (the thermodynamic treatment best fits unoriented radiation whereas Kirchhoff's law concerns oriented radiation).
71. Ernst Pringsheim, "Herleitung des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 360-364, on 361. Pringsheim presented his proof first in Berlin under the eyes of Planck as "Einfache Herleitung des Kirchhoff'schen Gesetzes," Deutschen Physikalischen Gesellschaf, Verhandlungen, 3 (1901), 77, 81-84. In his first presentation, Prinsheim also introduced his assumptions in the course of the argument, while in 1903 he presented them at the outset.
72. Ernst Pringsheim, "Herleitung des Kirchhoffschen Gesetzes," Zeitschrift für wissenschaftliche Photographie, 1 (1903), 360-364, on 361. Pringsheim presented his proof first in Berlin under the eyes of Planck as "Einfache Herleitung des Kirchhoff'schen Gesetzes," Deutschen Physikalischen Gesellschaf, Verhandlungen, 3 (1901), 77, 81-84. In his first presentation, Prinsheim also introduced his assumptions in the course of the argument, while in 1903 he presented them at the outset.
73. Ibid., 363.
74. Max Planck, Vorlesungen über die Theorie der Wärmestrahlung (Leipzig, 1906), v. "Hierbei bin ich öfters, wo es mir sachliche oder didaktische Gründe nahelegten, von der sonst üblichen Art der Betrachtung abgewichen." The English edition, Theory of heat radiation (New York, 1959, first published 1914), xi, translates "sachliche oder didaktische Gründe" as "the matter presented or considerations regarding the form of presentation."
75. Max Planck, Vorlesungen über die Theorie der Wärmestrahlung (Leipzig, 1906), v. "Hierbei bin ich öfters, wo es mir sachliche oder didaktische Gründe nahelegten, von der sonst üblichen Art der Betrachtung abgewichen." The English edition, Theory of heat radiation (New York, 1959, first published 1914), xi, translates "sachliche oder didaktische Gründe" as "the matter presented or considerations regarding the form of presentation."
76. Planck, Vorlesungen (ref. 53), 2 (English trans., 2).
77. Ibid., 27 (English trans., 25).
78. Ibid., 43 (English trans., 40).
79. Ibid., 39 (English trans., 37).
80. Ibid., 43 (English trans., 40).
81. Wien (ref. 25), 282-357, on 285-287.
82. Woldemar Voigt, "Über die Proportionalität von Emissions- und Absorptionsvermögen," Annalen der Physik, 67 (1899), 366-387. Here he demonstrated that, for the emission and absorption of periodic and homogeneous oscillations, Kirchhoff's law does not hold (p. 373).
83. Max Born and Rudolf Ladenburg, "Über das Verhältnis von Emissions- und Absorptionsvermögen bei stark absorbierenden Körpern," Physikalische Zeitschrift, 12 (1911), 198-202, on 198. "The possibility that in this case the combination of the thermodynamic and the electrodynamic point of view might give rise to contradictions exists and has only gotten a bit out of sight by the far greater difficulties that arise from the derivation of the complete radiation formula."
84. Leo Corry, "Hilbert and physics (1900-1915)," in Jeremy Gray, ed., The symbolic universe. Geometry and physics 1890-1930 (Oxford, 1999), 145-188; Arne Schirrmacher: "Planting in his neighbor's garden: David Hilbert and early Göttingen quantum physics," Physics in perspective, 5 (2003), 4-20.
85. Leo Corry, "Hilbert and physics (1900-1915)," in Jeremy Gray, ed., The symbolic universe. Geometry and physics 1890-1930 (Oxford, 1999), 145-188; Arne Schirrmacher: "Planting in his neighbor's garden: David Hilbert and early Göttingen quantum physics," Physics in perspective, 5 (2003), 4-20.
86. On Hilbert's reputation for controversial presentations cf. the report on the 1903 meeting in Naturwissenschaftliche Rundschau, 18 (1903), 553-556, on 554, with the following characterization of a Hilbert-Boltzmann dispute: "At the end [of the talk] the speaker and Mr. L. Boltzmann (Vienna) engaged in an extremely lively argument. We all know that nothing can raise one's own self-esteem as much as watching accepted authorities quarrel over a question and the fight of words was received by the audience with noisy amusement. It would be correct to say that the case of stability under discussion can be maintained readily in a physical-experimental sense, while the question of 'transcendental stability' in which not even one infinitesimal particle may acquire a finite velocity from an infinitesimal impulse, must remain undecided." For the physicists, Hilbert's problem was "transcendental," not something many of them would want to discuss.
87. Hilbert (ref. 1), 5. The manuscript deviates from the published paper only in marked passages, like those quoted. Hilbert provided reprints of his "Begründung der kinetischen Gastheorie," Mathematische Annalen, 72 (1912), 562-577 at the meeting.
88. Hilbert (ref. 1), 5. The manuscript deviates from the published paper only in marked passages, like those quoted. Hilbert provided reprints of his "Begründung der kinetischen Gastheorie," Mathematische Annalen, 72 (1912), 562-577 at the meeting.
89. Hilbert remarked that this book gave rise to his work on radiation theory. David Hilbert, "Begründung der elementaren Strahlungstheorie," Deutschen Mathematiker Vereinigung, Jahresberichte, 22 (1913), 1-20, on 18.
90. Hermann Minkowski, "Wärmestrahlung," notes to his lecture course, summer term 1907, in HP, 707, p. 2.
91. David Hilbert, Integralgleichungen (Leipzig, 1912).
92. Hilbert to Einstein, 30 Feb 1912, asking for Einstein's "theoretical works on gas and radiation theory," Einstein collected papers. Vol. 5, 439.
93. Ewald to Hilbert, 11 Apr 1912, HP, 98, item 1.
94. "Strahlungstheorie," summer 1912, notes taken by Erich Hecke, typescript at Mathematisches Institut Göttingen.
95. David Hilbert, "Begründung der elementaren Strahlungstheorie, " in Akademie der Wissenschaften, Göttingen, Math.-Phys. Klasse, Nachrichten (1912), 773-789, Physikalische Zeitschrift, 13 (1912), 1056-1064.
96. David Hilbert, "Begründung der elementaren Strahlungstheorie, " in Akademie der Wissenschaften, Göttingen, Math.-Phys. Klasse, Nachrichten (1912), 773-789, Physikalische Zeitschrift, 13 (1912), 1056-1064.
97. Gesellschaft deutscher Naturforscher und Ärzte, Verhandlungen, 84 (1913), part II, 78. According to Physikalische Zeitschrift, 13 (1912), 1009, ninety physicists attended the meeting and the main interest for them was the joint session with the mathematical section with talks by Hilbert, Nernst and von Smoluchowski.
98. Gesellschaft deutscher Naturforscher und Ärzte, Verhandlungen, 84 (1913), part II, 78. According to Physikalische Zeitschrift, 13 (1912), 1009, ninety physicists attended the meeting and the main interest for them was the joint session with the mathematical section with talks by Hilbert, Nernst and von Smoluchowski.
99. Hilbert (ref. 71), 1062.
100. Hilbert (ref. 1), p. 15f.
101. Ibid; Hilbert (ref. 71), 1064.
102. Ibid; Hilbert (ref. 71), 1064.
103. Kayser (ref. 9), 30.
104. Hilbert (ref. 71), 1064.
105. 1; A, the absorption along the path, i.e. |α ds|.
106. Ibid., 1057.
107. Kayser (ref. 9), 27, 37-38; Wien (ref. 26), 285.
108. Kayser (ref. 9), 27, 37-38; Wien (ref. 26), 285.
109. Max Born, "Hilbert und die Physik," Die Naturwissenschaften, 10 (1922), 88-93, on 90f; Leo Corry, "Hilbert on kinetic theory and radiation theory (1912-1914)," The mathematical intelligencer, 20 (1998), 52-58.
110. Max Born, "Hilbert und die Physik," Die Naturwissenschaften, 10 (1922), 88-93, on 90f; Leo Corry, "Hilbert on kinetic theory and radiation theory (1912-1914)," The mathematical intelligencer, 20 (1998), 52-58.
111. Carathéodory to Hilbert, 12 Dec 1912, HP, 55, item 4.
112. Ibid. This criticism was not one of Hilbert's arguments, but one of his assumptions, since Hilbert had explicitly required that there was no heat conduction. Hubert (ref. 65), 2.
113. Born to Hilbert, 7 Jan 1913, HP, 40A, item 4.
114. Born characterized Pringsheim as a "quiet thinker, elegant in manners and attire, cautious and reserved in his statements, modest and unobtrusive." Max Born, My life (New York, 1978), 123.
115. Hilbert (ref. 65).
116. Carathéodory to Hilbert, 4 Apr, 1913, HP, 55, item 5.
117. Ernst Pringsheim, "Bemerkungen zu der Abhandlung des Herrn D. Hilbert 'Begründung der elementaren Strahlungstheorie'," Physikalische Zeitschrift, 14 (1913), 589-591, dated 15 Apr.
118. David Hilbert, "Bemerkungen zur Begründung der elementaren Strahlungstheorie," Akademie der Wissenschaften, Göttingen, Math-Phys. Klasse, Nachrichten (1913), 409-416 and Physikalische Zeitschrift, 14 (1913), 592-595, on 592.
119. David Hilbert, "Bemerkungen zur Begründung der elementaren Strahlungstheorie," Akademie der Wissenschaften, Göttingen, Math-Phys. Klasse, Nachrichten (1913), 409-416 and Physikalische Zeitschrift, 14 (1913), 592-595, on 592.
120. Hilbert (ref. 65), 19.
121. Pringsheim (ref. 88), 589.
122. Ibid., 590.
123. Ibid., 591.
124. Hilbert (ref. 89), 594. Hilbert's paper was received by the Journal three weeks after Pringsheim's critique.
125. Pringsheim (ref. 88), 590.
126. Ernst Pringsheim "Über Herrn Hilberts axiomatische Darstellung der elementaren Strahlungstheorie," Physikalische Zeitschrift, 14 (1913), 847-850, on 847.
127. Leo Corry, "David Hilbert and the axiomatization of physics (1894-1905)," Archive for history of exact sciences, 51 (1997), 83-198.
128. Pringsheim (ref. 96), 848f.
129. Hilbert (ref. 65), 18.
130. Planck to Hilbert, 4 Oct 1912, HP, 308A, item 1.
131. Max Abraham, Theorie der Elektrizität. Vol. 2. Elektromagnetische Theorie der Strahlung (Leipzig, 1905, 1908). Planck to Hilbert, 20 Oct 1912, and 24 Jan 1913, HP, 308 A, items 2 and 3. Planck explained to Hilbert that a certain equation in Abraham's book (no. 227, p. 340, 2nd edn.) is a simple consequence of the second law of thermodynamics.
132. Constructing counter-examples was a typical ingredient of Hilbert's axiomatic method. Cf. his demonstration of the independence of the parallel axiom in Euclidean geometry in David Hilbert, "Grundlagen der Geometrie," Festschrift zur Feier der Enthüllung des Gauss-Weber Denkmals in Göttingen (Leipzig, 1899), chapt. 2 §10.
133. Hilbert (ref. 65), 18.
134. Planck to Hilbert, 4 Apr 1913, HP, 308A, item 4. Hilbert acknowledged the criticism regarding the velocity of propagation in David Hilbert, "Zur Begründung der elementaren Strahlungstheorie (Dritte Mitteilung)," Akademie der Wissenschaften, Göttingen, Math.-Phys. Klasse, Nachrichten (1914), 275-298, on 277; also in Physikalische Zeitschrift, 15 (1914) 878-889, and Hilbert, Gesammelte Abhandlungen. Vol. 3 (New York, 1965), 238-257. In the text of the Gesammelte Abhandlungen the phase velocity that Hilbert initially took as propagation velocity was tacitly corrected to the more appropriate group velocity.
135. Planck to Hilbert, 4 Apr 1913, HP, 308A, item 4. Hilbert acknowledged the criticism regarding the velocity of propagation in David Hilbert, "Zur Begründung der elementaren Strahlungstheorie (Dritte Mitteilung)," Akademie der Wissenschaften, Göttingen, Math.-Phys. Klasse, Nachrichten (1914), 275-298, on 277; also in Physikalische Zeitschrift, 15 (1914) 878-889, and Hilbert, Gesammelte Abhandlungen. Vol. 3 (New York, 1965), 238-257. In the text of the Gesammelte Abhandlungen the phase velocity that Hilbert initially took as propagation velocity was tacitly corrected to the more appropriate group velocity.
136. Planck to Hilbert, 4 Apr 1913, HP, 308A, item 4. Hilbert acknowledged the criticism regarding the velocity of propagation in David Hilbert, "Zur Begründung der elementaren Strahlungstheorie (Dritte Mitteilung)," Akademie der Wissenschaften, Göttingen, Math.-Phys. Klasse, Nachrichten (1914), 275-298, on 277; also in Physikalische Zeitschrift, 15 (1914) 878-889, and Hilbert, Gesammelte Abhandlungen. Vol. 3 (New York, 1965), 238-257. In the text of the Gesammelte Abhandlungen the phase velocity that Hilbert initially took as propagation velocity was tacitly corrected to the more appropriate group velocity.
137. Planck to Hilbert, 15 Apr 1913, HP, 308A, item 5.
138. Hilbert (ref. 89), 593.
139. Hilbert (ref. 104), 276, Hilbert's emphasis.
140. Wilhelm Behrens, "Lichtfortpflanzung in parallel geschichteten Medien," Mathematische Annalen, 76 (1915), 380-430. Behrens acknowledged (p. 382f) that this work, which showed how to derive the laws of radiation theory from Maxwell's theory in approximation, was motivated by Hilbert's publications, 382f.
141. Hilbert (ref. 104), 276f.
142. 2η/a.
143. Hilbert (ref. 104), 291.
144. Ibid., 297. See also Wien (ref. 22).
145. Ibid., 297. See also Wien (ref. 22).
146. David Hilbert, "Die Grundlagen der Physik (Erste Mitteilung)," Akademie der Wissenschaffen, Göttingen, Math-Phys. Klasse (1915), 395-407, on 395.
147. Cf. David Rowe, "Einstein meets Hilbert: At the crossroads of physics and mathematics," Physics in perspective, 3 (2001), 379-424.
148. Albert Einstein, "Strahlungs-Emission und Absorption nach der Quantentheorie, Deutschen Physikalischen Gesellschaft, Verhandlungen, 18 (1916), 318-323, on 321.
149. Ludwig Wittgenstein, Tractatus logico philosophicus (London 1922), sentence no. 6.54.
150. J.L. Heilbron, "The virtual oscillator as a guide to physics students lost in Plato's cave," Science and education, 3 (1994), 177-188.
151. Helmholtz (ref. 29), 169, and (ref. 34), §42.
152. Helmholtz (ref. 29), 169, and (ref. 34), §42.
153. Planck (ref. 53), §46.
154. Rudolf Straubel, "Über einen allgemeinen Satz der geometrischen Optik und einige Anwendungen," Physikalische Zeitschrift, 4 (1903) 114-117, on 115.
155. Hilbert (ref. 70), 59; Manuscript of this part of his 1912 lectures in HP, 728.
156. Hilbert (ref. 70), 59; Manuscript of this part of his 1912 lectures in HP, 728.
157. E.g., Walter Heitler, The quantum theory of radiation (Oxford, 1936).
158. Max Born, "Die Theorie der Wärmestrahlung und die Quantenhypothese," Naturwissenschaften, 1 (1913) 499-504, on 501; lectures on "Kinetische Theorie der Materie" (Winter term 1922) worked out by Luise Spieker, Göttingen Mathematical Institute, on 170; "Über den Sinn der physikalischen Theorien," Naturwissenschaften, 17 (1929), 109-118, on 114; and Born (ref. 85).
159. Max Born, "Die Theorie der Wärmestrahlung und die Quantenhypothese," Naturwissenschaften, 1 (1913) 499-504, on 501; lectures on "Kinetische Theorie der Materie" (Winter term 1922) worked out by Luise Spieker, Göttingen Mathematical Institute, on 170; "Über den Sinn der physikalischen Theorien," Naturwissenschaften, 17 (1929), 109-118, on 114; and Born (ref. 85).
160. Max Born, "Die Theorie der Wärmestrahlung und die Quantenhypothese," Naturwissenschaften, 1 (1913) 499-504, on 501; lectures on "Kinetische Theorie der Materie" (Winter term 1922) worked out by Luise Spieker, Göttingen Mathematical Institute, on 170; "Über den Sinn der physikalischen Theorien," Naturwissenschaften, 17 (1929), 109-118, on 114; and Born (ref. 85).
161. Arnold Sommerfeld, Thermodynamik und Statistik (Wiesbaden, 1952), 131f.
162. Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970), 3, Armin Hermann, Frühgeschichte der Quantentheorie (1899-1913) (Moosbach, 1969). 126. Leon Rosenfeld, "Gustav Robert Kirchhoff," in Dictionary of scientific biography, ed. Charles Coulston Gillispie. Vol. 7 (New York, 1973), 379-383, on 382. Hentschel (ref. 39), 430.
163. Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970), 3, Armin Hermann, Frühgeschichte der Quantentheorie (1899-1913) (Moosbach, 1969). 126. Leon Rosenfeld, "Gustav Robert Kirchhoff," in Dictionary of scientific biography, ed. Charles Coulston Gillispie. Vol. 7 (New York, 1973), 379-383, on 382. Hentschel (ref. 39), 430.
164. Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970), 3, Armin Hermann, Frühgeschichte der Quantentheorie (1899-1913) (Moosbach, 1969). 126. Leon Rosenfeld, "Gustav Robert Kirchhoff," in Dictionary of scientific biography, ed. Charles Coulston Gillispie. Vol. 7 (New York, 1973), 379-383, on 382. Hentschel (ref. 39), 430.
165. Hans Kangro, Vorgeschichte des Planckschen Strahlungsgesetzes (Wiesbaden, 1970), 3, Armin Hermann, Frühgeschichte der Quantentheorie (1899-1913) (Moosbach, 1969). 126. Leon Rosenfeld, "Gustav Robert Kirchhoff," in Dictionary of scientific biography, ed. Charles Coulston Gillispie. Vol. 7 (New York, 1973), 379-383, on 382. Hentschel (ref. 39), 430.
166. Thomas S. Kuhn, Black-body theory and the quantum discontinuity (New York, 1978).
167. Dieter Hoffmann, "Schwarze Körper im Labor, Experimentelle Vorleistungen für Plancks Quantenhypothese," Physikalische Blätter, 56 (2000), 43-47, "On the experimental context of Planck's foundation of quantum theory," Centaurus, 43 (2001), 240-259.
168. Dieter Hoffmann, "Schwarze Körper im Labor, Experimentelle Vorleistungen für Plancks Quantenhypothese," Physikalische Blätter, 56 (2000), 43-47, "On the experimental context of Planck's foundation of quantum theory," Centaurus, 43 (2001), 240-259.
169. Orest D. Chwolson, Lehrbuch der Physik. Vol. 2. Lehre vom Schall (Akustik) - Lehre von der strahlenden Energie (Braunschweig, 1904), 230.
170. Karl Schwarzschild, "Astrophysik," lecture notes taken by Max Born for the winter term, 1904, Manuscript Department, Niedersächsische Staats- und Universitätsbibliothek, Göttingen, Cod. Ms. K. Schwarzschild 13, item 1, 115-119.