Advertisement

Archive for History of Exact Sciences

, Volume 58, Issue 2, pp 97–141 | Cite as

Paul Ehrenfest on the Necessity of Quanta (1911): Discontinuity, Quantization, Corpuscularity, and Adiabatic Invariance

  • Luis NavarroEmail author
  • Enric Pérez
Article

Abstract

Our object in this paper is to study the antecedents, contents, implications, and impact of a not well-known or appreciated paper by EHRENFEST in 1911 on the essential nature of the different quantum hypotheses in radiation theory. After a careful analysis of EHRENFEST’s notebooks, correspondence, and publications, we conclude that the essential points of EHRENFEST’s paper were not perceived to a large extent, and hence that its implications were not considered thoroughly. Specifically, we show that EHRENFEST contributed significantly to the clarifications of the differences between PLANCK’s and EINSTEIN’s respective quantum hypotheses, as well as to those of the concepts ‘‘discontinuity,’’ ‘‘quantization,’’ and ‘‘corpuscularity.’’

Keywords

Radiation Clarification Careful Analysis Essential Point Essential Nature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    BAUER, E. (1913): ‘‘Sur la loi du rayonnement noir et la théorie des quanta. Remarques sur un travail de M. J. de Boissoudy.’’ Comptes Rendus 153, 641–649.Google Scholar
  2. 2.
    BECK, A. (1989): The Collected Papers of Albert Einstein. Vol. 2.The Swiss years: writings, 1900–1909. English translation. Princeton University Press, Princeton.Google Scholar
  3. 3.
    BECK, A. (1993): The Collected Papers of Albert Einstein. Vol. 3.The Swiss years: writings, 1909–1911. English translation. Princeton University Press, Princeton.Google Scholar
  4. 4.
    BECK, A. (1995): The Collected Papers of Albert Einstein. Vol. 5. The Swiss years: correspondence, 1902–1914. English translation. Princeton University Press, Princeton.Google Scholar
  5. 5.
    BERGIA, S., LUGLI, N., and ZAMBONI, N. (1979): ‘‘Zero-point energy, Planck’s law and the pre-history of stochastic electrodynamics. Part I: Einstein and HOPF’s paper of 1910.’’ Annales de la Fondation Louis de Broglie 4, 295–317.Google Scholar
  6. 6.
    BERGIA, S. and NAVARRO, L. (1988): ‘‘Recurrences and continuity in Einstein’s research on radiation between 1905 and 1916.’’ Archive for History of Exact Sciences 38, 79–99.Google Scholar
  7. 7.
    BERGIA, S. and NAVARRO, L. (1997): ‘‘Early quantum concepts and the theorem of equipartition of energy in Einstein’s work (1905–1925).’’ Physis 34, 183–223.Google Scholar
  8. 8.
    BOISSOUDY, J. DE (1913): ‘‘Sur une nouvelle forme de la loi du rayonnement noir et de l’hypothèse des quanta.’’ Comptes Rendus 153, 385–396.Google Scholar
  9. 9.
    BUCKINGHAM, E. (1912): ‘‘On the deduction of Wien’s displacement law.’’ Philosophical Magazine 23, 920–931.Google Scholar
  10. 10.
    BUCKINGHAM, E. (1914): ‘‘On physically similar systems; illustrations of the use of dimensional equations.’’ Physical Review 4, 345–376.Google Scholar
  11. 11.
    COHEN, R. S. and STACHEL, J. J. (eds.) (1979): Selected Papers of Léon Rosenfeld. (Boston Studies in the Philosophy of Science, Vol. XXI.) D. Reidel, Dordrecht.Google Scholar
  12. 12.
    DARRIGOL, O. (1991): ‘‘Statistics and combinatorics in early quantum theory, II: Early symptoma of indistinguishability and holism.’’ Historical Studies in the Physical Sciences 21, 237–298.Google Scholar
  13. 13.
    DEBYE, P. (1910): ‘‘Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung.’’ Annalen der Physik 33, 1427–1434.Google Scholar
  14. 14.
    EHRENFEST, P. (1905): ‘‘Über die physikalische Vorausetzungen der Planck’schen Theorie der irreversiblen Strahlungsvorgänge.’’ Sitzungberichte, Akademie der Wissenschaften, Wien, Abteilung II, 1301–1314. Reprinted in KLEIN (1959a), 88–101.Google Scholar
  15. 15.
    EHRENFEST, P. (1906a): ‘‘Bemerkung zu einer neuen Ableitung des Wienschen Verschiebungsgesetzes.’’ Physikalische Zeitschrift 7, 527–528. Reprinted in KLEIN (1959a), 119–120.Google Scholar
  16. 16.
    EHRENFEST, P. (1906b): ‘‘Zur Planckschen Strahlungstheorie.’’ Physikalische Zeitschrift 7, 528–532. Reprinted in KLEIN (1959a), 120–124.Google Scholar
  17. 17.
    EHRENFEST, P. (1906c): ‘‘Bemerkung zu einer neuen Ableitung des Wienschen Verschiebungsgesetzes. Antwort auf Herr Jeans’ Entgegnung.’’ Physikalische Zeitschrift 7, 850–852. Reprinted in KLEIN (1959a), 125–127.Google Scholar
  18. 18.
    EHRENFEST, P. (1911): ‘‘Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle?’’ Annalen der Physik 36, 91–118. Reprinted in KLEIN (1959a), 185–212.Google Scholar
  19. 19.
    EHRENFEST, P. (1913): ‘‘A mechanical theorem of BOLTZMANN and its relation to the theory of energy quanta.’’ Proceedings Amsterdam Academy 16, 591–597. Reprinted in KLEIN (1959a), 340–346.Google Scholar
  20. 20.
    EHRENFEST, P. (1914): ‘‘Zum Boltzmannschen Entropie-Wahrscheinlichkeits-Theorem.’’ Physikalische Zeitschrift 15, 657–663. Reprinted in KLEIN (1959a), 347–352.Google Scholar
  21. 21.
    EHRENFEST, P. (1916): ‘‘On adiabatic changes of a system in connection with the quantum theory.’’ Proceedings Amsterdam Academy 19, 576–597. Reprinted in KLEIN (1959a), 378–399.Google Scholar
  22. 22.
    EHRENFEST, P. (1923): ‘‘Adiabatische Transformationen in der Quantentheorie und ihre Behandlung durch Niels Bohr.’’ Die Naturwissenschaften 11, 543–550. Reprinted in KLEIN (1959a), 463–470.Google Scholar
  23. 23.
    EHRENFEST, P. and T. (1990): The conceptual foundations of the statistical approach in mechanics (English translation by J. Moravcsik). Dover Publications, New York. (Originally published in 1959 by Cornell University Press, Ithaca.) The original German version appeared in 1912: Encyklopädie der Mathematischen Wissenschaften. B. G. Teubner, Leipzig, IV 2, II, Heft 6. Reprinted in KLEIN (1959a), 213–302.Google Scholar
  24. 24.
    EHRENFEST, P. and KAMERLINGH-ONNES, H. (1914): ‘‘Simplified deduction of the formula from the theory of combinations which Planck uses as the basis of his radiation theory.’’ Proceedings Amsterdam Academy 17, 870–873. Reprinted in KLEIN (1959a), 353–356.Google Scholar
  25. 25.
    EINSTEIN, A. (1905): ‘‘Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtpunkt.’’ Annalen der Physik 17, 132–148. Reprinted in STACHEL (1989), 149–169. English translation in BECK (1989), 86–103.Google Scholar
  26. 26.
    EINSTEIN, A. (1906): ‘‘Zur Theorie der Lichterzeugung und Lichtabsorption.’’ Annalen der Physik 20, 199–206. Reprinted in STACHEL (1989), 349–358. English translation in BECK (1989), 192–199.Google Scholar
  27. 27.
    EINSTEIN, A. (1909): ‘‘Über die Entwickelung unserer Anschauungen über das Wesen und die Konstitution der Strahlung.’’ Physikalische Zeitschrift 10, 817–825. Reprinted in STACHEL (1989), 563–583. English translation in Beck (1989), 379–394.Google Scholar
  28. 28.
    EINSTEIN, A. (1912a): ‘‘Thermodynamische Begründung des photochemischen Äquivalentgesetzes.’’ Annalen der Physik 37, 832–838 and 38, 881–884. Reprinted in KLEIN et al. (1995), 114–121 and 165–170.Google Scholar
  29. 29.
    EINSTEIN, A. (1912b): ‘‘Anwort auf eine Bemerkung von J. Stark:,, Über Anwendung des Planckschen Elementargesetzes\(\ldots\) ‘’.’’ Annalen der Physik 38, 888. Reprinted in KLEIN et al. (1995), 171–173.Google Scholar
  30. 30.
    EINSTEIN, A. (1916): ‘‘Zur Quantentheorie der Strahlung.’’ Physikalische Gesellschaft Zürich. Mitteilungen 16, 47–62. A reedition of this paper was published in 1917 in Physikalische Zeitschrift 18, 121–128; this is the paper usually quoted. Reprinted in KOX et al. (1996), 381–398. English translation in ENGEL (1997), 220–233.Google Scholar
  31. 31.
    EINSTEIN, A. and HOPF, L. (1910): ‘‘Statistische Untersuchung der Bewegung eines Resonators in einem Strahlungsfeld.’’ Annalen der Physik 33, 1105–1115. Reprinted in KLEIN et al. (1993), 270–280. English translation in BECK (1993), 220–230. English translation and commentary in BERGIA et al. (1979).Google Scholar
  32. 32.
    ENGEL, A. (1997): The Collected Papers of Albert Einstein. Vol. 6.The Berlin years: writings, 1914–1917. English translation. Princeton University Press, Princeton.Google Scholar
  33. 33.
    EWALD, P (1913): ‘‘Bericht über die Tagung der British Association in Birmingham (10 bis 17. September).’’ Physikalische Zeitschrift 14, 1297–1307.Google Scholar
  34. 34.
    GARBER, E. (1976): ‘‘Some reactions to Planck’s law, 1900–1914.’’ Studies in History and Philosophy of Science 7, 89–126.Google Scholar
  35. 35.
    GIBBS, J. W. (1902): Elementary principles in statistical mechanics. Yale University Press, Yale. Reprinted in 1981: Woodbridge (Connecticut), Ox Bow Press.Google Scholar
  36. 36.
    GILLISPIE, C. C. (ed.) (1978): Dictionary of Scientific Biography. Charles Scribner’s Sons, New York. (8 Vols.)Google Scholar
  37. 37.
    GRIGORIAN, A. T. (1978): ‘‘Ioffé, Abram Fedorovich.’’ In GILLISPIE (1978), Supplement I, 251–252.Google Scholar
  38. 38.
    HENTSCHEL, A. M. (1998): The Collected Papers of Albert Einstein. Vol. 8. The Berlin years: correspondence, 1914–1918. English translation. Princeton University Press, Princeton.Google Scholar
  39. 39.
    HERMANN, A. (1971): The genesis of quantum theory (1899–1913). MIT Press, Cambridge. (English translation by Claude W. Nash.) Original German version, 1969: Frühgeschichte der Quantentheorie (1899–1913). Physik Verlag, Mosbach/Baden.Google Scholar
  40. 40.
    IOFFÉ, A. (1911): ‘‘Zur Theorie der Strahlungserscheinungen.’’ Annalen der Physik 36, 534–552.Google Scholar
  41. 41.
    ISHIWARA, J. (1912): ‘‘Das photochemische Gesetz und die molekulare Theorie der Strahlung.’’ Physikalische Zeitschrift 13, 1142–1151.Google Scholar
  42. 42.
    JAMMER, M. (1966): The conceptual development of quantum mechanics. Mc-Graw Hill, New York.Google Scholar
  43. 43.
    JEANS, J. H. (1905): ‘‘On the laws of radiation.’’ Proceedings of the Royal Society of London 76, 545–552.Google Scholar
  44. 44.
    JEANS, J. H. (1906): ‘‘Bemerkung zu einer neuen Ableitung des WIENschen Verschiebungsgesetzes. Erwiderung auf Herrn P. Ehrenfests Abhandlung.’’ Physikalische Zeitschrift 7, 667.Google Scholar
  45. 45.
    JEANS, J. H. (1910): ‘‘On non-Newtonian mechanical systems, and Planck’s theory of radiation.’’ Philosophical Magazine 20, 943–954.Google Scholar
  46. 46.
    JEANS, J. H. (1914): Report on radiation and the quantum-theory. The Electrician, London.Google Scholar
  47. 47.
    KANGRO, H. (1976): Early history of Planck’s radiation law. Taylor and Francis. London. Original German version, 1970: Vorgeschichte des Planckschen Strahlungsgesetzes. Franz Steiner Verlag GmbH, Wiesbaden.Google Scholar
  48. 48.
    KLEIN, M. J. (ed.) (1959a): Paul Ehrenfest: collected scientific papers. North-Holland, Amsterdam; Interscience, New York.Google Scholar
  49. 49.
    KLEIN, M. J. (ed.) (1959b): ‘‘Ehrenfest’s contributions to the development of quantum statistics. I and II.’’ Proc. Koninklijke Akademie van Wettenschapen te Amsterdam B62, 41–50, 51–62.Google Scholar
  50. 50.
    KLEIN, M. J. (1985): Paul Ehrenfest. Vol. 1. The making of a theoretical physicist. Elsevier Science Publishers, Amsterdam. First edition 1970.Google Scholar
  51. 51.
    KLEIN, M. J., KOX, A. J., RENN, J., and SCHULMANN, R. (eds.) (1993): The Collected Papers of Albert Einstein. Vol. 3. The Swiss years: writings, 1909-1911. Princeton University Press, Princeton.Google Scholar
  52. 52.
    KLEIN, M. J., KOX, A. J., RENN, J., and SCHULMANN, R. (eds.) (1995): The Collected Papers of Albert Einstein. Vol. 4. The Swiss years: writings, 1912–1914. Princeton University Press, Princeton.Google Scholar
  53. 53.
    KOX, A. J., KLEIN, M. J., and SCHULMANN, R. (eds.) (1996): The Collected Papers of Albert Einstein. Vol. 6. The Berlin years: writings, 1914–1917. Princeton University Press, Princeton.Google Scholar
  54. 54.
    KRUTKOW, G. (1914a): ‘‘Aus der Annahme unabhängiger Licht-quanten folgt die Wiensche Strahlungsformel.’’ Physikalische Zeitschrift 15, 133–136.Google Scholar
  55. 55.
    KRUTKOW, G. (1914b): ‘‘Bemerkung zu Herrn Wolfkes Note: Welche Strahlungsformel folgt aus der Annahme der Lichtatome?’’ Physikalische Zeitschrift 15, 363–364.Google Scholar
  56. 56.
    KUHN, T. S. (1978): Black–body theory and the quantum discontinuity, 1894–1912. Oxford University Press, New York.Google Scholar
  57. 57.
    KUHN, T. S., HEILBRON, J. L., FORMAN, P., and ALLEN, L. (1967): Sources for history of quantum physics. An inventary and report. The American Philosophical Society, Philadelphia.Google Scholar
  58. 58.
    LANGEVIN, P. and DE BROGLIE, M. (eds.) (1912): La théorie du rayonnement et les quanta. Gauthier-Villars, Paris.Google Scholar
  59. 59.
    LARMOR, J. (1910): ‘‘On the statistical theory of radiation.’’ Philosophical Magazine 20, 350–353.Google Scholar
  60. 60.
    LORENTZ, H. A. (1901a): ‘‘The theory of radiation and the second law of thermodynamics.’’ Proceedings Amsterdam Academy 3, 436–450.Google Scholar
  61. 61.
    LORENTZ, H. A. (1901b): ‘‘Boltzmann’s and Wien’s laws of radiation.’’ Proceedings Amsterdam Academy 3, 607–620.Google Scholar
  62. 62.
    LORENTZ, H. A (1910): ‘‘Alte und neue Fragen der Physik.’’ Physikalische Zeitschrift 11, 1234–1257.Google Scholar
  63. 63.
    McCORMMACH, R. (1967): ‘‘Henri Poincaré and the quantum theory.’’ Isis 58, 37–55.Google Scholar
  64. 64.
    MOSKOVCHENKO, N. Ia. and FRENKEL, V. Ia. (eds.) (1990): Ehrenfest-Ioffe. Nauchnaya perepiska 1907–1933 gg. Nauka, Leningrad. Google Scholar
  65. 65.
    NATANSON, L. (1911): ‘‘Über die statistische Theorie der Strahlung.’’ Physikalische Zeitschrift 12, 659–666.Google Scholar
  66. 66.
    NERI, D. (1986): ‘‘Una nota su come Ehrenfest giunse alla formulazione del principio adiabatico.’’ Rivista di Storia della Scienza 3, 375–383.Google Scholar
  67. 67.
    PLANCK, M. (1901): ‘‘Ueber das Gesetz der Energieverteilung in Normalspectrum.’’ Annalen der Physik 4, 553–563. Reprinted in PLANCK (1958), Vol. 1, 717–727.Google Scholar
  68. 68.
    PLANCK, M. (1906): Vorlesungen über die Theorie der Wärmestrahlung. J. A. Barth, Leipzig. Reprinted in PLANCK (1988), 241–470.Google Scholar
  69. 69.
    PLANCK, M. (1910): ‘‘Zur Theorie der Wärmestrahlung.’’ Annalen der Physik 31, 758–768. Reprinted in PLANCK (1958), Vol. 2, 237–247.Google Scholar
  70. 70.
    PLANCK, M. (1958): Physikalische Abhandlungen und Vorträge. 3 Vols. F. Vieweg und Sohn, Braunschweig.Google Scholar
  71. 71.
    PLANCK, M. (1988): The theory of heat radiation. Tomash, Los Angeles. This book contains the original German edition of Vorlesungen über die Theorie der Wärmestrahlung, 1906; it also contains the English translation, 1914, of the second German edition, 1913.Google Scholar
  72. 72.
    POINCARÉ, H. (1911): ‘‘Sur la théorie des quanta.’’ Comptes Rendus 153, 1103–1108.Google Scholar
  73. 73.
    POINCARÉ, H. (1912): ‘‘Sur la théorie des quanta.’’ Journal de Physique Théorique et Appliquée 2, 5–34.Google Scholar
  74. 74.
    PRENTIS, J. J. (1995): ‘‘Poincaré’s proof of the quantum discontinuity of nature.’’ American Journal of Physics 63, 339–350.Google Scholar
  75. 75.
    RAYLEIGH, LORD (1902). ‘‘On the pressure of vibrations.’’ Philosophical Magazine 3, 338–346.Google Scholar
  76. 76.
    ROSENFELD, L. (1936): ‘‘La première phase de l’évolution de la théorie des quanta.’’ Osiris 2, 149–196. English translation in COHEN and STACHEL (1979), 193–234.Google Scholar
  77. 77.
    SIGEKO, N. (2000): ‘‘Ishiwara Jun’s Quantum Theory.’’ Historia Scientarum 71, 112–119.Google Scholar
  78. 78.
    SOMMERFELD (2000): Wissentschaftlicher Briefwechsel. Band 1. 1892–1918. Deutsches Museum, München.Google Scholar
  79. 79.
    STACHEL, J. (ed.) (1989): The Collected Papers of Albert Einstein. Vol. 2. The Swiss years: writings, 1900–1909. Princeton University Press, Princeton.Google Scholar
  80. 80.
    WHEATON, B. (1977): Catalogue of the Paul Ehrenfest Archive at the Museum Boerhaave. Leiden. Communication 151 of the National Museum for the History of Science and Medicine ‘‘Museum Boerhaave’’, Leiden.Google Scholar
  81. 81.
    WIEN, W. (1894): ‘‘Temperatur und Entropie der Strahlung.’’ Annalen der Physik und Chemie 288, 132–165.Google Scholar
  82. 82.
    WILSON, H. A. (1910): ‘‘On the statistical theory of heat radiation.’’ Philosophical Magazine 20, 121–125.Google Scholar
  83. 83.
    WOLFKE, M. (1913a): ‘‘Zur Quantentheorie. Vorläufige Mitteilung.’’ Deutsche Physikalische Gessellschaft, Verhandlungen 15, 1123–1129.Google Scholar
  84. 84.
    WOLFKE, M. (1913b): ‘‘Zur Quantentheorie. Zweite vorläufige Mitteilung.’’ Deutsche Physikalische Gessellschaft, Verhandlungen 15, 1215–1218.Google Scholar
  85. 85.
    WOLFKE, M. (1914a): ‘‘Welche Strahlungsformel folgt aus der Annahme der Lichtatome?’’ Physikalische Zeitschrift 15, 308–310.Google Scholar
  86. 86.
    WOLFKE, M. (1914b): ‘‘Antwort auf die Bemerkung Herrn Krutkows zu meiner Note: Welche Strahlungsformel folgt aus der Annahme der Lichtatome?’’ Physikalische Zeitschrift 15, 463–464.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Departament de Física FonamentalUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations