Abstract
We analyze the collaboration between Bohr and Ehrenfest on the quantum theory in the early 1920s (1920–1923). We focus on their reflections and developments around the adiabatic principle and the correspondence principle, the two pillars of Bohr’s quantum theory of 1922–23. We argue that the evolution of Bohr’s ideas after 1918 brought the two principles closer, subordinating the former to the latter. The examination of the weight Bohr attributed to each principle along the years illustrates very clearly the vicissitudes of Bohr’s theory before the emergence of quantum mechanics, especially with regards to its rejection/inclusion of mechanics.
Similar content being viewed by others
References
Aaserud, F. and H. Kragh (eds.). 2015. One hundred years of the Bohr atom: Proceedings from a conference. Scientia Danica, Series M – Mathematica et physica (Royal Danish Academy of Sciences and Letters, Copenhagen), Vol. 1
Alberts, G. 1994. On connecting socialism and mathematics: Dirk Struik, Jan Burgers, and Jan Tinbergen. Historia Mathematica 21: 280–305
Bohr, N. 1913. On the constitution of atoms and molecules. Philosophical Magazine 26: 1–25, 476–502 and 857–875. Reprinted in [Hoyer 1981, pp. 159–185, 187–214 and 215–233]
Bohr, N. 1916. On the application of the quantum theory to periodic systems. Unpublished paper, intended to appear in the Philosophical Magazine. Reprinted in [Hoyer 1981, pp. 431–461]
Bohr, N. 1918a. On the quantum theory of line spectra, part I: On the general theory. Det Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddeleser 4: 1–36. Reprinted in [Nielsen 1976, pp. 65–102]
Bohr, N. 1918b. On the quantum theory of line spectra, part II: On the hydrogen spectrum. Det Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddeleser 4: 36–100. Reprinted in [Nielsen 1976, pp. 103–166]
Bohr, N. 1921a. Abhandlungen über Atombau aus den Jahren 1913–1916. Geleitwort (Friedrich Vieweg & Sohn, Braunschwieg), IV-XIX. Reprinted in [Nielsen 1976, pp. 308–323]. English version in [Nielsen 1976, pp. 325–337]
Bohr, N. 1921b. Atomic structure. Nature 107: 1921. Reprinted in [Nielsen 1977, pp. 71–82]
Bohr, N. 1921c. Atomic structure. Nature 108: 1921. Reprinted in [Nielsen 1977, pp. 175–180]
Bohr, N. 1921d. The difference between the series spectra of isotopes. Nature 109: 746. Reprinted in [Nielsen 1976, p. 453]
Bohr, N. 1923a. Linienspektren und Atombau. Annalen der Physik 71: 228–288. English version in [Nielsen 1977, pp. 611–656]
Bohr, N. 1923b. The Effect of Electric and Magnetic Fields on Spectral Lines. (The Seventh Guthrie Lecture). Proceedings of the Physical Society of London 35: 275–302. Reprinted in [Nielsen 1976, pp. 415–446]
Bohr, N. 1923c. On the application of the quantum theory to atomic structure. Part II, Theory of the Series Spectra. In [Nielsen 1976, pp. 501–558]. Original German version of the manuscript and English translation
Bohr, N. 1924. On the application of the quantum theory to atomic structure. Part I, The fundamental postulates. Proceedings of the Cambridge Philosophical Society. Supplement (Cambridge University Press, Cambridge). Reprinted in [Nielsen 1976, pp. 457–499]. English version of “Über die Anwendung der Quantentheorie auf den Atombau. I. Die Grundpostulate der Quantentheorie”. Zeitschrift für Physik 13, 1923: 117–165
Bohr, N. 1925. Atomic theory and mechanics. Nature (Suppl.) 116: 845–852 Reprinted in [Stolzenburg 1984, pp. 272–280]. There were seven versions of this paper, three of them in English, two in German, and two in Danish. On the differences among them see [Stolzenburg 1984, pp. 270–271]
Bohr, N., H.A. Kramers and J.C. Slater, 1924. The Quantum Theory of Radiation. Philosophical Magazine 47: 785–802. Reprinted in [Stolzenburg 1984, pp. 99–118]
Born, M. 1922. Über das Modell der Wasserstoffmolekel. Die Naturwissenschaften 10: 677–678. In [Born 1963, pp. 13–14]
Born, M. 1925. Vorlesungen über Atommechanik (Springer, Erster Band, Berlin)
Born, M. 1926. Das Adiabatenprinzip in der Quantenmechanik. Zeitschrift für Physik 40: 167–192. Reprinted in [Born 1963, pp. 258–283]
Born, M. 1960. The mechanics of the atom (Frederick Ungar, New York). English version of [Born 1925]
Born, M. 1963. Ausgewählte Abhandlungen (Vandenhoeck & Ruprecht, Göttingen), Vol. 2
Born, M. (ed.). 1971. The Born-Einstein letters. Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955, with commentaries by Max Born (MacMillan, London). English version by Irene Born from the original German version, of 1969
Burgers, J.M. 1918. Het Atommodel van Rutherford-Bohr. Haarlem, De Erven Loosjes, Ph.D. thesis
Darrigol, O. 1992. From c-numbers to q-numbers: The classical analogy in the history of quantum theory (University of California Press, Berkeley)
Debye, P. 1910. Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung. Annalen der Physik 33: 1427–1434
Debye, P. 1914. Zustandsgleichung und Quantenhypothese mit einen Anhang über Wärmeleitung. In [Planck et al.. 1914, pp. 17–60]
Duncan, A. and M. Janssen. 2015. The Stark effect in the Bohr-Sommerfeld theory and in Schrödinger’s wave mechanics. In [Aaserud 2015, pp. 217–271]
Eckert, M. and K. Märker (eds.). 2000. Arnold Sommerfeld. Wissenschaftlicher Briefwechsel. Band 1: 1892–1918. (Deutsches Museum, München)
Eckert, M. and K. Märker (eds.). 2004. Arnold Sommerfeld. Wissenschaftlicher Briefwechsel. Band 2: 1919–1951 (Deutsches Museum, München)
Ehrenfest, P. 1906. Zur Planckschen Strahlungstheorie. Physikalische Zeitschrift 7: 528–532 Reprinted in [Klein 1959a, pp. 120–124]
Ehrenfest, P. 1913. Bemerkung betreffs der spezifischen Wärme zweiatomiger Gase. Verhandlungen der Deutschen Physikalischen Gesellsachft 12: 451–457. Reprinted in [Klein 1959a, pp. 333–339]
Ehrenfest, P. 1916. On adiabatic changes of a system in connection with the quantum theory. Proceedings of the Amsterdam Academy 19: 576–597. Reprinted in [Klein 1959a, pp. 378–399]
Ehrenfest, P. 1922. The difference between the series spectra of isotopes. Nature 109: 745. Reprinted in [Klein 1959a, p. 451]
Ehrenfest, P. 1923a. Le principe de correspondance. Paper read in the Third Solvay Conference. In [Solvay 1923, pp. 248–254]. Reprinted in [Klein 1959a, pp. 436–442]
Ehrenfest, P. 1923b. Adiabatische Transformationen in der Quantentheorie und ihre Behandlung durch Niels Bohr. Die Naturwissenschaften 11: 543–550. Reprinted in [Klein 1959a, pp. 463–470]
Ehrenfest, P. 1923c. Kann die Bewegung eines Systemes von s Freiheitsgraden mehr als (2s −1)-fach-periodisch sein? Zeitschrift für Physik 19: 242–245. Reprinted in [Klein 1959a, pp. 481–484]
Ehrenfest, P. and G. Breit 1922. A remarkable case of quantization. Proceedings of the Amsterdam Accademy 25: 2–5. Reprinted in [Klein 1959a, pp. 447–450]
Ehrenfest, P. and R.C. Tolman 1924. Weak quantization. Physical Review 24: 287–295. Reprinted in [Klein 1959, pp. 498–506]
Ehrenfest, P. and V. Trkal 1920. Deduction of the dissociation equilibrium from the theory of quanta and a calculation of the chemical constant based on this. Proceedings of the Amsterdam Accademy 23: 162–183. Reprinted in [Klein 1959a, pp. 414–435]
Einstein, A. 1916a. Strahlungs-Emission und – Absorption nach der Quantentheorie. Verhandlungen der Deutschen Physikalischen Gesellsachft 18: 318–323. Reprinted in [Kox et al. 1996, pp. 362–370]. English version in [Engel 1997, pp. 212–216]
Einstein, A. 1916b. Zur Quantentheorie der Strahlung. Physikalische Gesellschaft Zürich. Mitteilungen 16: 47–62. This version was also published in Physikalische Zeitschrift 18 (1917): 121–128. Reprinted in [Kox et al. 1996, pp. 381–398]. English version in [Engel 1997, pp. 220–233]
Einstein, A. and P. Ehrenfest 1922. Quantentheoretische Bemerkungen zum Experiment von Stern und Gerlach. Zeitschrift für Physik 11: 31–34. Reprinted in [Klein 1959, pp. 452–455]. English version in [Kormos 2012b, pp. 243–247]
Engel, A. 1997. The collected papers of Albert Einstein, in The Berlin years: Writings, 1914–1917 (Princeton University Press, Princeton), Vol. 6, English translation of selected texts
Frenkel, V.Ia. 1971. Paul Ehrenfest (Atomizdat, Moscow)
Friedrich, B. and D. Herschbach. 1998. Space quantization: Otto Stern’s lucky star. Daedalus 127: 165–191
Friedrich, B. and D. Herschbach. 2003. Stern and Gerlach: How a bad cigar helped reorient atomic physics. Physics Today 56: 53–59
Gearhart, C.A. 2010. “Astonishing successes” and “bitter disappointment”: The specific heat of hydrogen in quantum theory. Archive for History of Exact Sciences 64: 113–202
Gerlach, W. and O. Stern. 1922. Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Zeitschrift für Physik 9: 349–352
Halpern, O. 1923a. Über den Einfluβ gekreuzter elektrischer und magnetischer Felder auf das Wasserstoffspektrum. Zeitschrift für Physik 18: 287–303
Halpern, O. 1923b. Eine Anwendung der Adiabatenhypothese auf das Ortoheliummodell. Zeitschrift für Physik 18: 344–351
Heisenberg, W. 1925. Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33: 879–893. English version in [Van der Waerden 1968, pp. 261–276]
Hermann, A., K. von Meyenn and V.F. Weisskopf (eds.). 1979. Wolfgang Pauli. Wissenschaftlicher Briefwechsel. Vol I: 1919–1929 (Berlin, Springer)
Hoyer, U. (ed.). 1981. Niels Bohr. Collected works, in Work on atomic physics (1912-1917) (North-Holland, Amsterdam), Vol. 2
Klein, M.J. (ed.). 1959a. Paul Ehrenfest. Collected scientific papers (with an introduction by H.B.G. Casimir) (North-Holland, Amsterdam)
Klein, M.J. 1959b. Ehrenfest’s contributions to the development of quantum statistics. I and II. Proceedings of the Amsterdam Academy B 62: 41–50 and 51–62
Klein, M.J. 1981. Not by discoveries alone: the centennial of Paul Ehrenfest. Physica A 106: 3–14
Klein, M.J. 1985. Paul Ehrenfest. The making of a theoretical physicist (North-Holland, Amsterdam). First edition 1970
Klein, M.J. 1986. Great connections come alive: Bohr, Ehrenfest and Einstein. In The lesson of quantum theory, edited by J. de Boer et al. (North-Holland, Amsterdam), pp. 325–342
Klein, M.J. 2010. Paul Ehrenfest, Niels Bohr, and Albert Einstein: Colleagues and Friends. Physics in Perspective 12: 307–337
Klein, O. 1924. Über die gleichzeitige Wirkung von gekreuzten homogenen elektrischen und magnetischen Feldern auf das Wasserstoffatom. I. Zeitschrift für Physik 22: 109–118
Kormos, D., J. Illy, Z. Rosenkranz and T. Sauer (eds.). 2012a. The Collected Papers of Albert Einstein, in The Berlin years: Writings and Correspondence, January 1922–March 1923 (Princeton University Press, Princeton), Vol. 13
Kormos, D., J. Illy, Z. Rosenkranz and T. Sauer (eds.) 2012b. The collected papers of Albert Einstein. in The Berlin years: Writings and Correspondence, January 1922–March 1923 (Princeton University Press, Princeton), Vol. 13 (English translation supplement)
Kox, A., M.J. Klein and R. Schulmann (eds.). 1996. The collected papers of Albert Einstein, in The Berlin years: Writings, 1914-1917 (Princeton University Press, Princeton), Vol. 6
Kragh, H. 1979. Niels Bohr’s second atomic theory. Historical Studies in the Physical Sciences 10: 123–186
Kragh, H. 2012. Niels Bohr and the Quantum Atom (Oxford University Press, Oxford)
Kramers, H.A. 1919. Intensities of spectral lines. On the application of the quantum theory to the problem of the relative intensities of the components of the fine structure and of the Stark effect of the lines of the hydrogen spectrum. Det kongelige Danske Videnskabernes Selskab. Skrifter. Naturvidenskabelig og Matematisk Afdeling 8: 285–386
Kuhn, T.S., J.L. Heilbron, P. Forman and L. Allen. 1967. Sources for history of quantum physics. An inventory and report (Memoirs of the American Philosophical Society, Philadelphia), Vol. 68
Landé, A. 1919. Das Serienspektrum des Heliums. Physikalische Zeitschrift 20: 228–234
Langevin, P. and M. de Broglie (eds.). 1912. La théorie du rayonnement et les quanta. Rapports et discussions de la réunion tenue à Bruxelles, du 30 octobre au 3 novembre 1911 (Gauthier–Villars, Paris)
Lenz, W. 1924. Über den Bewegungsablauf und die Quantenzustände der gestörten Keplerbewegung. Zeitschrift für Physik 24: 197–207
Mehra J. and H. Rechenberg. 1982. The historical development of quantum theory. Vol. 1 (The quantum theory of Planck, Einstein, Bohr and Sommerfeld: Its foundation and the rise of its difficulties 1900–1925). Vol. 3 (The formulation of matrix mechanics and its modifications) (Springer, New York)
Moskovchenko, N.Ia., V.Ia. Frenkel (eds.) 1990. Ehrenfest-Ioffe. Nauchnaya perepiska 1907-1933 gg (Nauka, Leningrad)
Navarro, L. and E. Pérez. 2004. Paul Ehrenfest on the necessity of quanta (1911): Discontinuity, quantization, corpuscularity, and adiabatic invariance. Archive for History of Exact Sciences 58: 97–141
Navarro, L. and E. Pérez. 2006. Paul Ehrenfest: The genesis of the adiabatic hypothesis, 1911-1914. Archive for History of Exact Sciences 60: 209–267
Nielsen, J.R. (ed.) 1976. Niels Bohr. Collected works, The correspondence principle (1918-1923) (North-Holland, Amsterdam), Vol. 3
Nielsen, J.R. (ed.). 1977. Niels Bohr. Collected works,The periodic system (1920-1923) (North-Holland, Amsterdam), Vol. 4
Pauli, W. 1926. Quantentheorie. In Handbuch der Physik (Springer, Berlin), Vol. 23, pp. 1–278. Reprinted in [Pauli 1964, Vol. 1, pp. 269–548]
Pauli, W. 1964. Collected scientific papers. Edited by R. Kronig and V. F. Weisskopf in two volumes (John Wiley & Sons, New York)
Pérez, E. 2009. Ehrenfest’s adiabatic hypothesis and the old quantum theory, 1916-1918. Archive for History of Exact Sciences 63: 81–127
Pérez, E. and B. Pié i Valls. 2015. Ehrenfest’s adiabatic hypothesis in Bohr’s quantum theory. In [Aaserud 2015, pp. 272–289]
Pié i Valls, B. 2015. Stern-Gerlach experiment in its theoretical context (In Catalan), Ph.D thesis, Barcelona, Universitat de Barcelona
Planck, M. 1906. Vorlesungen über die Theorie der Wärmestrahlung (Barth, Leipzig)
Planck, M., P. Debye, W. Nernst, M. von Smoluchowsky, A. Sommerfeld and H.A. Lorentz. 1914. Vorträge über die kinetische Theorie der Matherie und der Elektrizität (Teubner, Leipzig)
Rayleigh, L. 1902. On the pressure of vibrations. Philosophical Magazine 3: 338–346
Serwer, D. 1977. Unmechanischer Zwang: Pauli, Heisenberg, and the rejection of the mechanical atom, 1923–1925. Historical Studies in the Physical Sciences 8: 189–256
Solvay 1923. Atomes et électrons. Rapports et discussions du Conseil de Physique tenu a Bruxelles, du 1 er au 6 avril 1921 sous les auspices de l’Institut International de Physique Solvay (Gauthier Villars, Paris)
Sommerfeld, A. 1911. Das Plancksche Wirkungsquantum und seine allgemeine Bedeutung für die Molekularphysik. Physikalische Zeitschrift 12: 1057–1069. This is the talk he gave on September 25th in the 83th Naturforscherversammlung in Karlsruhe. Reprinted in [Sommerfeld 1968, Vol. 3, pp. 1–19]
Sommerfeld, A. 1915a. Zur Theorie der Balmerschen Serie. Sitzungsberichte der mathematisch-physikalischen Klasse der K. B. Akademie der Wissenshcaften zu München, pp. 425–458
Sommerfeld, A. 1915b. Die Feinstruktur der Wasserstoff- und der Wasserstoff-ähnlichen Linien. Sitzungsberichte der mathematisch-physikalischen Klasse der K.B. Akademie der Wissenshcaften zu München, pp. 459–500
Sommerfeld, A. 1922. Atombau und Spektrallinien, 3rd edn. (Friedrich Vieweg & Sohn Akt.-Ges, Braunschweig). English translation of 1923 by Henry L. Brose: Atomic Structure and Spectral Lines (Methuen & Co. Ltd, London)
Sommerfeld, A. 1968. Gesammelte Schriften (Friedrich Vieweg & Sohn, Braunschweig), 3 Vols.
Speziali, P. (ed.). 1972. Albert Einstein. Michele Besso. Correspondance 1903-1955 (Hermann, Paris)
Stolzenburg, K. 1984 (ed.). Niels Bohr. Collected works, in The emergence of quantum mechanics (mainly 1924-1926) (North-Holland, Amsterdam), Vol. 5
Unna, I. and T. Sauer 2013. Einstein, Ehrenfest, and the quantum measurement problem. Annalen der Physik 525: A15-A19
Van der Waerden, B.L. 1968. Sources of quantum mechanics (Dover, New York)
Weinert, F. 1995. Wrong theory − right experiment: The significance of the Stern-Gerlach experiments. Studies in History and Philosophy of Science Part B: Studies in History and Phylosophy of Modern Physics 26: 75–86
Wheaton, B. 1977. Catalogue of the Paul Ehrenfest Archive at the Museum Boerhaave. Leyden. Leyden, Communication 151 of the National Museum for the History of Science and Medicine ‘Museum Boerhaave’
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Pérez, E., Pié i Valls, B. Bohr and Ehrenfest: transformations and correspondences in the early 1920s. EPJ H 41, 93–136 (2016). https://doi.org/10.1140/epjh/e2016-60028-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjh/e2016-60028-1