PSA 1974 pp 33-75 | Cite as

Theory Generalization Problem Reduction and the Unity of Science

  • Thomas Nickles
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 32)


Although doubtlessly aimed at later developments in physics, Einstein’s famous remark, if interpreted so as to include classical statistical mechanics, nicely captures the spirit of work on the early quantum theory by men like Bohr and Ehrenfest, who, despite their conviction that the classical theories failed, nevertheless mined their riches to the fullest in the development of the new theory. In this paper I try to exhibit and characterize the patterns of reasoning involved in Ehrenfest’s attempts to generalize Planck’s early theory of the linear harmonic oscillator, and I then employ the same historical case as a basis for arguing that the reduction of problems to problems is an important phenomenon which cannot be fully understood in terms of the reduction of theories. Before turning to Ehrenfest, let me point out the central relevance of these issues to the problem of the unity of science.


Theory Reduction Anharmonic Oscillator Problem Reduction Quantization Problem Adiabatic Invariant 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bohr, N.: 1913, ‘On the Constitution of Atoms and Molecules’, Part I, reprinted in D. ter Haar (ed.), The Old Quantum Theory, Pergamon Press, Oxford, 1967, pp. 132–159.Google Scholar
  2. [2]
    Bohr, N.: 1918, ‘On the Quantum Theory of Line-Spectra’, Part I, reprinted in (36), pp. 95–137.Google Scholar
  3. [3]
    Burgers, J. M.: 1917, ‘Die adiabatischen Invarianten bedingt periodischer Systeme’, Annalen der Physik 52, 195–202.CrossRefGoogle Scholar
  4. [4]
    Debye, P.: 1914, ‘Zustandgleichung und Quantenhypothese mit einem Anhang über Wärmeleitung’, in Vorträge über die Kinetische Theorie der Materie und der Elektrizität, Teubner, Leipzig, pp. 19–60.Google Scholar
  5. [5]
    Ehrenfest, P.: 1905, ‘Uber die physikalischen Voraussetzungen der Planck’schen Theorie der irreversiblen Strahlungsvorgänge’, reprinted in (16), pp. 88–101.Google Scholar
  6. [6]
    Ehrenfest, P.: 1911, ‘Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle?’ Reprinted in (16), pp. 185–212.Google Scholar
  7. [7]
    Ehrenfest, P.: 1913, ‘A Mechanical Theorem of Boltzmann and its Relation to the Theory of Quanta’, reprinted in (16), pp. 340–346.Google Scholar
  8. [8]
    Ehrenfest, P.: 1914, ‘Zum Boltzmannschen Entropie-Wahrscheinlichkeits-Theorem’, reprinted in (16), pp. 347–352.Google Scholar
  9. [9]
    Ehrenfest, P.: 1916, ‘On Adiabatic Changes of a System in Connection with the Quantum Theory’, reprinted in (16), pp. 378–399. An abbreviated version, reprinted in (36), appeared in 1917 with the title, ‘Adiabatic Invariants and the Theory of Quanta’.Google Scholar
  10. [10]
    Ehrenfest, P.: 1923, ‘Adiabatische Transformationen in der Quantentheorie und ihre Behandlung durch Niels Bohr’, reprinted in (16), pp. 463–470.Google Scholar
  11. [11]
    Einstein, A.: 1905, ‘On a Heuristic Viewpoint About the Creation and Conversion of Light’, reprinted in D. ter Haar (ed.), The Old Quantum Theory, Pergamon Press, Oxford, 1967, pp. 91–107.Google Scholar
  12. [12]
    Einstein, A.: 1936, ‘Physics and Reality’, reprinted in Ideas and Opinions, Crown Publishers, New York, 1954.Google Scholar
  13. [13]
    Heilbron, J. L. and Kuhn, T. S.: 1969, ‘The Genesis of the Bohr Atom’, Historical Studies in the Physical Sciences, Vol. I, pp. 211–290.Google Scholar
  14. [14]
    Jammer, M.: 1966, The Conceptual Development of Quantum Mechanics, McGraw-Hill, New York.Google Scholar
  15. [15]
    Jeans, J. H.: 1905, ‘A Comparison between Two Theories of Radiation’, Nature 72, 293–4.CrossRefGoogle Scholar
  16. [16]
    Klein, M. J. (ed.): 1959, Paul Ehrenfest: Collected Scientific Papers, North Holland Publ. Co., Amsterdam.Google Scholar
  17. [17]
    Klein, M. J.: 1962, ‘Max Planck and the Beginnings of the Quantum Theory’, Archive for History of Exact Sciences 1, 459–479.CrossRefGoogle Scholar
  18. [18]
    Klein, M. J.: 1964, ‘The Origins of Ehrenfest’s Adiabatic Principle’, in H. Guerlac (ed.), Proceedings of the Tenth International Congress on the History of Science, Hermann, Paris, pp. 801–804.Google Scholar
  19. [19]
    Klein, M. J.: 1967, ‘Thermodynamics in Einstein’s Thought’, Science 157, 509–516.CrossRefGoogle Scholar
  20. [20]
    Klein, M. J.: 1970, ‘Maxwell, His Demon, and the Second Law of Thermodynamics’, American Scientist 58, 84–97.Google Scholar
  21. [21]
    Klein, M. J.: 1970, Paul Ehrenfest, Vol. I: The Making of a Theoretical Physicist, North-Holland Publ. Co., Amsterdam.Google Scholar
  22. [22]
    Nickles, T.: 1973, ‘Two Concepts of Intertheoretic Reduction’, Journal of Philosophy 70, 181–201.CrossRefGoogle Scholar
  23. [23]
    Nickles, T.: 1974, ‘Heuristics and Justification in Scientific Research: Comments on Shapere’, in F. Suppe (ed.), The Structure of Scientific Theories, Univ. of Illinois Press, Urbana, pp. 571–589.Google Scholar
  24. [24]
    Planck, M.: 1906, Vorlesungen über die Theorie der Wärmestrahlung, Johann Barth Verlag, Leipzig. The second edition, 1913, appeared in English translation.Google Scholar
  25. [25]
    Planck, M.: 1912, ‘Rapport sur la Loi du Rayonnement Noir et L’Hypothèse des Quantités Élémentaires D’Action’, in P. Langevin and M. De Broglie (eds.), La Théorie du Rayonnement et les Quanta, Gauthier-Villars, Paris. (Proceedings of the First Solvay Congress, 1911.)Google Scholar
  26. [26]
    Post, H. R.: 1971, ‘Correspondence, Invariance, and Heuristics’, Studies in the History and Philosophy of Science 2, 213–255.CrossRefGoogle Scholar
  27. [27]
    Putnam, H.: 1965, ‘How Not to Talk about Meaning’, in R. S. Cohen and M. War-tofsky (eds.), Boston Studies in the Philosophy of Science, Vol. II, D. Reidel, Dordrecht, pp. 205–222.Google Scholar
  28. [28]
    Rayleigh (Lord): 1902, ‘On the Pressure of Vibrations’, Philosophical Magazine 3, 338–346.Google Scholar
  29. [29]
    Richtmyer, F. K., Kennard, E. H., and Lauritsen, T.: 1955, Introduction to Modern Physics, 5th ed., McGraw-Hill, New York.Google Scholar
  30. [30]
    Rosenfeld, L.: 1936, ‘La Première Phase de L’Évolution de la Théorie des Quanta’, Osiris 2, 149–196.CrossRefGoogle Scholar
  31. [31]
    Shapere, D.: 1964, ‘The Structure of Scientific Revolutions’, Philosophical Review 73, 383–394.CrossRefGoogle Scholar
  32. [32]
    Shapere, D.: 1966, ‘Meaning and Scientific Change’, in R. G. Colodny (ed.), Mind and Cosmos, Univ. of Pittsburgh Press, Pittsburgh, pp. 41–85.Google Scholar
  33. [33]
    Shapere, D.: 1971, ‘The Paradigm Concept’, Science 172, 706–709.Google Scholar
  34. [34]
    Tisza, L.: 1963, ‘The Conceptual Structure of Physics’, Reviews of Modern Physics 35, 151–185.CrossRefGoogle Scholar
  35. [35]
    Tomonaga, S.: 1962, Quantum Mechanics, Vol. I, North-Holland Publ. Co., Amsterdam.Google Scholar
  36. [36]
    van der Waerden, B. L. (ed.): 1968, Sources of Quantum Mechanics, Dover Publications, New York.Google Scholar
  37. [37]
    Whittaker, E. T.: 1960, A History of Theories of Aether and Electricity, Vol. II, Harper & Brothers, New York.Google Scholar
  38. [38]
    Yourgrau, W. and Mandelstam, S.: 1968, Variational Principles in Dynamics and Quantum Theory, W. B. Saunders, Philadelphia.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1976

Authors and Affiliations

  • Thomas Nickles
    • 1
  1. 1.University of Illinois at Champaign-UrbanaUSA

Personalised recommendations