Crisis and the construction of modern theoretical physics

British Journal for the History of Science

Volumn 40, Issue 1, 2007, Pages 25-51

  Seth, Suman ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847710303     PISSN: 00070874     EISSN: 1474001X     Source Type: Journal    
DOI: 10.1017/S0007087406009101     Document Type: Article

References (169)

1. T. S. Kuhn, The Structure of Scientific Revolutions, 2nd edn, Chicago, 1970, 174-210, 181.
2. T. S. Kuhn, The Structure of Scientific Revolutions, Chicago, 1962, 89.
3. For early criticisms of Kuhn's theory and his responses see I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, Volume 4, Cambridge, 1970;
4. Frederick Suppe (ed.), The Structure of Scientific Theories, 2nd edn, Urbana and Chicago, 1977.
5. On 'epistemological crises' and their relationship with Kuhn's theory see A. Macintyre, 'Epistemological crises, dramatic narrative, and the philosophy of science', in Paradigms and Revolutions: Appraisals and Applications of Thomas Kuhn's Philosophy of Science (ed. Gary Gutting), London, 1980, 54-74.
6. In 'Autobiographical notes', written in 1946, Einstein, for example, spoke of two 'fundamental cris[e]s ' that faced physics at the end of the nineteenth century: the instability of Lorentz's electron and Planck's law of heat radiation. 'Reflection of this type', he wrote, 'made it clear to me as long ago as shortly after 1900, i.e. shortly after Planck's trailblazing work, that neither mechanics nor thermodynamics could (except in limiting cases) claim exact validity. By and by I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results'. Albert Einstein, 'Autobiographical notes (in German, and in English translation)', in Albert Einstein: Philosopher-Scientist (ed. Paul Arthur Schilpp), Menasha, WI, 1949, 37, 51, 53.
7. In this account, therefore, crisis and despair become the cause of a search for a new approach. Miller, for example, makes use of this retrospective account in reconstructing Einstein's path towards special relativity. A. I. Miller, 'On Einstein's invention of special relativity', in PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 2: Symposia and Invited Papers (1982), 377-402.
8. See also, originally published in 1961, T. S. Kuhn, 'The function of measurement in modern physical science', in idem, The Essential Tension: Selected Studies in Scientific Tradition and Change, Chicago and London, 1977, esp. 202-13.
9. Kuhn, op. cit. (1), 72.
10. On the crisis around 1900 see e.g. R. McCormmach, 'Editor's foreword', Historical Studies in the Physical Sciences (1970) 2, xi-xx.
11. J. L. Heilbron, 'Fin-de-siècle physics', in Science, Technology and Society in the Time of Alfred Nobel (ed. C. G. Bernhard, E. Crawford and P. Sörbom), Oxford, 1982, 51-73.
12. L. Pyenson, 'The relativity revolution in Germany', in The Comparative Reception of Relativity (ed. T. Glick), Dordrecht, 1987, 59-111.
13. Porter notes the historiographical trend, but contests it, arguing that what Heilbron calls 'descriptionism' should be understood as a 'more optimistic, almost exuberant, view of physics', at least for two prominent philosophers of science: E. Mach and K. Pearson. T. M. Porter, 'The death of the object: fin-de-siècle philosophy of physics', in Modernist Impulses in the Human Sciences, 1870-1930 (ed. Dorothy Ross), Baltimore, 1994, 130.
14. Holton makes a distinction between forces 'outside the laboratory' that spoke of the 'death and decay of science' around 1900 (G. Holton, 'Spengler, Einstein, and the controversy over the end of science', Physis (1991), 28, 543-56, 543, 544) and scientists themselves who were, on the whole, upbeat: 'Some, such as Kelvin and Poincaré, discerned clouds; but the predominant feeling was that of satisfaction, even enthusiasm, with the momentum and direction in which the work was going.'
15. G. Holton, 'Einstein's search for the "Weltbild"', Proceedings of the American Philosophical Society (1981) 125, 1-15, 2.
16. Holton's point is polemical, but not without merit as a historiographical distinction. Many of those, post-Kuhn, who would argue for a fin de siècle crisis of physics would also argue for connections between science and the broader social context, McCormmach, for example, drawing a connection between German physicists and other academics, on the grounds of their collective 'participation in the general crisis mentality of their class'. Talk of this crisis mentality is far less prevalent in his two-volume text on the history of theoretical physics, co-authored with Jungnickel, which largely eschews social and cultural history. C. Jungnickel and R. McCormmach, Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein. Volume 1, The Torch of Mathematics, 1800-1870, Chicago and London, 1990, 22.
17. On the crisis around 1925 see e.g. P. Forman, 'Weimar culture, causality, and quantum theory, 1918-1927: adaptation by German physicists and mathematicians to a hostile intellectual environment', Historical Studies in the Physical Sciences (1971), 3, 1-115;
18. O. Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory, Berkeley, Los Angeles and Oxford, 1992, 175-212;
19. H. Kragh, Quantum Generations: A History of Physics in the Twentieth Century, Princeton, 1999, 155-60.
20. Forman, op. cit. (8); Heilbron, op. cit. (7).
21. T. S. Kuhn, 'Revisiting Planck', Historical Studies in the Physical Sciences (1984), 14, 231-52.
22. Kuhn, op. cit. (1), 84.
23. According to T. K. Rabb, it is this 'retrospective' identification of crisis through its effects that distinguishes the term from any other word used to denote times of trouble: 'crisis is always followed by resolution ... To the extent that, as in medicine, a resolution offers the best proof that a "crisis" has occurred, our evidence of a dividing point will derive mainly from what ensues'. T. K. Rabb, The Struggle for Stability in Early Modern Europe, New York, 1975, 31.
24. It is worth noting that, although Kuhn claimed that the issue of crisis was relatively unimportant in the structure of his overall argument, the response to crisis formed one of only two areas where he modified the main text of Structure for the second edition. The discussion of three responses to crisis replaced the claim of the earlier edition (Kuhn, op. cit. (2), 84) that 'all crises close with the emergence of a new candidate for paradigm and with the subsequent battle over its acceptance'.
25. T. S. Kuhn, 'Reflections on my critics', in Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, Volume 4 (ed. I. Lakatos and A. Musgrave), Cambridge, 1970, 258.
26. L. Boltzmann, 'Josef Stefan', in idem, Populäre Schriften (Leipzig, 1925), 94.
27. Cf. C. Jungnickel and R. McCormmach, Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein. Volume 2, The Now-Mighty Theoretical Physics, Chicago and London, 1990, 347.
28. A. Sommerfeld, 'Die naturwissenschaftlichen Ergebnissen und die Ziele der modernen technischen Mechanik', Physikalische Zeitschrift (1903), 4, 773-82, 782.
29. The translation here is altered from A. Sommerfeld, 'The scientific results and aims of modern applied mechanics', Mathematical Gazette (1903), 3, 26-31.
30. On theoretical physics as a German-dominated speciality see P. Forman, J. L. Heilbron and S. Weart, 'Physics circa 1900: Personnel, funding, and productivity of the academic establishments', Historical Studies in the Physical Sciences (1974), 5, 1-185.
31. L. Pyenson and D. Skopp, "Educating physicists in Germany circa 1900," Social Studies of Science (1977) 7, 329-66. Jungnickel and McCormmach, op. cit. (7).
32. On the 'Cambridge Programme' see P. M. Harman (ed.), Wranglers and Physicists: Studies on Cambridge Physics in the Nineteenth Century, Manchester, 1986.
33. A. Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics, Chicago, 2003.
34. L. Boltzmann, 'On the methods of theoretical physics (Orig. 1892)', in Ludwig Boltzmann: Theoretical Physics and Philosophical Problems (ed. B. McGuiness), Dordrecht, 1974, 11-12, n. 1.
35. 'Vorwort' by F. Klein to E. J. Routh, Die Dynamik der Systeme starrer Körper (Leipzig, 1898), pp. iii-iv.
36. Cf. D. E. Rowe, 'Klein, Hilbert, and the Göttingen mathematical tradition', Osiris (1989), 5, 186-203;
37. Warwick, op. cit. (18), 252-3.
38. K. M. Olesko, Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics, Cornell History of Science Series, Ithaca, 1991, 366-450.
39. The novelty of theoretical physics as a discipline, once a key part of the literature, has been challenged by the periodization offered in what is, on most issues, the definitive account, C. Jungnickel and R. McCormmach's Intellectual Mastery of Nature.
40. Their defence of their dating of the beginning of the field to 1800, however, is weak, and depends on a problematic elision between theoretical physics and physical theory. If the two are assumed to mean the same thing, one wonders why one should stop in 1800, rather than with Newton's natural philosophy, an earlier contribution to 'physical theory'. The authors write, 'Although there had been a body of physical theories for centuries, in Ohm's day, the early nineteenth century, theoretical physics was not a specialized field of study, and it was not to emerge as one for a good part of the century, until nearly the time of Einstein. So, for much of the period covered by our study, our subject, strictly speaking, did not exist. But of course it did, in a practical sense, right from the start. Major contributions to physical theory were made by Ohm and his contemporaries and by their successors throughout the nineteenth century. In the second half of the century, teaching positions were gradually created for theoretical physics...and these positions laid the foundation for the partial separation of physics into the fields of experimental physics and theoretical physics.' Jungnickel and McCormmach, op. cit. (7), 16; added emphasis.
41. Forman has noted this peculiarity of the two-volume history in P. Forman, 'Review: intellectual mastery of nature', Philosophy of Science (1991), 58, 130: 'volume 1 never does arrive at the announced subject, the history of theoretical physics, which scarcely existed as a separate intellectual, let alone institutional, enterprise before 1870'; original emphasis. E. Garber makes a related point, arguing that it is ahistorical to label G. S. Ohm's work 'physics'.
42. She writes, 'To label Ohm as a physicist and his mathematical work as physics was to miss the point of what he was actually trying to accomplish. ... Ohm's experimental results were physically important but his goal was not to produce a physical interpretation of those results in mathematical form.' E. Garber, Language of Physics: The Calculus and the Development of Theoretical Physics in Europe, 1750-1914, Boston, 1999, 159.
43. In general, however, it should be stressed that Garber's desire to draw a sharp line between mathematical and theoretical physics seems overly dogmatic. In particular, her claim that no one 'in Germany used the terms mathematical and theoretical physics interchangeably or simultaneously' (167) is belied by the naming of chairs alone. Note, to take merely one example, that the chair created in 1883 for Woldemar Voigt at Göttingen was in 'theoretical (mathematical) physics'. See, more generally, K. M. Olesko, 'The emergence of theoretical physics in Germany: Franz Neumann and the Königsberg School of Physics, 1830-1890', Cornell University dissertation, 1980.
44. The ambiguity in terms of dominant and shared research areas would not last long. After 1900 theoretical physics can be increasingly defined by the interests of the growing number of its practitioners in what Buchwald has called 'microphysics'. J. Z. Buchwald, From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century, Chicago and London, 1985;
45. J. Z. Buchwald and A. Warwick, Histories of the Electron: The Birth of Microphysics, Cambridge, MA, 2001.
46. Sommerfeld, for example, would be hired to the Munich chair in 1906 - after Lorentz and Boltzmann had both declined it - in large part due to his work on what he described in December of that year as the 'burning questions of electrons'. Sommerfeld to Lorentz, 12 December 1906, reproduced in M. Eckert and K. Märker (eds.), Arnold Sommerfeld: Wissenschaftlicher Briefwechsel, 2 vols., Berlin, Diepholz and München, 2000-4, i, 257-8.
47. See also M. Eckert and W. Pricha, 'Boltzmann, Sommerfeld und die Berufungen auf die Lehrstühle für theoretische Physik in München und Wien, 1890-1914', Mitteilungen der Österreichischen Gesellschaft für Geschichte der Naturwissenschaften (1984), 4, 101-19.
48. McCormmach, op. cit. (7), 16.
49. For an excellent discussion of these debates see Jungnickel and McCormmach, op. cit. (15), 211-53.
50. M. J. Klein, 'Max Planck and the Beginnings of the Quantum Theory', Archive for History of the Exact Sciences (1962), 1, 459-79, 459. Klein shows that Planck paid little attention to a speech Lord Kelvin delivered in 1900 on 'Nineteenth century clouds over the dynamical theory of heat and light', once taken to be evidence of a widespread crisis-sensibility over the questions raised by the equipartition theory and the problems of the ether. Proponents of the electromagnetic view of nature never believed in the applicability of this mechanical principle to what they saw as a fundamentally electromagnetic ether.
51. Kuhn, op. cit. (10), 245.
52. For a discussion of Kuhn's book on black-body theory see M. J. Klein, A. Shimony and T. J. Pinch, 'Paradigm lost? A review symposium', Isis (1979), 70, 429-40.
53. J. Büttner, J. Renn and M. Schemmel, 'Exploring the limits of classical physics: Planck, Einstein, and the structure of a scientific revolution', Max Planck Institute for the History of Science, Preprint Series (2000), 150.
54. Pyenson, op. cit. (7), 84.
55. O. Darrigol, 'The electrodynamic origins of relativity theory', Historical Studies in the Physical and Biological Sciences (1996), 26, 241-312, 276-7.
56. See also O. Darrigol, 'Henri Poincaré's criticism of fin-de-siècle electrodynamics', Studies in History and Philosophy of Modern Physics (1995), 26, 1-44, 23, where he writes, 'at the close of the century Poincaré, and to a lesser extent Wien, seem to have been the only experts to worry about the fate of Newton's third law. In any case, Poincaré was the only one to perceive a major crisis in electromagnetic theory and to expect major modifications'.
57. W. Wien, 'Über die Möglichkeit einer elektromagnetischen Begründung der Mechanik', Annalen der Physik (1901), 5, 501-13.
58. On the electromagnetic world view see T. Hirosige, 'Origins of Lorentz' theory of electrons and the concept of the electromagnetic field', Historical Studies in the Physical Sciences (1969), 1, 151-209;
59. R. McCormmach, 'H. A. Lorentz and the electromagnetic view of nature', Isis (1970), 61, 459-97;
60. R. McCormmach, 'Einstein, Lorentz, and the electron theory', Historical Studies in the Physical Sciences (1970), 2, 41-87;
61. S. Seth, 'Quantum theory and the electromagnetic world-view', Historical Studies in the Physical and Biological Sciences (2004), 35, 67-93.
62. R. McCormmach, Night Thoughts of a Classical Physicist, Cambridge, MA, 1991.
63. Pyenson, op. cit. (7), 65.
64. Heilbron, op. cit. (7), 51.
65. The question of whether descriptionism can be understood as a response to crisis is considered below. Porter (op. cit. (7)) makes the argument for seeing descriptionism as a positive and liberating move, not merely a defensive one. On reformulations of mechanics in the late nineteenth century see e.g. M. J. Klein, 'Mechanical explanation at the end of the nineteenth century', Centaurus (1972), 17, 58-82.
66. M. Planck, 'Antrittsrede zur Aufnahme in die Akademie vom 28. Juni 1894', in Physikalische Abhandlungen und Vorträge, Braunschweig, 1958, 1-5.
67. M. Planck, 'Das Einheit des physikalischen Weltbildes (Lecture, 9 December 1908, at the University of Leiden)', Physikalische Zeitschrift (1909), 10, 62-75.
68. J. L. Heilbron, The Dilemmas of an Upright Man: Max Planck as Spokesman for German Science, Berkeley, 1986.
69. L. Boltzmann, 'On the development of the methods of modern theoretical physics in recent times (Orig. 1899)', in Ludwig Boltzmann: Theoretical Physics and Philosophical Problems (ed. B. McGuiness), Dordrecht, 1974, 82.
70. Cf. Pyenson, op. cit. (7), 64-5.
71. For a discussion of Boltzmann's use of the term 'classical' see Richard Staley, 'On the co-creation of classical and modern physics', Isis (2005), 96, 530-58.
72. On Boltzmann see E. Broda, Ludwig Boltzmann: Man, Physicist, Philosopher (tr. L. Gay and E. Broda), Woodbridge, CT, 1983;
73. J. Blackmore (ed.), Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906, 2 vols., Dordrecht, Boston and London, 1995, i ;
74. A. D. Wilson, 'Mental representation and scientific knowledge: Boltzmann's Bild theory of knowledge in historical context', Physis (1991) 28, 769-95.
75. For a recent description of Boltzmann's life and philosophy (upon which a sizeable literature now exists) see the discussion and references in C. Cercignani, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford, New York and Melbourne, 1998.
76. L. Boltzmann, 'On the principles of mechanics (Orig. 1900)', in Ludwig Boltzmann: Theoretical Physics and Philosophical Problems (ed. B. McGuiness), Dordrecht, 1974, 129.
77. In Ludwig Boltzmann: Theoretical Physics and Philosophical Problems (ed. B. McGuiness), Dordrecht, 1974, 133.
78. In Ludwig Boltzmann: Theoretical Physics and Philosophical Problems (ed. B. McGuiness), Dordrecht, 1974, 139.
79. W. Ostwald, 'Die Überwindung des Wissenschaftlichen Materialismus', in idem, Abhandlungen und Vorträge; allgemeinen Inhaltes, 1887-1903, Leipzig, 1904.
80. Boltzmann, op. cit. (37), 136-7.
81. Boltzmann's journey into the realm of the sociopolitical in this last statement may have been a response to Ernst Mach's critique of mechanics, written in a similar register. In an essay on the history of the principle of energy, written in 1872, Mach noted that two things had puzzled him since childhood. 'In the first place, I did not understand how people could like letting themselves be ruled by a king even for a minute. The second difficulty was that which Lessing so deliciously put into an epigram, which may be roughly rendered: "One thing I've often thought is queer,"/Said Jack to Ted, "the which is/That wealthy folk upon our sphere,/Alone possess the riches." The many fruitless attempts of my mother to help me over these two problems must have led her to form a very poor opinion of my intelligence'. E. Mach, History and Root of the Principle of the Conservation of Energy (tr. P. E. B. Jourdain), Chicago, 1911, 15, 46. The relation between these questions and the intellectual hegemony of mechanics in the contemporary world was provided by Mach's assertion that both the social situations that would puzzle us in youth and the propositions (like those of mechanics) taught us in school could only fully be understood in historical terms. No God guarantees the truth of our particular beliefs in the make-up of the physical (and, by implication, the social) world. Our understandings, as Mach would repeat like a mantra through the text, are 'purely historical, accidental, and conventional. Neither the mechanical world-view nor the rule of kings could be justified in any manner other than by an appeal to convention'.
82. Heilbron, op. cit. (7), 51. My italics.
83. Heilbron, op. cit. (7), 57.
84. The most famous contemporary chronicler of the 'fact' of European degeneracy was Max Nordau, whose book Entartung, Berlin, 1892, was dedicated to the criminal psychologist and physiologist Caesar Lombroso. In the dedication Nordau notes that 'Degenerates are not always criminals, prostitutes, anarchists, and pronounced lunatics; they are often authors and artists. These, however, manifest the same mental characteristics, and for the most part the same somatic features, as the members of the above-mentioned anthropological family who satisfy their unhealthy impulses with the knife of the assassin or the bomb of the dynamiter, instead of which pen and pencil.'
85. M. Nordau, Degeneration, Lincoln, NE, 1993, p. v. Nonetheless, though almost everyone gets called a degenerate at some point by Nordau, scientists are, in general, excluded from his opprobrium;
86. ibid., 105-11.
87. H. W. Paul, 'The debate over the bankruptcy of science in 1895', French Historical Studies (1968), 5, 299-329, 299-300: 'some intellectuals, infatuated with positivism, which in its extreme form tackled even problems connected with ultimate origins and final ends, promised too many results, especially in moral, social and religious areas'.
88. See also, on the 'social-idealist' reaction in France to the 'bankruptcy of science', M. J. Nye, Molecular Reality: A Perspective on the Scientific Work of Jean Perrin, New York, 1972.
89. E. N. Hiebert, 'The transformation of physics', in Fin-de- siècle and its Legacy (ed. Mikulás Teich and Roy Porter), Cambridge, 1990, 235-53, 243.
90. Certainly funding allocations would add to this feeling. In the years from 1882 to 1908, when Friedrich Althoff was in control of universities within the ministry, regular budget allocations to Prussian universities climbed from 5.6 to 12.25 million marks. F. K. Ringer, The Decline of the German Mandarins: The German Academic Community, 1890-1933, Cambridge, MA, 1969, 51.
91. From 1872 to 1915 twenty-three physics institutes were built, of which more than half were established in the 1880s and 1890s, and the half-century from the mid-1860s to the beginning of the Great War marked an astonishing tenfold increase in the number of students studying the natural sciences. D. Cahan, An Institute for an Empire: The Physikalisch-Technische Reichsanstalt, 1871-1918, Cambridge and New York, 1989.
92. Sommerfeld quoted in Abraham Pais, 'Subtle is the Lord...' The Science and the Life of Albert Einstein, Oxford, 1982, 83.
93. On the energetics debate see E. N. Hiebert, 'The energetics controversy and the new thermodynamics', in Perspectives in the History of Science and Technology (ed. D. H. D. Roller), Norman, OK, 1971, 67-92;
94. R. J. Deltete, 'The energetics controversy in late nineteenth-century Germany: Helm, Ostwald, and their critics', Yale University dissertation, 1983;
95. A. Leegwater, 'The development of Wilhelm Ostwald's chemical energetics', Centaurus (1986), 29, 314-37.
96. C. Hakfoort, 'Wilhelm Ostwald's energeticist world-view and the history of scientism', Annals of Science (1992), 49, 525-44.
97. Jungnickel and McCormmach, op. cit. (15), 217-27;
98. R. J. Deltete, 'Gibbs and the energeticists', in No Truth Except in the Details (ed. A. J. Kox and D. M. Siegel), Dordrecht, 1995, 135-69.
99. R. McCormmach, 'Editor's foreword', Historical Studies in the Physical Sciences (1975), 6, 11-14.
100. Porter, op. cit. (7), 129, 128.
101. M. Heidegger, 'The age of the world-picture', in The Question Concerning Technology and Other Essays (ed. W. Lovitt), New York, 1977.
102. Planck, 'Das Einheit', op. cit. (35). M. Planck, 'Zur Machschen Theorie der physikalischen Erkenntnis: Eine Erwiderung', Physikalische Zeitschrift (1910), 11, 1186-90.
103. Heilbron, op. cit. (35), 59-60.
104. For two cases where crisis has already been interrogated in this way see Richard Staley's analysis of Planck's invocation of the 'relativity revolution' as an analogue of the Copernican revolution. R. Staley, 'On the histories of relativity: the propagation and elaboration of relativity theory in participant histories in Germany, 1905-1911', Isis (1998), 89, 285-90;
105. T. Pinch, Confronting Nature: The Sociology of Solar-Neutrino Detection, Dordrecht, 1986, 146-51.
106. S. Seth, 'Principles and problems: constructions of theoretical physics in Germany, 1890-1918', Princeton, NJ, 2003.
107. On Poincaré's 'physics of principles' see e.g. J. Giedymin, 'The physics of the principles and its philosophy: Hamilton, Poincaré and Ramsey', in idem, Science and Convention: Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition, Oxford, 1982, 42-89;
108. Darrigol, 'Henri Poincaré's criticism', op. cit. (30).
109. On Planck's philosophy and the importance of his engagement with Mach see S. Goldberg, 'Max Planck's philosophy of nature and his elaboration of the special theory of relativity', Historical Studies in the Physical Sciences (1976), 7, 125-60.
110. E. N. Hiebert, 'The conception of thermodynamics in the scientific thought of Mach and Planck, in Wissenschaftlicher Bericht Nr. 5/68.
111. Heilbron, op. cit. (35).
112. There exists a vast literature on the importance of principles, and of Mach's philosophy, to Einstein. For an introduction see G. Holton, 'Mach, Einstein, and the search for reality', in idem, Thematic Origins of Scientific Thought, Cambridge, MA, 1973;
113. J. Stachel, Einstein from 'B' to 'Z', Boston, Basel, Berlin, 2002;
114. and the first two volumes of P. Galison, M. Gordin and D. Kaiser (eds.), Science and Society: The History of Modern Physical Science in the Twentieth Century, 4 vols., New York and London, 2001.
115. Einstein's first explicit enunciation of his famous principle theory/constructive theory distinction is to be found in Albert Einstein, 'What is the theory of relativity?' in The Collected Papers of Albert Einstein: English Translation, Princeton, NJ and Oxford, 2002, 100-5.
116. For the importance of the Danish philosopher Harald Høffding's critique of late nineteenth-century methodologies of science on Bohr's philosophy of physics see J. Faye, 'The influence of Harald Høffding's philosophy on Niels Bohr's interpretation of quantum mechanics', Danish Yearbook of Philosophy (1979), 16, 37-72.
117. M. Norton Wise, 'How do sums count? On the cultural origins of statistical causality', in The Probabilistic Revolution: Ideas in History (ed. L. Krüger, L. J. Daston and M. Heidelberger), Cambridge, MA, 1989, 395-425.
118. J. Faye, Niels Bohr: His Heritage and Legacy, Dordrecht, 1991.
119. D. Kaiser, 'More roots of complementarity: Kantian aspects and influences', Studies in History and Philosophy of Science (1992), 23, 213-39.
120. Sommerfeld to Einstein, 11 January 1922, document 50 in M. Eckert and K. Märker (eds.), Arnold Sommerfeld:Wissenschaftlicher Briefwechsel, 2 vols., Berlin, Diepholz and München, 2000-4, ii, 110-11.
121. For biographical data on Sommerfeld see A. Sommerfeld, 'Autobiographische Skizze [Incl. a short addendum by Fritz Bopp]', in Arnold Sommerfeld : Gesammelte Schriften (ed. F. Sauter), 4 vols., Braunschweig, 1968, iv, 672-82,
122. and M. Born, 'Arnold Johannes Wilhelm Sommerfeld', Obituary Notices of the Fellows of the Royal Society (1952), 8, 275-96.
123. Most other short accounts tend to rely on these for information about Sommerfeld's early life. Of book-length biographies see U. Benz, Arnold Sommerfeld: Lehrer und Forscher an der Schwelle zum Atomzeitalter, 1868-1951, Stuttgart, 1975.
124. More recent and detailed is M. Eckert, Die Atomphysiker: Eine Geschichte der theoretischen Physik am Beispiel der Sommerfeldschule, Braunschweig, 1993.
125. See also the articles in both volumes of Eckert and Märker, op. cit. (23).
126. Cited in W. Moore, Schrödinger: Life and Thought, Cambridge, 1992, 269. My thanks to David Kaiser for bringing this quotation to my attention.
127. On Sommerfeld's work during his time in Aachen see (as well as the references above) A. Hermann, 'Der Brückenschlag zwischen Mathematik und Technik', Physikalische Blätter (1967), 23, 442-9;
128. M. Eckert, 'Propaganda in science: Sommerfeld and the spread of the electron theory of metals', Historical Studies in the Physical and Biological Sciences (1986), 17, 191-233, 192-6.
129. S. Hirzel to A. Sommerfeld, 15 February 1909, in Eckert and Märker, op. cit. (23), i, 353-4.
130. In asking for a short, new and especially modern textbook, Hirzel may have had in mind the relative failure of a textbook written by the Göttingen theoretician Woldemar Voigt, in the mid-1890s. Jungnickel and McCormmach, op. cit. (15), 123-4, note,
131. 'In 1895 and 1896, Voigt published in two volumes his Kompendium der theoretischen Physik, the express purpose of which was to present a unified view of the whole field of theoretical physics with a physical, as opposed to a mathematical emphasis throughout. There was no German textbook like it at the time.' Yet Voigt was soon to regret all his hard work. 'Voigt's compendium was difficult, dense, and, in Voigt's eyes, something of a failure. He came to see that he had tried to put too much in two volumes, to present and connect the whole of theoretical physics "at one stroke". He had composed the book too fast, which resulted in errors and in a case of nervous exhaustion. Then the timing could not have been worse; he soon considered revising the text, for it had come out just before the penetration into physics of the electron theory, vector analysis, and the Zeeman effect, which influenced great parts of optics. "So the book was obsolete almost with its appearance! - and the great work and joy I have invested in it almost make me sorry now"'.
132. Max Planck to Arnold Sommerfeld, 24 February 1909 in Eckert and Märker, op. cit. (58), i, 355.
133. Born cited in S. Sigurdsson, 'Hermann Weyl, mathematics and physics, 1900-1927', Harvard University dissertation, 1991, 80.
134. Sigurdsson, op. cit. (64).
135. Heilbron, op. cit. (35), 7. Heilbron's biography is, in general, the best source for material on Planck's professional and intellectual activities post-1918.
136. Max Born, 'Sommerfeld als Begründer einer Schule, Naturwissenschaften (1928), 16, 1035-6.
137. M. Jammer, The Conceptual Development of Quantum Mechanics, New York, St Louis, San Francisco, Toronto, London and Sydney, 1966, 196.
138. T. S. Kuhn, 'Interview with Hans Bethe, 01/17/1964', Archive for the History of Quantum Physics (hereafter AHQP), 9; original emphasis.
139. A. Sommerfeld, 'Zur Frage nach der Bedeutung der Atommodelle', Zeitschrift für Elektrochemie und angewandte physikalische Chemie (1928), 34, 426-30.
140. Reproduced in Arnold Sommerfeld: Gesammelte Schriften (ed. F. Sauter), 4 vols., Braunschweig, 1968, iii, 845-9, 847.
141. Kuhn, op. cit. (69), 9. Cf. Eckert, op. cit. (60), 205-8.
142. 'This notion of a crisis in or of learning, although it had roots running back into the previous century, emerged as a universally cogent cliché only in the aftermath of Germany's defeat.' Forman, op. cit. (8), 27.
143. Darrigol, op. cit. (8), 177.
144. Pauli quoted in A. Pais, Niels Bohr's Times: In Physics, Philosophy, and Polity, Oxford, 1991, 199.
145. Pauli also provides Kuhn, op. cit. (1), 83-4, with an example of the crisis before the advent of matrix mechanics.
146. Paul Forman, 'The doublet riddle and atomic physics circa 1924', Isis (1968), 59, 156-74;
147. P. Forman, 'Alfred Landé and the anomalous Zeeman effect, 1919-1921', Historical Studies in the Physical Sciences (1970), 2, 153-261;
148. Darrigol, op. cit. (8);
149. D. Serwer, "Unmechanischer Zwang: Pauli, Heisenberg, and the rejection of the mechanical atom, 1923-25', Historical Studies in the Physical Sciences (1977), 8, 189-256.
150. As Helge Kragh has noted, however, the hydrogen atom - the subject of Sommerfeld's famous work on fine structure - was not implicated in the growing dissatisfaction with standard explanations: 'In the process that eventually transformed the old quantum theory into quantum mechanics experimental anomalies contributed strongly, but there was no feeling of crisis at all as far as the hydrogen atom was concerned.' H. Kragh, 'The fine structure of hydrogen and the gross structure of the physics community, 1916-26," Historical Studies in the Physical Sciences (1985), 15(2), 67-125, 84.
151. T. S. Kuhn, 'Interview with P. A. M. Dirac, 04/01/1962', AHQP, 14. Dirac seems to have had a similar response to Bohr's worries, in 1929, about the need for a 'drastic alteration' to quantum mechanics as it then stood. 'I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes, namely with regard to its method of application, and by those means most of the difficulties now confronting the theory will be removed. If any of the concepts now used (e.g. potentials at a point) are found to be incapable of having an exact meaning, one will have to replace them by something a little more general, rather than make some drastic alteration in the whole theory.'
152. Quoted in Silvan S. Schweber, QED and the Men Who Made It : Dyson, Feynman, Schwinger, and Tomonaga, Princeton, NJ, 1994, 65.
153. T. S. Kuhn, 'Interview with Werner Heisenberg, 02/11/1963', AHQP, 7.
154. J. L. Heilbron, 'Interview with Linus Pauling, 03/27/1964', AHQP, 17. My italics.
155. Sommerfeld to Einstein, 11 January 1922, document 50 in Eckert and Märker, op. cit. (58), ii, 110-11.
156. Arnold Sommerfeld, Atombau und Spektrallinien: Wellenmechanischer Ergänzungsband, 1st edn, Braunschweig, 1929.
157. Kuhn, op. cit. (69), 12.
158. Kuhn, op. cit. (69), 12.
159. Bethe would note that 'looking back on this period from five years later I had the impression that I had really missed the development'. A much more recent interview, however, would suggest that his approach to physics was very close indeed to that of his former teacher. 'I'm not searching that much', he said, 'In fact, I've never tried to go into the really deep fundamentals of physics, into the philosophical part of physics. I'm much more interested in phenomena that you can observe. Now, I am searching for solution for some equations also, but that's not the kind of thing that Bohr was doing.' Judith Goodstein, 'A conversation with Hans Bethe', Physics in Perspective (1999), 1, 253-81, 279.
160. Heilbron, op. cit. (78). Cf. Eckert, op. cit. (60), 206.
161. Kuhn, op. cit. (69), 12.
162. Forman termed this, pejoratively, a 'craving for crises'. Forman, op. cit. (8), 58-63.
163. Kuhn, op. cit. (2), 102.
164. Which explains in part, of course, the turn in the 1970s towards histories of research schools. See G. Geison, Michael Foster and the Cambridge School of Physiology: The Scientific Enterprise in Late Victorian Society, Princeton, NJ, 1978;
165. G. Geison, 'Scientific change, emerging specialties, and research schools', History of Science (1981), 19, 20-40;
166. G. Geison and F. L. Holmes (eds.), 'Research schools: historical reappraisals', Osiris (1993), 8;
167. J. B. Morrell, 'The chemist breeders: the research schools of Liebig and Thomas Thomson', Ambix (1972), 19, 1-46.
168. S. S. Schweber has described a similar situation with regard to the development of quantum electrodynamics. Where 'leaders of the discipline' like Bohr, Pauli, Heisenberg and Dirac were insistent on the need for a 'revolution', the actual solution of the divergence difficulties was provided by those who looked rather for incremental, technical solutions to particular problems, like Kramers, Schwinger, Tomonaga, Feynman, Dyson and Bethe. Schweber, op. cit. (76), 25-6. Bethe's significant contribution provides a certain continuity in what could be described as another round in a debate about principles/revolutions versus problems/ incremental technical development.
169. Kuhn, op. cit. (2), 24.