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Heinrich Hertz’s Mechanics: A Model for Werner Heisenberg’s April 1925 Paper on the Anomalous Zeeman Effect

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Heinrich Hertz: Classical Physicist, Modern Philosopher

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 198))

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Abstract

In this paper, I will show that Heisenberg’s last paper before his invention of matrix mechanics in the summer of 19251 contains striking parallels to Hertz’s Mechanics. Although other philosophical influences on the young Heisenberg, as well as his physics and mathematics background, have already been examined extensively,2 this particular Hertzian strand in Heisenberg’s writings at that specific time has not been pointed out in the pertinent secondary literature.3

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Notes

  1. See Werner Heisenberg, “Zur Quantentheorie der Multiplettstruktur und der anomalen Zeemaneffekte,” Zeitschrift far Physik 32 (1925), pp. 841–860 [reprinted in Werner Heisenberg, Gesammelte Werke: Collected Works,edited by W. Blum, H.P. Dürr, and H. Rechenberg, vol. A I, pp. 306–328]. The paper was received on April 10, 1925 and published in issue no. 10/11 of June 30, 1925. Cf., e.g., Friedrich Hund’s introduction to Heisenberg’s papers on atomic and molecular structure (1922–1925) in Heisenberg, Collected Works,vol. A I, pp. 127–133, and Jagdish Mehra and Helmut Rechenberg’s The Discovery of Quantum Mechanics 1925,volume 2 of their Historical Development of Quantum Theory (Berlin: Springer, 1982), section 1I.5; cf. also chapter V, pp. 261ff., for an account of Heisenberg’s discovery of quantum mechanics in the second half of June and early July, 1925.

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  2. See, e.g., Armin Hermann, Werner Heisenberg in Selbstzeugnissen und Bilddokumenten (Reinbek: Rowohlt, 1976); David Cassidy, Uncertainty: The Science and Life of Werner Heisenberg (New York: Freeman, 1992), pp. 46–48, chapters 6 to 8; M. Stöckler, C. Liesenfeld, and H. Seidel, in Bodo Geyer et al. (eds.), Werner Heisenberg: Physiker und Philosoph,pp. 335–355; for the physics context, see in particular Paul Forman, “Alfred Landé and the Anomalous Zeeman Effect, 1919–1921,” Historical Studies in the Physical Sciences 2 (1970), pp. 153–261; Edward MacKinnon, “Heisenberg, Models, and the Rise of Matrix Mechanics,” Historical Studies in the Physical Sciences 8 (1977), pp. 137–188; Daniel Serwer, “Unmechanischer Zwang: Pauli, Heisenberg, and the Rejection of the Mechanical Atom, 1923–1925,” Historical Studies in the Physical Sciences 8 (1977), pp. 189–256; and the secondary texts mentioned in notes 1 and 3. See also T.S. Kuhn’s interview with Heisenberg, November 30, 1962 in Sources for History of Quantum Physics.

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  3. Apart from the more specific studies mentioned in the previous note, I have also checked broader overviews on the development of quantum theory and quantum mechanics, such as Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw Hill, 1966), chapter 3; Friedrich Hund, Geschichte der Quantentheorie,third edition (Mannheim: Bibliographisches Institut, 1984), chapters 9 to 12; Mehra and Rechenberg, op.cit. (note 1); Olivier Darrigol, From c-numbers to q-numbers: The Classical Analogy in the History of Quantum Mechanics (Berkeley: University of California Press, 1992), chapters 7 to 10.

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  4. The German terms used by Heisenberg are “modellmäßige Bilder” and “Schema,” later he also introduces “quasimechanical models of schemes” with “Bild” and “Schema” used interchangeably, while Hertz only uses the word “Bild”: I will consistently leave the term “Bild” untranslated, and translate “Schema” as “scheme,” and “Modell” as “model.”

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  5. Cf. PM 2 for a discussion of the criteria for permissibility, correctness and appropriateness [Zulässigkeit, Richtigkeit and Zweckmässigkeit] of Bilder; see also Alfred Nordmann’s contribution to this volume.

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  6. In the future the book may prove to be of great heuristic value as a guide to the discovery of new and general characteristics of natural forces“ (Helmholtz in PM xxxvi). The usual evaluation of the impact of Hertz’s textbook by scientists as well as by historians sounds different, such as Boltzmann’s ”I have often heard Hertz’s mechanics praised yet never seen anybody pursue the path he indicated“ (Boltzmann 1974, 88), or McCormmach 1972, p. 348: ”It seems that the heuristic value was not realized.“ Cf. also Reden 1988, pp. 69f.

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  7. Heisenberg, op.cit. (note 1), p. 842; in his earlier papers on the Zeeman effect and related spectroscopic matters, Heisenberg did not use this vocabulary - nor did other quantum theorists such as Kramers, Landé, or Pauli. The latter, however, was very important for Heisenberg due to his “insistence that atomic models could not be considered realistic representations of atoms”; the earliest use that I have found of the word “symbolic” in Heisenberg’s correspondence is in his letter to Landé, Jan. 4, 1925: (Archive for History of Quantum Physics: AHQP, 6,2 = Deutsches Museum Munich: DMM, microfilm no. 123). See also the Pauli quote on p. 202 below and McKinnon op.cit. (note 2), p. 177.

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  8. I follow Nordmann’s critique of the English translation of the third sentence in just using “things” instead of “things themselves’; the emphasis is original in both versions of the text. Mach also interpreted Hertz’s Bild as synonymous with Begriff (concept): ”The constructive images (or better, perhaps, the concepts), which we consciously and purposely form of objects [...]“ (1960, p. 318). According to G. Frey’s classification, Hertz’s Bilder are thus ”non-iconic symbolic models,“ cf. Frey’s ”Symbolische and ikonische Modelle,“ Synthese 12 (1960), pp. 213–221. See also Gregor Schiemann’s contribution on the origin and development of the concept of image in this volume.

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  9. See, e.g., Boltzmann 1974, pp. 89ff.; d’Agostino 1990, pp. 382; on the many meanings and functions of “models” cf. also the contributions of Leo Apostel, G. Frey, H.J. Groenewold, and Patrick Suppes to Hans Freudenthal’s Colloquium on “The Concept and the Role of the Model in Mathematics and Natural and Social Sciences,” Synthese 12 (1960), pp. 125–161, 213–227, 287–301; Mary Hesse, Models and Analogies in Science (Notre Dame: University of Notre Dame Press, 1966), pp. 7ff.; and the contribution by Simon Saunders to this volume.

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  10. Gustav Robert Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik (Leipzig: Teubner, 1876), § 1: “als ihre Aufgabe bezeichnen wir: die in der Natur vor sich gehenden Bewegungen vollständig and auf die einfachste Weise zu beschreiben.” See also Mach 1960, p. 325; Voss 1901–08, §3, pp. 13f.; Boltzmann 1974, pp. 88f.; Conrad Heinrich Müller and Georg Prange, Allgemeine Mechanik (Hannover: Helwigsche Verlagsbuchhandlung, 1923), p. 1. For Kirchhoff’s influence on Hertz see Reden 1988, p. 77, and Hermann 1988, pp. 8–9. For a discussion of conventionalism in physics see Werner Diederich, Konventionalität in der Physik (Berlin: Duncker and Humblot, 1974); and for the history and implications of the concept “model” see Frey, op.cit. (note 8); Mary Hesse’s “Models and Analogy in Science,” in Paul Edwards (ed.), The Encyclopedia of Philosophy (New York: Macmillan, 1967), vol. 5, pp. 354–359; Boris Spassky “Le développement du concept de modèle en physique,” XII. Int. Congrès d’Histoire des Sciences (Paris, 1971), 5, pp. 91–94; Gereon Wolters, “Modell,” in J. Mittelstraß et al. (eds.), Enzyklopädie Philosophie and Wissenschaftstheorie (Mannheim: Bibliographisches Institut, 1984), vol. 2, pp. 911–913; and Margaret Morrison: “A Pragmatic View of Modeling in Physics,” forthcoming in Philosophia Naturalis (1997). II Hertz’s motive for writing this book is perhaps most succinctly put in his letter to Emil Cohn, Nov. 27, 1891: “This past summer I reflected a lot about ordinary mechanics [...] Here I would like to put some things in order and to determine the order of concepts in such a manner that one can see more clearly what is definition and what empirical fact, e.g., in the concept of force, of inertia, etc. I am already convinced that great simplifications are possible here. For example, as to what a mechanical force is, I have only now clarified this in a manner that satisfies me. But I have neither written these things down, nor do I know whether they would later satisfy others, too” (# 3206 in the collection of the Deutsches Museum in Munich, cf. also pp. 160 and 169 in this volume).

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  11. Hertz’s motive for writing this book is perhaps most succinctly put in his letter to Emil Cohn, Nov. 27, 1891: “This past summer I reflected a lot about ordinary mechanics [...] Here I would like to put some things in order and to determine the order of concepts in such a manner that one can see more clearly what is definition and what empirical fact, e.g., in the concept of force, of inertia, etc. I am already convinced that great simplifications are possible here. For example, as to what a mechanical force is, I have only now clarified this in a manner that satisfies me. But I have neither written these things down, nor do I know whether they would later satisfy others, too” (# 3206 in the collection of the Deutsches Museum in Munich, cf. also pp. 160 and 169 in this volume).

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  12. Cambridge: Cambridge University Press, 1879), vol. 1, §§207f.: “[W]e cannot, of course, give a definition of matter which will satisfy the metaphysician.”

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  13. See also Mach 1960, p. 319; Sommerfeld 1952a, p. 60.

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  14. For Hertz’s own interest in scheme II see PM 24; for the energetics movement of the 1880’s and 1890’s, see, e.g., Wilhelm Ostwald, “Studien zur Energetik,” Sitzungsberichte der sächsischen Akademie der Wissenschaften (Leipzig), 43 (1891), pp. 271–288, and 44 (1892), pp. 211–237; Georg Helm, Die Lehre von der Energetik, historisch-kritisch dargestellt (Leipzig: Felix, 1887); Erwin Hiebert, “The Energetics Controversy and the New Thermodynamics,” in Duane Roller (ed.), Perspectives in the History of Science and Technology (Norman: University of Oklahoma Press, 1971), pp. 67–86.

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  15. Hence, the idea of force as such cannot in this system involve any logical difficulties: nor can it come in question in estimating the correctness of the system; it can only increase or diminish its appropriateness “ (PM 16).

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  16. See, e.g., PM 17f.; for the debates pitting Ostwald and Helm versus Boltzmann and Planck see Ludwig Boltzmann, “Ein Wort der Mathematik an die Energetik,” Annalen der Physik (3. Folge) 57 (1895), pp. 39–71, and “Zur Energetik,” Annalen der Physik (3. Folge) 58 (1896), pp. 595–598; George Francis FitzGerald, “Ostwald’s Energetics,” in his Scientific Writings,(London: Longmans Green, 1902), pp. 387–391; Gustav Helm, “Uber den gegenwärtigen Zustand der Energetik,” Annalen der Physik (3. Folge) 55 (1895), pp. iii-xviii, and “Zur Energetik,” Annalen der Physik and Chemie (3. Folge) 7 (1896), pp. 646–659; Hiebert op.cit. (note 14); Jungnickel & McCormmach 1986, pp. 217ff.

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  17. PM 24: “avoid the harshness and ruggedness [die Härten and Rauhigkeiten] which were so disagreeable in the first image.” See, however, Mach 1960, p. 319: “Neither is the case with energetic mechanics so bad as Hertz would have it.”

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  18. See again the quote in note 11 above.

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  19. See Mach 1960, pp. 320f. and Kirchhoff op.cit. (note 10) who kept “force” but eliminated “mass” as a fundamental notion.

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  20. See, e.g., Paulus 1916, p. 849 for a specific example of this reinterpretation, and ibid., pp. 859ff. for its limitation to the first order approximation; cf. also Voss 1901–08, for an idea similar to one already discussed in Joseph John Thomson’s Applications of Dynamics to Physics and Chemistry ( London: Macmillan, 1888 ).

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  21. Cf., e.g., Helmholtz in PM xxxvi, also PM 26, Brill 1900b, pp. 202f. about Kelvin’s vortex atoms and Maxwell’s rotatory aether models as possible illustrations of these cyclic systems whose interposition might help in accounting for the usual force laws. See also Voss 1901–08, §26 for William Thomson’s and J.J. Thomson’s kinetic theories as predecessors of Hertz’s mechanics.

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  22. For some further examples, see, for instance, Brill 1900b, Boltzmann 1900b, Paulus 1916; cf. also Boltzmann 1974, p. 111, Reden 1988, pp. 88ff.

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  23. Compare the quote from Heisenberg on p. 210 below.

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  24. Cf., e.g., McCormmach 1972, p. 348, Reden 1988, p. 81.

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  25. This brief account of the main idea of Hertz’s third scheme of mechanics is adapted from Sommerfeld 1952a, pp. 212ff., cf. p. 213 for the interpretation of K as curvature of a N-dimensional Euclidean representation space of the mechanical system, and Unsöld 1970 for the further geometrization of mechanics, electrodynamics, and gravitation in Einstein’s general theory of relativity, which also dispensed with forces. See also the contribution by Jesper Lützen to this volume.

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  26. PM 27 and §309: “Every natural motion of an independent material system consists herein, that the system follows with uniform velocity one of its straightest paths.” Cf. Hertz’s entry in his diary, May 8, 1892 (MLD 323), Mach 1960, pp. 320f., Voss 1901–08, pp. 159–163.

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  27. Actually, for holonomous systems, this “straightest path” is identical with a geodetic path, i.e., a path for which S Ids = 0 compared with all infinitesimally adjacent paths. Cf. Unsöld 1970, pp. 340ff. for the reappearance of geodetic paths in Einstein’s general theory of relativity.

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  28. This reference to Gauss’s Prinzip vom kleinstem Zwang actually highlights the parallels between Hertz’s version of mechanics of n masses with 3n coordinates and higher-dimensional Euclidean geometry. Hertz clearly perceived them but did not emphasize them further; rather he wanted to stress the immediate connection of his mechanics with experience, see PM 30f. Cf. also Mach 1960, p. 323, Sommerfeld 1952a, pp. 212–214, and further references given by Jesper Lützen in this volume on the geometrization of mechanics.

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  29. PM 28: “a mathematical aid whose properties are entirely in our power. It cannot, therefore, in itself have anything mysterious to us.” Cf. d’Agostino 1990, pp. 385f. and Darrigol 1993a, pp. 243ff. as well as the contribution by d’Agostino in this volume, for Hertz’s theory ideal and its connection to his interpretation of Maxwell’s electrodynamics.

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  30. For the holistic aspect of Hertz’s view of theories, see, e.g., d’Agostino 1990, p. 391.

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  31. For references and a detailed account of the interaction of theory and experiment in this episode, which includes a successful prediction of the polarizations of the splitting components in the normal Zeeman effect, see Pieter Zeeman, Magnetooptische Untersuchungen mit besonderer Berücksichtigung der magnetischen Zerlegung der Spektrallinien (Leipzig: Barth, 1914); Theodore Arabatzis, “The Discovery of the Zeeman Effect: A Case Study of the Interaction of Theory and Experiment,” Studies in History and Philosophy of Science 23 (1992),pp. 365–388.

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  32. Friedrich Paschen and Ernst Back, “Liniengruppen magnetisch vervollständigt,” Physica 1 (1921), pp. 261–273; for a fuller account of the history of experiments and theories of the Zeeman effect and associated phenomena, see Ernst Back and Alfred Landé, Zeemaneffekte and Multiplettstruktur der Spektrallinien (Berlin: Springer, 1925); Arnold Sommerfeld, Atombau and Spektrallinien (Braunschweig: Vieweg, 1919; fourth edition 1924); or Zeeman, op.cit. (note 31).

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  33. This quantum number was renamed orbital quantum number 1 = k - 1 in Heisenberg op.cit. (note 1) who removed any connection with a mechanical interpretation; cf. also MacKinnon op.cit. (note 2), p. 160.

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  34. Cf., however, Heisenberg in his interview with T.S. Kuhn, February 11th, 1963, AHQP, roll 1419/2 (=DMM, no. 269), transcript p. 20 on Sommerfeld’s reluctance to interpret the inner quantum number as the total angular momentum, and ibid., July 2, 1963, transcript pp. 14f. on his general reluctance to interpret formulas in terms of a model: “So he would just say, `Well, never mind; we will understand it later on, but isn’t it nice that we have these simple laws?’ This was an attitude that he had quite frequently.”

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  35. Space does not permit a more detailed description of these attempts predating Heisenberg’s 1925 paper; see, however, Back and Landé, op.cit. (note 32); Paul Forman, op.cit. (note 2) and “The Doublet Riddle and Atomic Physics circa 1924,” Isis 59 (1968), pp. 156–174; MacKinnon, op.cit. (note 2); Serwer, op.cit. (note 2); Jammer, op.cit. (note 3), chapter 3; Mehra and Rechenberg, op.cit. (note 1); Darrigol, op.cit. (note 3), chapters 7 and 8.

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  36. Arnold Sommerfeld, “Ein Zahlenmysterium in der Theorie des Zeemaneffektes,” Naturwissenschaften 8 (1920), pp. 61–64; cf. also Mehra and Rechenberg, op.cit. (note 1), section L6.

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  37. Arnold Sommerfeld and Ernst Back, “25 Jahre Zeemaneffekt,” Zeitschrift für Physik 9 (1921), pp. 911–916, cf. p. 913.

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  38. Werner Heisenberg in an interview with T.S. Kuhn, AHQP, roll 1419/2 (= DMM, no. 269), transcript of session November 30, 1962, p. 6; see also Sommerfeld’s pencilled remarks to Heisenberg’s letter to him, dated December 4, 1922, DMM, call number: 1977–28, A-136, p.7: “imprecise half numbers [ungenaue halbe Zahlen]” and “cheating [Mogelei]”; cf. furthermore Sommerfeld’s letter to Toshio Takamine, September 30, 1923 (AHQP: 34,6) about his hope to be able to discriminate between half-integral and integral quantum numbers in measurements of the Stark effect: “I am afraid that the problem I suggested to you is not very fruitful, after all. Precision of measurement would have to be extraordinary in order to permit, aside from the Stark effect, a distinction between whole and half quanta”

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  39. In 1922, in the Nachtrag of the third edition of his op.cit. (note 32), Sommerfeld tried to circumvent half-integral quantum numbers by letting m change by ±2 or 0 instead of ±1 or 0 as prescribed in Rubinowicz’s selection rule, that is by an ad hoc modification for the selection rule of the magnetic quantum number m: cf., the interview of Kuhn with Heisenberg, February 11, 1963, AHQP, roll 1419/2, transcript pp. 18f: “Sommerfeld liked integral numbers, as I told you. He liked precise mathematical laws and integral numbers. So the half quantum was for him just something awful. He disliked that intensely, but, of course, he saw on the other hand that by means of this half number, one could get order into the anomalous Zeeman effect. [...] But I remember that for a long time, even in the Sommerfeld institute, the attitude of the others was, Well, this half quantum number of Heisenberg is quite an interesting, but certainly wrong idea. For such a young man it’s very nice that he thought about it. There may be something in it. But certainly that can’t be true because if you start with half integral numbers where do you end?”’

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  40. See, e.g., the interview of T.S. Kuhn with Heisenberg, February 7, 1963, transcript in AHQP, roll 1419/2, p. 13 and February 11, 1963, p. 19 for further support from zero point energy; cf., e.g., Forman op.cit. (note 2), p. 186 for the contrast between the earlier “a priori” principle approach and the later “a posteriori” and somewhat ad hoc model-building. See also Mehra and Rechenberg op.cit. (note 1 ), pp. 30f.

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  41. See Werner Heisenberg, “Zur Quantentheorie der Linienstruktur and der anomalen Zeemaneffekte,” Zeitschrift für Physik 8 (1922), pp. 273–297, pp. 276ff. [reprinted in Gesammelte Werke, op.cit. (note 1), pp. 134–158]; Heisenberg’s letters to Sommerfeld in 1922, DMM, Sommerfeld papers, call number: 1977–28, A-136; Heisenberg’s letter to Pauli, Dec. 17, 1921, published in Karl von Meyenn (ed.), Wolfgang Pauli: Das Gewissen der Physik (Braunschweig: Vieweg, 1988), pp. 48f.; Heisenberg’s interview with T.S. Kuhn, AHQP, roll 1419/2, DMM 269, February 11, 1963, transcript pp. 9ff., and Kuhn’s questionnaire, ibid.,p. 4. See also Jammer, op.cit. (note 3), pp. 128f.; MacKinnon, op.cit. (note 2), pp. 141f.; Serwer, op.cit. (note 2), pp. 202f., 208ff.; Mehra and Rechenberg, op.cit. (note 1), pp. 37–39; Cassidy, op.cit. (note 2), pp. 121ff.; Darrigol, op.cit. (note 3), pp. 184ff., and p. 208 below for a more general description of Heisenberg’s approach towards model building.

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  42. From now on, all angular momentum values are given in units of h/2.

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  43. See Heisenberg, op.cit. (note 41), pp. 286ff.: Prediction: Ov = 0.32 cm’, Kent’s measurement: 0v = 0.34 cm-I.

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  44. -1928,“ Naturwissenschaften 17 (1929) pp. 490–496, p. 491: ”formal synopsis of the experimental findings, [...] the model-like interpretation of which was still unknown.“ Cf. also Back and Landé, op.cit. (note 32), p. V; also Werner Heisenberg’s 1968 talk ”Erinnerungen an die Entwicklung der Atomphysik in den letzten 50 Jahren,“ in his Gesammelte Werke, op.cit. (note 1), vol. C IV, pp. 22–36, especially p. 23.

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  45. See Alfred Landé, “Termstruktur und Zeemaneffekt des Multipletts,” Zeitschrift für Physik 15 (1923), pp. 189–205; and Wolfgang Pauli, “Über die Gesetzmäßigkeit des anomalen Zeemaneffektes,” Zeitschrift für Physik 16 (1923) pp. 155–164 (Pauli’s terminology is given in the following formula). For more on Landé’s and Pauli’s work on the anomalous Zeeman effect (which is better known today by the term “vector model’) see, e.g., Back and Landé, op.cit. (note 32), §5–9; Jammer, op.cit. (note 3), pp. 128ff.; Forman, op.cit. (note 2); MacKinnon, op.cit. (note 2), pp. 141f., 157f.; Serwer, op.cit. (note 2), pp. 206f., 214f.; Hund in Heisenberg’s Gesammelte Werke, op.cit. (note 1), pp. 131f.; Mehra and Rechenberg, op.cit. (note 1), pp. 31ff.; Hund, op.cit. (note 3), pp. 116ff. Cf. also the right half of figure 3 on page 199 below.

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  46. See Serwer, op.cit. (note 2), p. 190 for translation difficulties presented by this term “unmechanischer Zwang,” also pp. 232ff., 248ff. for the history of its introduction.

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  47. Wolfgang Pauli, “über den Einfluß der Geschwindigkeitsabhängigkeit der Elektronenmasse auf den Zeemaneffekt,” Zeitschrift für Physik 31 (1925), pp. 371–385.

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  48. Wolfgang Pauli, “Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren,” Zeitschrift für Physik 31 (1925), pp. 765–783, p. 765: “a peculiar, classically indescribable kind of two-valuedness [Zweideutigkeit] of the quantum-theoretical properties of the valence electron”; although this amounted to another degree of freedom for the electron, the implications of this postulate were not realized until several months later. For the history and impact of the exclusion principle see, e.g., Jammer, op.cit. (note 3), pp. 133ff.; MacKinnon, op.cit. (note 2), p. 158; Serwer, op.cit. (note 2), pp. 233ff.; Hund, op.cit. (note 3), pp. 120ff.; Pauli in Meyenn (ed.), op.cit. (note 41), pp. 201ff.; Darrigol, op.cit. (note 3), pp. 201ff. The exclusion principle remained valid in the new quantum mechanics which reinterpreted the fourth quantum number as spin, a kind of internal angular momentum of the electron.

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  49. Heisenberg, op.cit. (note 41), and Pauli, op.cit. (note 48). See Heisenberg, op.cit. (note 1), p. 842, especially notes 1 and 2; also Serwer, op.cit. (note 2), p. 242, footnote 164.

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  50. Heisenberg op.cit. (note 1), p. 842: “I. Das Elektron wirkt auf den Atomrest durch einen unmechanischen Zwang derart, daß sich der stationäre Zustand des Elektrons scheinbar verdoppelt. II. Der Atomrest wirkt auf das Elektron durch einen unmechanischen Zwang derart, daß sich der stationäre Zustand des Elektrons scheinbar verdoppelt.” Note that Heisenberg had already discussed alternative assumptions in earlier papers, see, e.g., Heisenberg op. cit. (note 41), p. 288 or in his letter to Landé, February 2, 1925, AHQP 6,2 = DMM, microfilm no. 123, pp. 2–3 here quoted in note 89 below. However, Heisenberg did not use the Hertzian terminology in these two earlier quotes, which suggests that he became aware of the structural similarity with Hertz’s mechanics between February and April 1925.

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  51. Cf. here note 7 above for Heisenberg’s rare usage of the term in other papers; cf., e.g., Voss, 1901–08, p. 14f. for occurrences of the term “Bild” immediately coupled to Hertz’s mechanics as its source. Incidentally, the same personification can be found with Kirchhoff’s dictum of the “simplest description possible,” and with Mach’s terminus “economy of thinking” [Denkökonomie].

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  52. Finn Aaserud, director of the Niels Bohr Archive at Copenhagen was so kind as to check this for me; Hertz’s mechanics is listed neither in the catalogues of the institute library nor in the collection of Bohr’s personal books.

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  53. See, e.g., Heisenberg’s interview with T.S. Kuhn, AHQP, roll 1419/2 (= DMM, no. 269), February 7, 1963, transcript p. 8. According to the Vorlesungsverzeichnisse of the Ludwig-Maximilians-Universität-München,Sommerfeld lectured on mechanics in the winter terms of 1920/21, lasting from October 21 to March 15, with lectures between 9 and 10 a.m. each Monday, Tuesday, Thursday and Friday, and then again in the winter term of 1923/24; the course also included major lectures on hydrodynamics, Maxwell’s theory and electron theory, optics, thermodynamics, and partial differential equations in the subsequent terms. See also Hermann 1988, pp. 3f. for Sommerfeld’s account of how deeply he in turn was impressed with Hertz’s electrodynamics.

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  54. See Sommerfeld 1952a, pp. 212–214. Since Sommerfeld’s lectures were only published in 1943, it is likely that the Hertz strand in Sommerfeld’s lectures at that time was even stronger, since Sommerfeld had already studied Hertz’s textbook soon after its appearance. Unfortunately, Heisenberg either did not make his own lecture notes or they were not preserved in the Heisenberg papers (personal communication from Dr. H. Rechenberg, Munich). See, however, Heisenberg’s review of the Sommerfeld lectures on mechanics in Naturwissenschaften 31 (1943), pp. 350f. [reprinted in his Gesammelte Werke, op.cit. (note 1), vol. C IV, pp. 254f.], p. 350: “The lectures about theoretical physics which over the course of the years Sommerfeld repeatedly held in Munich, and which served as the foundation of the schooling Sommerfeld provided his numerous students, including this reviewer... [Grundlage... für die Schule, in der Sommerfeld seine zahlreichen Schüler... erzogen hat].”

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  55. See, e.g., the transcripts of the Heisenberg interviews by T.S. Kuhn, AHQP, roll 1419/2 (=DMM, no. 269), November 30, 1962, pp. 6f.: “I had first to learn classical mechanics”; February 7, 1963, pp. If. on Sommerfeld’s “very rigorous way of educating the students,” pp. 4f. on the textbooks read by Heisenberg, and February 11, 1963, p. 9.

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  56. See Müller and Prange, op.cit. (note 10), pp. 140 on holonomous and non-holonomous constraints, and pp. 159ff. on Hertz’s principle of straightest path.

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  57. See Kuhn’s interview with Heisenberg, AHQP, roll 1419/2, (DMM, no. 269), November 30, 1962, transcript p. 7.

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  58. See Voss 1901–08, §§l, 3, 12, 23, 28, 37, 39 and 42, here especially §§26–28.

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  59. Heisenberg, op.cit. (note 1), p. 843. It might be helpful in this regard to quote from Heisenberg’s interview with T.S. Kuhn, February 11, 1963 (AHQP, 1419/2, DMM microfilm no. 269), transcript pp. 16f., illustrating the kind of connotations the term “picture” [Bild] had for the late Heisenberg: “What quite frequently happens in physics is that, from seeing some part of the experimental situation, you get a feeling of how the general experimental situation is. That is, you get some kind of picture. Well, there should be quotation marks around the word `picture.’ This `picture’ allows you to guess how other experiments might come out, and, of course, then you try to give to this picture some definite form in words or in mathematical formula. Then what frequently happens later on is that the mathematical formulation of the `picture’ or the formulation of the `picture’ in words, turns out to be rather wrong. Still, the experimental guesses are rather right. That is, the actual `picture’ that you had in mind was much better than the rationalization that you tried to put down in the publication. [...]. The picture changes over and over again and it’s so nice to see how such pictures change.”

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  60. The existence of this fine-structure of the spectral lines predicted by Sommerfeld’s and Planck’s relativistic version of the Bohr-Sommerfeld atomic theory was confirmed by Paschen and others. However, for the intricacies of this experimental “confirmation,” see Helge Kragh, “The Fine Structure of Hydrogen and the Gross Structure of the Physics Community,” Historical Studies in the Physical Sciences 15 (1984/85), pp. 67–125.

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  61. See Heisenberg, op.cit. (note 1), p. 846; cf. also figure 3.

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  62. Ibid,p. 845; cf. Werner Heisenberg, “Uber eine Abänderung der formalen Regeln der Quantentheorie beim Problem der anomalen Zeemaneffekte,” Zeitschrift für Physik 26 (1924), pp. 841–860 [reprinted in his Gesammelte Werke, op.cit. (note 1), pp. 289–305, pp. 292, 299ff].

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  63. Heisenberg, op.cit. (note 1), pp. 847f.; cf. Alfred Landé and Werner Heisenberg, “Termstruktur des Multipletts höherer Stufe,” Zeitschrift flir Physik 25 (1924), pp. 279–286.

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  64. This remarkable duality of the two schemes foreshadowed Bohr’s later principle of cornplementarity, as will be discussed further in section 8; cf. also Niels Bohr, “The Quantum Postulate and the Recent Development of Atomic Theory,” Nature,April 25th, 1928, Supplement pp. 580–590; Mehra and Rechenberg, op.cit. (note 1), p. 206; Hund, op.cit. (note 3), p. 123; and Hund in Heisenberg’s Gesammelte Werke, op.cit. (note 1), p. 132.

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  65. Heisenberg op.cit. (note 1), p. 849f. Alkaline-earth atoms had just been discussed by Henri Norris Russell and F.A. Saunders, “New Regularities in the Spectra of Alkaline Earths,” Astrophysical Journal 61 (1925), pp. 38–61. This article also independently introduced a model description equivalent to Heisenberg’s scheme III.

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  66. See Heisenberg, op.cit. (note 1) pp. 850ff.; cf. also Ralph de Laer Kronig, “Über die Intensität der Mehrfachlinien und ihrer Zeemankomponenten,” Zeitschrift für Physik 31 (1925), pp. 885–897.

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  67. E.g., George Uhlenbeck and Samuel Goudsmit, “Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons,” Naturwissenschaften 13 (1925), pp. 953f. For the history of spin see also Samuel Goudsmit, “Die Entdeckung des Elektronenspins,” Physikalische Blätter 21 pp. 445–453, and “It might as well be spin,” Physics Today,June 1976, pp. 40–43; George Uhlenbeck, “Personal Reminiscences,” Physics Today,June 1976, pp. 43–48; MacKinnon, op.cit. (note 2), p. 158. However, see also Heisenberg’s interview with T.S.Kuhn, February 15, 1963, AHQP, roll 1419/2 (= DMM no. 269), transcript p. 30 for the reasons for the considerable resistance to any classical pictures for electron spin: “As you say, the fact that one was already so far away from classical mechanics made it much easier to throw away, to brush away, a classical picture because, after all, classical physics is not correct anyway, so therefore why bother about such a rather queer and odd picture as a spinning electron.”

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  68. Max Born and Pascual Jordan, “Zur Quantenmechanik,” Zeitschrift für Physik 34 (1925), pp. 858–888; Max Born, Werner Heisenberg, and Pascual Jordan, “Zur Quantenmechanik II,” Zeitschrift fir Physik 35 (1925), pp. 557–615.; see also the previous note. Cf. also, e.g., Jammer, op.cit. (note 3), chapters 3.4 and 4; Hund, op.cit. (note 3), chapters 10ff.; Mehra and Rechenberg, op.cit. (note 1), chapter 5, also volumes 3 and 4; Darrigol, op.cit. (note 3), pp. 201ff. and chapter 12.

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  69. According to Helmut Pulte’s “C.G.J. Jacobis Vermächtnis einer `konventionalen’ analytischen Mechanik,” Annals of Science 51 (1994), pp. 497–516, a similar conventionalistic move can already be found in Jacobi’s lectures on mechanics; cf. also Gregor Schiemann’s contribution to this volume.

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  70. Heisenberg, op.cit. (note 1), p. 842 [the English translation of the second sentence was provided by Mehra and Rechenberg, op.cit. (note 1), p. 202]; for the part omitted from this quote, see section 8 below.

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  71. with a suitable arrangement of the coordinates for both systems the equations of condition exist“ (PM §418).

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  72. Cf., e.g., Pauli’s letter to Kronig, Oct. 9, 1925: “beim heutigen allgemeinen Wirrwarr in der Atomphysik...” In the same letter, Pauli describes his search for one single “substitute model” [Ersatzmodell], that could replace all three schemes presented in Heisenberg’s 1925 paper, op.cit. (note 1 ).

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  73. Heisenberg op.cit. (note 1), p. 851; cf. also p. 845.

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  74. See, e.g., Heisenberg’s interview with T.S. Kuhn, AHQP, roll no. 1419/2 (= DMM, no. 269), February 15, 1963, transcript pp. 18f., or Werner Heisenberg, Physics and Beyond (New York: Harper, 1971) [translation of Der Teil und das Ganze],chapter 5.

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  75. Pauli letter to Bohr, Dec. 12, 1924, in Meyenn (ed.), op.cit. (note 41), p. 189: “The (as of yet unattained) goal must be to deduce these and all other physically real, observable properties of stationary states from (whole) quantum numbers and quantum-theoretical laws.” Cf. also Serwer, op.cit. (note 2), pp. 243ff.; Mehra and Rechenberg, op.cit. (note 1), p. 196.

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  76. Pauli letter to Sommerfeld, Dec 6, 1924, in Meyenn (ed.), op.cit. (note 41), p. 182; cf., e.g., Serwer, op.cit. (note 2 ), p. 223.

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  77. See especially MacKinnon, op.cit. (note 2) for Heisenberg’s changing attitude towards models and its interdependency upon his theoretical studies at that time.

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  78. Heisenberg letter to Pauli, Oct. 9, 1923, in Meyenn (ed.) op.cit. (note 4), p. 125: “Die Modellvorstellungen haben prinzipiell nur einen symbolischen Sinn, sie sind das klassische Analogon zur `diskreten’ Quantentheorie.” [English translation in Mehra and Rechenberg, op.cit. (note 1), p. 113.] Heisenberg does not yet use the term Bild here. For Bohr’s related emphasis on the “renunciation as to visualisation in the ordinary sense” and the view of the new quantum mechanics as a “symbolic transcription” of classical mechanics, see Bohr op.cit. (note 64), pp. 580, 586, 590. For the changing emphasis on visualizability [Anschaulichkeit] which was lost and regained in the history of quantum theory, see esp. Arthur Ian Miller, Imagery in Scientific Thought (Cambridge: MIT Press, 1986), chapter 4, esp. p. 128.

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  79. Heisenberg letter to Pauli, Dec. 15, 1924, in Meyenn (ed.) op.cit. (note 4), p. 192f.: “Sie [haben] den Schwindel auf eine bisher ungeahnte, schwindelhafte Höhe [getrieben] und damit alle bisherigen Rekorde deren Sie mich beschimpft, spielend geschlagen [...] (indem Sie einzelne Elektronen mit 4 Freiheitsgraden einführen) [...]. Und wenn Sie selbst meinen, etwas gegen die bisherigen Arten von Schwindel geschrieben zu haben, so ist das natürlich Mißverständnis, denn Schwindel x Schwindel gibt nichts richtiges und daher können sich zwei Schwindel nie widersprechen” (original emphasis omitted). Cf. also Heisenberg’s interview with T.S. Kuhn, February 11, 1963, AHQP, roll no. 1419/2 (DMM, no. 269), transcript p. 21, and Mehra and Rechenberg, op.cit. (note 1 ), p. 198.

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  80. See Heisenberg to Landé, January 4, 1925, quoted in Mehra and Rechenberg, op.cit. (note 1), p. 199. For a general comparison of Pauli’s and Heisenberg’s approaches see MacKinnon, op.cit. (note 2), p. 159; and Serwer, op.cit. (note 2 ), pp. 195f.

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  81. We shall denote as incorrect any permissible pictures if their essential relations contradict the relations of external things“ (PM 2). For these three criteria see Mach 1960, p. 318; Schaffner 1970, pp. 318ff.; d’Agostino 1990, pp. 384f. and Alfred Nordmann’s contribution in this volume; contrary to him, I do not read Hertz as saying that his first scheme actually contradicts the first two criteria.

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  82. Cf. PM 40f. and Nordmann in this volume for Hertz’s comparative evaluation of the three Bilder of mechanics.

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  83. Mach 1960, p. 318. Cf. Schaffner 1970, p. 326. Conspicuously absent from Hertz’s evaluation scheme are pragmatic criteria.

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  84. Heisenberg, op.cit. (note 1), p. 860: “Obwohl die quantentheoretischen Gesetze der Wechselwirkung der Elektronen im Atom sich zweifellos durch große Einfachheit auszeichnen, scheint es zurzeit jedoch keinen anderen Weg zur Deutung dieser Gesetze zu geben, als den über modellmäßige Bilder symbolischer Bedeutung, bei denen diese Einfachheit kaum genügend zum Ausdruck kommt.” [English translation from Mehra and Rechenberg, op.cit. (note 1), p. 205.] Cf., e.g., PM 24.

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  85. Cf., e.g., Sommerfeld 1952a, pp. 5, 60, 212–214.

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  86. See, however, Heisenberg’s account from 1929, op.cit. (note 44), section IV; op.cit. (note 74); and his Gesammelte Werke, op.cit. (note 1), pp. 478ff.; cf., e.g., Jammer, op.cit. (note 3), chapter 7; Catherine Chevalley, “Physical Reality and Closed Theories in Werner Heisenberg’s Early Papers,” in D. Batens and J.P. van Bendegem (eds.), Theory and Experiment (Dordrecht: Reidel, 1988), pp. 159–167; and Darrigol, op.cit. (note 3), chapter 13.

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  87. For Heisenberg’s relation to Bohr, see, e.g., Kuhn’s interview with Heisenberg, AHQP, roll 1419/2 (DMM, no. 269), November 30, 1962, transcript pp. 12–14; cf. Mehra and Rechenberg, op.cit. (note 1), sections III.1–3; Cassidy, op.cit. (note 2), pp. 83, 171ff, 244ff.

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  88. For the Como lecture see Bohr, op.cit. (note 64); also see, e.g., Bohr to Pauli, Dec. 22, 1924, for an early indication of the. concept that was slowly being formed: “Altogether, both kinds of insanity [the Bohr-Sommerfeld theory and Pauli’s new theory of 1924] may be connected too closely to the truth so that one cannot criticise them as isolated aspects” [in Meyenn (ed.), op.cit. (note 41), pp. 103ff.]. See also Heisenberg’s 1968-talk, op.cit. (note 44), p. 27: “At the time Bohr was already thinking of his complementarity.”

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  89. Heisenberg, op.cit. (note 1), p. 842: “Vielmehr werden sich die beiden Bilder eben wegen jener Eindeutigkeit in ihren Aussagen so ergänzen müssen, daß die Größen, die in dem einen Schema unbestimmt bleiben, im anderen bestimmt werden und umgekehrt; die beiden Schemata zusammen werden sozusagen ein konvergentes Rechenverfahren zur Bestimmung der Eigenschaft der stationären Zustände des Atoms bilden.” [English translation in Mehra and Rechenberg, op.cit. (note 1), p. 202.] Cf. also Heisenberg to Landé, February 2, 1925, AHQP 6,2 = DMM, microfilm no. 123, pp. 2–3: “What’s essential, it seems to me, is that such apparently so fundamentally different schemes as Pauli’s and the J-scheme, are only two sides of the same thing, where we will probably be forced to always maintain this duality [Zweiheit] of the visualizable conception [anschaulichen Vorstellungl” (emphasis in the original).

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  90. See Heisenberg’s account from 1929, op.cit. (note 44), p. 494: “The quantum-theory of the wave-Bild thus stands after these investigations as totally equally justified [völlig gleichberechtigt] next to the quantum theory of the particle-Bild” (emphasis in the original). According to Hund, op.cit. (note 3), p. 123, the indications of the later principle of complementarity before 1927 were more confusing than enlightening.

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  91. See, e.g, Heisenberg’s 1929-account, op.cit. (note 44), section 1; Jammer, op.cit. (note 3), sections 3.2; Hund, op.cit. (note 3), chapters 6f.; Serwer, op.cit. (note 2), p. 192.

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  92. Heisenberg to Sommerfeld, November 18, 1924, DMM, call number 1977–28, A-136: “Im übrigen glaube ich aber immer mehr, daß die Frage `Lichtquanten oder Korrespondenzprinzip’ eine Wortfrage ist. Alle Effekte in der Quantentheorie müssen ja ihr Analogon in der klassischen Theorie haben, denn die klassische Theorie ist doch fast richtig; also haben alle Effekte immer zwei Namen: einen klassischen and einen quantentheoretischen u. welchen man vorzieht, ist eine Art Geschmackssache.”

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  93. See Hertz to Emil Cohn, February 25, 1891, from DMM, manuscript number 3198–3207: “You write that certain concepts are now less clear to you than initially. I can’t say that for myself. While I cannot translate into the new language every question that is posed to me by someone or by myself in the language of the old theory, and while I thereby find myself for some time at a loss [in Verlegenheit gerathe],I have not found contradictions within the theory or with the facts.”

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  94. See, e.g., Sommerfeld, op.cit. (note 36); Sommerfeld and Back, op.cit. (note 37); Alfred Landé, “Ober den anomalen Zeemaneffekt,” Zeitschrift für Physik 5 (1921), pp. 231–241, 7 (1921), pp. 398–405; Landé, op.cit. (note 45); also, e.g., Forman, op.cit. (note 2); Serwer, op.cit. (note 2); Darrigol, op.cit. (note 3), chapters 7 and 8.

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  95. See, e.g., Back’s contribution to Back and Landé, op.cit. (note 32) for an overview of the experimental techniques used in the measurement of the Zeeman effects.

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  96. Apparently, Heisenberg also did not mention Hertz in later texts, either in his lectures on magneto-and electrooptics in the summer term of 1925 (`Sommersemester 1925,’ kindly checked for me by Dr. H. Rechenberg in the Heisenberg Archive, Munich), or in any of his later reflections on broader philosophical issues.

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  97. See note 2 above and the references given there, in particular pp. 2–4 of the transcript of T.S. Kuhn’s interview with Heisenberg, November 30, 1962 in AHQP, roll 1419/2 (= DMM, no. 269), on the importance of Plato, Kant and (to a much lesser extent) Mach for the young Heisenberg. Incidentally: Heisenberg’s early reading of Plato might have supported his acceptance of Hertz’s Bild-conception.

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  98. See, e.g., Kaiser 1981 and Buchwald 1985 for excellent overviews of the plethora of theories in electrodynamics in the late 19th century. See also Darrigol 1993a and d’Agostino 1990, p. 381, as well as Dugas 1988, chapter X for the plurality of theories in mechanics.

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  99. See, e.g., Heisenberg’s letter to Sommerfeld, January 4, 1923 “On the He-Question”: “E...] that I can’t comprehend how Bohr and P.[auli] can insist so vehemently on such an uncontrollable and unfruitful literal application of general quantum-principles. And as thoroughly as I am convinced that P.’s [Pauli’s] views are incorrect, I find equally inappropriate Bohr’s self-assured consistency [so unschicklich ist mir die sichere Konsequenz] by which he finds correct everything that comes out wrong and incorrect everything that comes out right. This state of physics is really uncongenial to me. I would therefore like to ask you to find an American or Japanese (Takamine?) who will as quickly and reliably as possible measure the Starkeffekt in the I. order of He and Li.”

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  100. See, e.g,. Heisenberg, op.cit. (note 44), section II; Forman, op.cit. (note 35) for the “doublet riddle” arising early in 1924; Serwer, op.cit. (note 2), section 1 for the “riddle of statistical weights” which was identified already in 1923.

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  101. Heisenberg, op.cit. (note 62), p. 291; see, e.g., the two introductory sentences of Heisenberg’s op.cit. (note 1); cf. also Mehra and Rechenberg, op.cit. (note 1), chapter II: “Towards the Recognition of the Crisis.”

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  102. See MacKinnon, op.cit. (note 2), p. 144; similarly Unsöld 1970, p. 342 interprets sections 4 and 5 of book 2 of Hertz’s mechanics as a late expression of his ideal of a mechanical model of the aether which was soon given up completely.

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  103. Mehra and Rechenberg, op.cit. (note 1), pp. 37, 39. See also Heisenberg’s interview with T.S. Kuhn in AHQP, roll 1419/2 (= DMM, no. 269), February 11, 1963, transcript p. 12 for Heisenberg’s own account of the difference between him and Sommerfeld: “I always liked Bohr’s correspondence principle just because it gave that kind of lack of rigidity, that flexibility in the picture, which could lead to real mathematical schemes. Well, Sommerfeld disliked any non-rigidity.” Cf. Cassidy, op.cit. (note 2), p. 125 for the motto and Heisenberg’s attitude towards models at that time. For a later reappearance of this attitude see Gerald Holton, “`Success sanctifies the means’: Heisenberg, Oppenheimer, and the Transition to Modern Physics,” in Everett Mendelsohn (ed.), Transformation and Transition in the Sciences ( Cambridge: Cambridge University Press, 1970 ), pp. 155–173.

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  104. See Heisenberg, op.cit. (note 41), p. 281; also, e.g., Mehra and Rechenberg, op.cit. (note 1), p. 38 and p. 43 for Bohr’s reaction in a letter to Sommerfeld, April 30, 1922: “I must confess that several of the assumptions employed by you and your collaborators in the very promising theory of the anomalous Zeeman effect hardly appears to me to be consistent with a unified picture of quantum theory.” See also Heisenberg’s interview with T.S. Kuhn (AHQP as quoted above), February 11, 1963, transcript pp. 13–15 for Heisenberg’s account of the different attitudes.

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  105. See section 4.2 above. It was this theoretical opportunism of the model-builder Heisenberg which Pauli found so “unphilosophical,” see his letter to Bohr, February 11, 1924, in Meyenn (ed.), op.cit. (note 41), p. 143; cf. Serwer, op.cit. (note 2 ), p. 238.

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  106. Pauli to Bohr, Dec. 12, 1924, in Meyenn (ed.), op.cit. (note 41), p. 188: “ich glaube, daß das, was ich hier mache, kein größerer Unsinn ist als die bisherige Auffassung der Komplexstruktur. Mein Unsinn ist zu dem bisherigen Unsinn konjugiert. Eben deshalb glaube ich, daß dieser Unsinn beim jetztigen Stand des Problems notwendigerweise gemacht werden muß. Der Physiker, dem es einmal gelingen wird, diese beiden Unsinne zu addieren, der wird die Wahrheit erhalten.” Cf. Serwer op.cit. (note 2 ), p. 241.

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  107. See, e.g., the letters by Heisenberg to Pauli, November 19, 1921, Bohr to Pauli, December 11, and December 22, 1924, Pauli to Bohr, December 12, 1924, all in Meyenn (ed.), op.cit. (note 41). See also Kuhn’s interview with Heisenberg, AHQP, roll 1419/2 (= DMM, No. 269), November 30, 1962, transcript p. 11 on Sommerfeld’s “mystic” enthusiasm for integral numbers.

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  108. See Heisenberg to Pauli, December 15, 1924, in Meyenn (ed.) op.cit. (note 41), p. 192.

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  109. Heisenberg in his interview with T.S. Kuhn, November 30, 1962, AHQP, transcript p. 11.

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  110. For instance, Bohr’s assumption of closed orbits of electrons around positively charged atomic cores contradicted Larmor’s theorem concerning the radiation of all accelerated charges; cf. also incompatible quantum number assignments (see note 100 above).

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  111. Cf., e.g., Pauli to Bohr, December 12, 1924 in Meyenn (ed.) op.cit. (note 41), p. 188, Heisenberg’s letter to Pauli, December 16, quoted here on p.36, or the quote on Heisenberg’s introduction of half quantum numbers on p. 192 above.

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  112. Conservation - in 1924, Bohr, Kramers and Slater also considered whether energy conservation might be violated in statistical processes and just conserved in the statistical average.

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  113. See, e.g., Niels Bohr, “Seven Lectures on the Theory of Atomic Structure” (Göttingen, 1992) vol. 4 of Niels Bohr’s Collected Works (Amsterdam: Elsevier, 1977), p. 391: “We must conclude from the occurrence of the anomalous Zeeman effect that the classical theory is inadequate”; or Heisenberg to Landé, undated, around the beginning of October 1922: “Gradually it is becoming the general conviction that one must really give up much of the present mechanics and physics if one wants to arrive in a different manner at the anomalous Zeeman effect,” quoted in Mehra and Rechenberg, op.cit. (note 1), p. 99.

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  114. See, e.g., Sommerfeld and Back, op.cit. (note 37), p. 913: “the electrodynamic mechanism of the anomalous Zeeman effects is still hidden from us” Cf. also Heisenberg’s interview with T.S. Kuhn, AHQP, roll 1419/2, transcript p. 15: “that looks as if it is correct physics. We don’t understand it anyway, but these formulas which we must stick to - they are good.”

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  115. See, e.g., Pauli to Bohr, December 12, 1924: “The goal (not yet achieved) must be to deduce these [energy and momentum] and all other physically real, observable quantities of the stationary states from the (integral) quantum numbers and quantum-theoretical laws” (cf. section 7 above).

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  116. See, e.g., Bohr to Pauli, December 22, 1924: “I have a feeling that we stand at a turning point, since now the extent of the entire swindle has been characterized so exhaustively.” Cf. Pauli to Sommerfeld, December 6, 1924, and MacKinnon, op.cit. (note 2 ) p. 140.

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  117. See, e.g., Pauli’s letter to Sommerfeld, July 19, 1923 in Meyenn (ed.), op.cit. (note 41), p. 106) about the “greatly lamentable state” [großer Jammer] of the theory of the anomalous Zeeman effect and of many-electron systems.

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  118. See, e.g., Heisenberg to Sommerfeld, January 4, 1923: “This state of physics is really uncongenial to me,” and Pauli to Kronig, May 21, 1925, in Meyenn (ed.), op.cit. (note 41), p. 216: “At the moment physics is once again quite convoluted [sehr verfahren], much too difficult for me at any rate, and I wish I were a film-comedian or something like that and had never even heard of physics.” Cf. also the quote from this letter on p. 210 below, and T.S. Kuhn’s questionnaire for his interview with Heisenberg, AHQP, roll 1419/2 (= DMM, no. 269), transcript p. 11: “How did people react to the gigantic equivocalness of the scientific situation?”

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  119. Cf. ibid.,p. 10: “In 1924 Born felt that the breakthrough in quantum theory was near enough to justify calling his Atommechanik Vol. I.”

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  120. See, e.g., Pauli to Bohr, December 12, 1924.

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  121. Hertz reports having once seriously considered scheme II (energetics) before favoring scheme III (PM 24) and Heisenberg had published papers fitting under his scheme I, namely op.cit. (note 4) and op.cit. (note 62).

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  122. Heisenberg, op.cit. (note 1), p. 860 in the concluding section “Schlußbemerkungen.” A similar tone was adopted by Back and Landé, op.cit. (note 32), p. v, noting the “provisional character of the current quantum-theory of the atom.”

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  123. Especially for Heisenberg, this entails the correction of a deeply-rooted myth spread by no one else but Heisenberg himself, who later reconstructed his path to quantum mechanics via an alleged self-imposed restriction of theory to the sole prediction of observables. See, e.g., Heisenberg, op.cit. (note 74), chapter 5.

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  124. According to Bohr, Kramers, and Slater, energy is conserved only in the statistical average, not in individual processes, cf. Niels Bohr, H.A. Kramer, and J.G. Slater, “The Quantum Theory of Radiation,” Philosophical Magazine 47 (1924), pp. 785–802. This was soon refuted by Walther Bothe and Hans Geiger with the help of coincidence measurements: see, e.g., the commentary in vol. 5 of Bohr’s Collected Works (Amsterdam: Elsevier, 1984), pp. 75ff.

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  125. Heisenberg in his interview with T.S. Kuhn, February 19, 1963, AHQP, roll 1419/2 (DMM, no. 269), transcript p. 22. See also Kuhn’s reply, ibid.: “It’s interesting to me that in ‘24, in both Göttingen and Copenhagen, it is clear that people know the thing’s all screwed up. [...]. The physicists are willing to take more drastic steps than they have ever been willing to take before.”

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  126. See, e.g., Heisenberg to Landé, AHQP 6,2 = DMM, microfilm no. 123: “if only one were to succeed to piece together the various formalisms about the Zeemaneffect into a unified description, that would probably be a theory.” With reference to Poincaré’s similar approach towards problems in the electrodynamics of moving bodies, Arthur Miller, op.cit. (note 78) has called this attitude “modificationism” and contrasted it against Einstein’s readiness toward a more radical break. Cf. ibid.,p. 27 for Hertz’s influence on Poincaré.

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  127. Heisenberg in the interview by T.S. Kuhn, February 19, 1963, AHQP, roll 1419/2 (= DMM, no. 269), transcript p. 20.

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  128. Pauli to Kronig, May 21, 1925, in Meyenn (ed.) 1979, p. 215: “Mich selbst interessieren die Multipletts and der anomale Zeemaneffekt momentan gar nicht mehr. Wenn nicht jemand eine wirklich physikalische Idee hat, wird man da kaum weiter kommen. Das bloße Ausdehnen der formalen Zoologie auf immer kompliziertere Fälle halte ich im Grund’ doch für eine unfruchtbare Sache.”

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  129. In this context, see the evaluation of Hertz’s mechanics by Sommerfeld 1952a, pp. 5 and 60: “interesting, but not very fruitful.”

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  130. This is Jungnickel and McCormmach’s 1986, p. 212 description of the situation of Hertz’s mechanics; cf. also Heidelberger’s and Schiemann’s contributions to this volume.

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  131. On the invention of matrix mechanics in June 1925, see, e.g., Heisenberg, op.cit. (note 44), section III; the third group of papers in his Gesammelte Werke, op.cit. (note 1), pp. 329–504; MacKinnon, op.cit. (note 2), pp. 163ff.; Mehra and Rechenberg, op.cit. (note 1), chapter IV.

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  132. See MLD 343: “Now that it is being set, I have very much the feeling of `God protect the house.’ The book could easily reduce my by and large good repute to rack and ruin, `if the casting fail.’ Even a minor fault can flaw the whole. It frightens me to come out with something that I have never talked over with any human being. At least I find comfort in knowing myself to be a member of several academies; where else to obtain confidence in oneself?”

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  133. Heisenberg in his interview with T.S. Kuhn, February 11, 1963, AHQP, roll 1419/2, DMM no. 269, transcript p. 16.

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  1. Institut für Wissenschaftsgeschichte, Georg-August-Universität Göttingen, Germany

    Klaus Hentschel

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  1. Department of Philosophy, University of South Carolina, USA

    Davis Baird , R. I. G. Hughes  & Alfred Nordmann ,  & 

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Hentschel, K. (1998). Heinrich Hertz’s Mechanics: A Model for Werner Heisenberg’s April 1925 Paper on the Anomalous Zeeman Effect. In: Baird, D., Hughes, R.I.G., Nordmann, A. (eds) Heinrich Hertz: Classical Physicist, Modern Philosopher. Boston Studies in the Philosophy of Science, vol 198. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8855-3_12

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  • DOI: https://doi.org/10.1007/978-94-015-8855-3_12

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