‘Let the stars shine in peace!’ Niels Bohr and stellar energy, 1929–1934

SUMMARY

Faced with various anomalies related to nuclear physics in particular, in 1929 Niels Bohr suggested that energy might not be conserved in the atomic nucleus and the processes involving it. By this radical proposal he hoped not only to get rid of the anomalies but also saw a possibility to explain a puzzle in astrophysics, namely the energy generated by stars. Bohr repeated his suggestion of stellar energy arising ex nihilo on several occasions but without ever going into detail. In fact, it is not very clear what he meant or how seriously he took the stellar energy hypothesis. This paper relates Bohr's comments to the period's attempts to find a mechanism for stellar energy and also to the role played by astrophysics at the Copenhagen institute. Moreover, it looks at how Bohr's hypothesis was received not only by physicists but also by astronomers. In this regard the disciplinary status of astrophysics and its contemporary relation to the new quantum mechanics is of relevance. It turns out that, with very few exceptions, the hypothesis was met with silence by astronomers and astrophysicists concerned with the problem of stellar energy production. And yet, for a brief period of time it did have an impact on how physicists thought about the interior of the stars.

Notes

1 Abraham Pais, Inward Bound: Of Matter and Forces in the Physical World (Oxford: Clarendon Press, 1986), pp. 296–324; Joan L. Bromberg, ‘The impact of the neutron: Bohr and Heisenberg’, Historical Studies in the Physical Sciences, 3 (1971), 307–41; Carsten Jensen, Controversy and Consensus: Nuclear Beta Decay 1911–1934 (Basel: Birkhäuser, 2000); Allan Franklin, Are There Really Neutrinos? An Evidential History (Cambridge, MA: Perseus Books, 2001), pp. 61–72; Tjerk Gauderis, ‘To envision a new particle or change an existing law? Hypothesis formation and anomaly resolution for the curious case of the β decay spectrum’, Studies in History and Philosophy of Modern Physics, 45 (2014), 27–45; Francesca Guerra, Matteo Leone, and Nadia Robotti, ‘When energy conservation seems to fail: The prediction of the neutrino’, Science and Education, 23 (2014), 1339–59; Wolfgang Pauli. Wissenschaftlicher Briefwechsel, vol. 4, part III, ed. Karl von Meyenn (Berlin: Springer, 2001), pp. xi–xxxii. In what follows I refer to the Pauli correspondence as PWB.

2 G. Gamow, Atomic Nuclei and Nuclear Transformations (Cambridge: Cambridge University Press, 1931), p. 5.

3 Roger H. Stuewer, ‘Gamow's theory of alpha-decay’, in The Kaleidoscope of Science, ed. Edna Ullmann-Margalit (Dordrecht: Reidel, 1986), pp. 147–86.

4 The crisis and Bohr's perception of it are analysed in Olivier Darrigol, ‘The quantum electrodynamical analogy in early nuclear theory, or the roots of Yukawa's theory’, Revue d’Histoires des Sciences, 41 (1988), 225–97.

5 To speak of a paradigm is no exaggeration. For a period of fifteen years no one doubted that ultimately matter consists of protons and electrons. Although several other particles were proposed between 1915 and 1930, such as Rutherford's ‘neutron’, these were conceived as proton-electron composites and not as elementary particles. Hideki Yukawa, of meson fame, recalled the situation at the time of his graduation from Kyoto University in 1929: ‘At this period the atomic nucleus was inconsistency itself, quite inexplicable. … From somewhere had come a divine message forbidding us to think about any other particle [than the proton and electron]. To think outside of these limits (except for the photon) was to be arrogant, not to fear the wrath of the gods’. H. Yukawa, Tabibito (The Traveler) (Singapore: World Scientific, 1982), p. 13.

6 For Meitner's explanations, see Jensen 2000 (note 1).

7 R. H. Stuewer, ‘The nuclear electron hypothesis’, in Otto Hahn and the Rise of Nuclear Physics, ed. William R. Shea (Dordrecht: Reidel, 1983), pp. 19–68 (p. 19).

8 Gamow 1931 (note 2), p. 27.

9 Finn Aaserud, Redirecting Science: Niels Bohr, Philanthropy and the Rise of Nuclear Physics (Cambridge: Cambridge University Press, 1990), pp. 48–51. See also Gauderis 2014 (note 1) for the connection between complementarity and energy conservation.

10 Niels Bohr Collected Works, vol. 6, ed. Jørgen Kalckar (Amsterdam: North Holland, 1985), pp. 24–25. I shall refer to volume X of Bohr's Collected Works as BCW X.

11 See Helge Kragh, Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913-1925 (Oxford: Oxford University Press, 2012), pp. 200, 328, and BCW 5, 13–19. For the BKS theory, see John Hendry, ‘Bohr-Kramers-Slater: A virtual theory of virtual oscillators and its role in the history of quantum mechanics’, Centaurus, 25 (1981), 189–221, and Max Dresden, H. A. Kramers: Between Tradition and Revolution (Berlin: Springer, 1987), pp. 41–78.

12 According to Pais 1986 (note 1), 312 and Gauderis 2014 (note 1), 38, Bohr's proposal of 1929 was not related at all to the earlier BKS theory. This is to go too far, I think. Although the two theories were different, Bohr can hardly have avoided being inspired by the BKS theory.

13 Bohr to Rutherford, 2 May 1932, quoted in Arthur S. Eve, Rutherford. Being the Life and Letters of the Rt Hon. Lord Rutherford, O.M. (Cambridge: Cambridge University Press, 1939), pp. 356–58. For details on the origin of the Faraday lecture paper, see Bromberg 1971 (note 1), 318, and, for the Rome congress paper, Guerra et al. 2014 (note 1). The Faraday lecture was summarized in Nature, 125 (1930), 788–89, but the summary did not mention Bohr's idea of energy non-conservation.

14 Rutherford to Bohr, 19 November 1929, Bohr Scientific Correspondence (BSC 15.3).

15 Bohr to Mott, 1 October 1929 (BSC 14.1).

16 Bohr Scientific Manuscripts, microfilm no. 12. The lecture of 2 May 1930 was the last of a series of three lectures by Bohr on ‘The Principles of Atomic Theory’ (BCW 6, 317).

17 Bohr to Kudar, 28 January 1930 (BCW 9, 605).

18 Pauli to Klein, 18 February 1929 (PWB 1, 490); Pauli to Bohr, 5 March 1929 (PWB 1, 493).

19 Léon Rosenfeld, ‘Quantum theory in 1929: Recollections from the first Copenhagen conference’, in Selected Papers of Léon Rosenfeld, eds. Robert S. Cohen and John J. Stachel (Dordrecht: Reidel, 1979), pp. 302–12; Gino Segré, Faust in Copenhagen: A Struggle for the Soul of Physics and the Birth of the Nuclear Age (London: Pimlico, 2007), pp. 31–32, 194–95. Ehrenfest was sympathetic to Bohr's idea of energy non-conservation. See Ehrenfest to Epstein, 15 November 1931, as quoted in PWB 4, part III, xxxi.

20 BCW 9, 87-89. Bohr to Pauli, 1 July 1929 (BCW 6, 443-4). See also Bromberg 1971 (note 1), p. 312.

21 G. Gamow, ’Über die Struktur des Atomkernes’, Physikalische Zeitschrift, 30 (1929), pp. 717–20 (p. 719). The proceedings of the conference were published in the same volume on pp. 645–55, 700–20.

22 Gamow to Kapitza, 15 February 1929, quoted in Victor Ya. Frenkel, ‘Correspondence between G. A. Gamow and P. L. Kapitza’, Physics-Uspekhi, 37 (1994), 803–11.

23 Gamow 1931 (note 2), p. 56. Gamow marked the latter part of the quotation, and generally ‘the more speculative passages about nuclear electrons’, with special signs.

24 Friedrich G. Houtermans, ‘Neuere Arbeiten über Quanthentheorie des Atomkerns’, Ergebnisse die exakten Naturwissenschaften, 9 (1930), 123–221 (p. 180).

25 Bohr to Fowler, 14 February 1929 (BCW 9, 555). Emphasis added.

26 A. S. Eddington, ‘The internal constitution of the stars’, Nature, 106 (1920), 14–20 (p. 15). For the Helmholtz-Thomson theory and other nineteenth-century theories of solar energy generation, see H. Kragh, ‘The source of solar energy, ca. 1840–1910: From meteoric hypothesis to radioactive speculations’, European Physical Journal H, 41 (2016), 365–94.

27 Karl Hufbauer, ‘Astronomers take up the stellar-energy problem’, Historical Studies in the Physical Sciences, 11 (1981), 277–302; François Wesemael ‘Harkins, Perrin and the alternative paths to the solution of the stellar-energy problem’, Journal for the History of Astronomy, 40 (2009), 277–96. See also Giora Shahiv, The Life of Stars: The Controversial Inception and Emergence of the Theory of Stellar Structure (Berlin: Springer-Verlag, 2009), pp. 275–312 for a valuable review of the stellar energy problem ca. 1920–1940.

28 J. Jeans, ‘The ages and masses of the stars’, Nature, 114 (1924), 828–29.

29 J. Jeans, ‘The wider aspects of cosmogony’, Nature, 121 (1928), 463–70 (p. 467). On the annihilation hypothesis of Jeans and others, see J. Bromberg, ‘The concept of particle creation before and after quantum mechanics’, Historical Studies in the Physical Sciences, 7 (1976), 161–91.

30 W. Nernst, ‘Physico-chemical considerations in astrophysics’, Journal of the Franklin Institute, 206 (1928), 135–42. On Nernst's work in astrophysics and cosmology, see H. Kragh, ‘Cosmology between the wars: The Nernst-MacMillan alternative’, Journal for the History of Astronomy, 26 (1995), 93–115.

31 D. H. Menzel, ‘The source of solar energy’, Science, 65 (1927), 431–38 (p. 437).

32 A. Eddington, The Internal Constitution of the Stars (Cambridge: Cambridge University Press, 1926), p. 315. The importance of Eddington's book is highlighted in K. Hufbauer, ‘Stellar structure and evolution, 1924-1939’, Journal for the History of Astronomy, 37 (2006), 203–27.

33 Eddington 1926 (note 32), p. 301.

34 Eddington 1926 (note 32), pp. 306, 297. For Eddington's ambivalence in deciding between the annihilation hypothesis and the element-building hypothesis, see A. Eddington, ‘Sub-atomic energy’, Memoirs and Proceedings, Manchester Literary and Philosophical Society, 72–73 (1927–1929), 101–17. Contrary to my reading of Eddington's work, Hufbauer 2006 (note 32) argues that Eddington preferred the annihilation hypothesis over the fusion hypothesis.

35 E. Rutherford, ‘Presidential address’, Proceedings of the Royal Society A, 122 (1929), 1–23 (p. 13). According to Houtermans 1930 (note 24), p. 177, ‘One of the main problems of astrophysics is to explain the source of the energy emitted by the stars’.

36 B. P. Gerasimovich and D. H. Menzel, ‘Subatomic energy and stellar radiation’, Publications of the Astronomical Society of the Pacific, 41 (1929), 79–97, 145–67 (pp. 157, 167).

37 E. A. Milne, ‘Stellar structure and the origin of stellar energy’, Nature, 126 (1930), 238; Roger J. Tayler, ‘E. A. Milne (1896–1950) and the structure of stellar atmospheres and stellar interiors’, Quarterly Journal of the Royal Astronomical Society, 37 (1996), 355–63.

38 Letter to Geoffrey Milne, 23 November 1930. In Meg Weston Smith, Beating the Odds: The Life and Times of E. A. Milne (London: College Press, 2013), 128. Fowler visited Bohr's institute from 11 to 21 September 1930 (Niels Bohr Institute, NBI, list of foreign guests).

39 R. d’E. Atkinson and F. G. Houtermans, ’Zur Frage der Aufbaumöglichkeiten in Sternen’, Zeitschrift für Physik, 54 (1929), 656–65. See also their letter of 13 April, ‘Transmutation of the lighter elements in stars’, Nature, 123 (1929), 567–68.

40 Atkinson and Houtermans 1929 (note 39), p. 665.

41 Gamow to Bohr, 15 March 1929, and Bohr to Gamow, 22 March 1929 (BSC).

42 R. d’E. Atkinson, ‘Atomic synthesis and stellar energy, I, II’, Astrophysical Journal, 73 (1931), 250–95, 308–47 (p. 346).

43 A. H. Wilson, ‘The transmutation of elements in stars’, Monthly Notices of the Royal Astronomical, 91 (1931), 283–90 (p. 283).

44 From 2 March to 13 April, and from 6 August to 17 September 1931 (NBI, list of foreign guests).

45 The subject only entered a supplementary volume published in 1936. See B. Strömgren, ‘Thermodynamik der Sterne und Pulsationstheorie’, in Handbuch der Astrophysik, Ergänzungsband, eds. G. Eberhard, A. Kohlschütter, and H. Ludendorff (Berlin: Springer, 1936), pp. 121–202.

46 P. Dirac, ‘The proton’, Nature, 126 (1930), 605–06. ‘Such processes probably occur in nature’, he wrote in Principles of Quantum Mechanics (Oxford: Oxford University Press, 1931), p. 257.

47 D. H. Menzel, ‘Annihilation of matter as the source of stellar energy’, Proceedings of the Astronomical Society of the Pacific, 43 (1931), pp. 191–202 (p. 196). See also Wilson 1931 (note 43), p. 283. In a paper of September 1931 Dirac abandoned the proton = anti-electron hypothesis and instead proposed a new positive particle of electron mass soon to be known as the positron. See H. Kragh, Dirac: A Scientific Biography (Cambridge: Cambridge University Press, 1990), pp. 95–105.

48 G. Good, ‘The assembly of geophysics: Scientific disciplines as frameworks of consensus’, Studies in History and Philosophy of Modern Physics, 31 (2000), 259–92 (p. 261). For other views of the identity and formation of disciplines, see Gerard Lemaine et al., Perspectives on the Emergence of Scientific Disciplines (The Hague: Walter de Gruyter, 1976) and Jan Golinski, Making Natural Knowledge: Constructivism and the History of Science (Cambridge: Cambridge University Press, 1998), pp. 47–78.

49 The reasons for the physics committee's changed view regarding the status of astrophysics are described in Robert M. Friedman, The Politics of Excellence: Behind the Nobel Prize in Science (New York: Henry Holt, 2001), pp. 144–51.

50 Rajinder Singh and Falk Riess, ‘C. V. Raman, M. N. Saha and the Nobel Prize for the year 1930’, Indian Journal of History of Science, 34 (1999), 61–75 (p. 70).

51 Kragh 2012 (note 11), pp. 68–74.

52 For historical reviews, see Shahiv 2009 (note 27), pp. 115–97 and Jean-Louis Tassoul and Monique Tassoul, A Concise History of Solar and Stellar Physics (Princeton: Princeton University Press, 2004), pp. 94–132.

53 Bohr to Eddington, 19 February and 17 May 1924; Kramers to Eddington, 15 December 1923; Russell to Bohr, 7 December 1923 and 31 January 1924; Saha to Bohr, 13 November 1926; Bohr to Saha, 18 February 1927 (BSC).

54 H. A. Kramers, ‘On the theory of X-ray absorption and on the continuous X-ray spectrum’, Philosophical Magazine, 46 (1923), 836–71. See also Eddington to Kramers, 12 December 1923 in Archive for History of Quantum Physics (Kramers file, AHQP 8.3) and Dresden 1987 (note 11), 134–38. S. Rosseland, ‘Note on the absorption within a star’, Monthly Notices of the Royal Astronomical Society, 84 (1924), 525–28. Eddington 1926 (note 32) cited both papers.

55 R. H. Fowler, ‘Notes on the theory of absorption lines in stellar spectra’, Monthly Notices of the Royal Astronomical Society, 85 (1925), 970–77; R. H. Fowler, ‘On dense matter’, Monthly Notices of the Royal Astronomical Society, 87 (1926), 114–22. It appears from the first of the papers that Fowler had discussed it with Bohr.

56 See Kameshwar C. Wali, Chandra: A Biography of S. Chandrasekhar (Chicago: University of Chicago Press, 1984), p. 102.

57 Wali 1984 (note 56), p. 102. The quotation is apparently from a series of taped conversations with Chandrasekhar which Wali conducted at some time after 1977. No further documentation is given. See also Arthur I. Miller, Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes (Boston: Houghton Mifflin, 2005), pp. 92–94. For Bohr on Chandrasekhar, see Bohr to Klein, 28 October 1932 (BCW 8, p. 715).

58 Segré 2007 (note 19); Niels Bohr, 1885-1962: Der Kopenhagener Geist in der Physik, eds. Karl von Meyenn, Klaus Stolzenburg and Roman Sexl (Braunschweig: Vieweg & Sohn, 1985), pp. 308–42; Mara Beller, ’Jocular commemorations: The Copenhagen spirit’, Osiris, 14 (1999), 252–73; Paul Halpern, ‘Quantum humor: The playful side of physics at Bohr's Institute for Theoretical Physics’, Physics in Perspective, 14 (2012), 279–99. The Faust play contained several references to the beta spectrum and Pauli's neutrino, but there is only one indirect reference to Bohr's hypothesis of energy non-conservation.

59 B. Strömgren, ‘The opacity of stellar matter and the hydrogen content of stars’, Zeitschrift für Astrophysik, 4 (1932), 118–53. Simon O. Rebsdorf, ‘Bengt Strömgren: Growing up with astronomy, 1908–1932’, Journal for the History of Astronomy, 34 (2003), 171–99.

60 G. Steensholt, ‘On the transmutation of elements in stars’, Zeitschrift für Astrophysik, 5 (1932), 140–52. Steensholt also visited Bohr's institute later in the 1930s, but from about 1941 he changed his research field from astrophysics to biochemistry.

61 S. Rosseland, On the Internal Constitution of the Stars (Oslo: Norwegian Academy of Science, 1925). Bohr to Rosseland, 6 January 1926 (BCW 5, p. 484).

62 S. Rosseland, Astrophysik auf atomtheoretischer Grundlage (Berlin: Springer, 1931), pp. 111–15.

63 E. Strömgren and B. Strömgren, Lærebog i Astronomi (Copenhagen: Gyldendal, 1931), 288–92.

64 Über eine mögliche Bedeutung des Versagens des Energieprincips bei Atomprozessen (AHQP, microfilm no. 27, section 16). The draft was part of an answer to Schrödinger's sympathetic response to the BKS theory. See Dresden 1987 (note 11), 196–98 and BCW 5, 31. None of these sources mention Kramers's speculation on stellar energy.

65 H. A. Kramers and H. Holst, Das Atom und die Bohrsche Theorie seines Baues (Berlin: Springer, 1925), pp. 139–40. The section on radiation theory also appeared in a special issue of Fysisk Tidsskrift dedicated to Bohr on his 40-year's birthday: H. A. Kramers, ‘Om vekselvirkningen mellem lys og stof’, Fysisk Tidsskrift, 23 (1925), 26–40. This paper, published in Danish only, is not included in H. A. Kramers, Collected Scientific Papers (Amsterdam: North-Holland, 1956).

66 Dresden 1987 (note 11), pp. 97, 303. I have been unable to locate the letter, which is not listed in AHQP and also not in PWB.

67 BCW 9, 88.

68 Pauli to Bohr, 17 July 1929 (BCW 6, 446). See also Pauli to Klein, 10 February 1930 (PWB 2, 4): ‘In my view, the idea of a violation of the energy law in the case of β-spectra is and will always be a cheap and coarse philosophy’.

69 Gamow to Meitner, 27 November 1929, quoted in Jensen 2000 (note 1), p. 149.

70 Luis W. Alvarez, ‘Nuclear K electron capture’, Physical Review, 52 (1937), 134–35.

71 W. Harkins and Webster B. Kay, ‘An attempt to add an electron to the nucleus of an atom’, Physical Review, 31 (1928), 940–45.

72 R. A. Millikan, ‘High frequency rays of cosmic origin’, Proceedings of the National Academy of Sciences, 12 (1926), 48–55.

73 Bohr to Dirac, 24 November 1929; Dirac to Bohr, 26 November 1929 (BCW 9, 547–49). Gamow gave a talk to the Kapitza Club, an informal Cambridge discussion club founded by Peter Kapitza in 1922, at its 235th meeting on 19 November 1929. The title of his talk was ‘Something about Nuclei: Perpetuum-Mobile According to N. Bohr’. Minute Book, AHQP 38.2. 

74 Bohr to Dirac, 5 December 1929 (BSC, 9.5). Reproduced in Donald A. Moyer, ‘Evaluations of Dirac's electron, 1928–1932’, American Journal of Physics, 49 (1981), 1055–62.

75 N. Bohr, ‘Chemistry and the quantum theory of atomic constitution’, Journal of the Chemical Society, 131 (1932), 349-84, on 380 and 382. Reproduced in BCW 6, 371–408.

76 Report, British Association for the Advancement of Science (London: J. Murray, 1932), p. 333. See BCW 6, 317, 355.

77 L. W. McKeehan, ‘Conservation of energy and the disintegration of RaE’, Physical Review, 38 (1931), 2292–93.

78 H. Dingle, ‘The evolution of the universe’, Nature (Supplement), 128 (1931), 700-01. For the symposium, see H. Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (Princeton: Princeton University Press, 1996), pp. 49–50.

79 G. Lemaître, ‘The beginning of the world from the point of view of quantum theory’, Nature, 127 (1931), 706. Although Lemaître did not refer to Bohr, there are reasons to believe that he was inspired by Bohr's thoughts. See Kragh 1996 (note 78), p. 47 and Jean-Pierre Luminet, ‘Editorial note to: Georges Lemaître, The beginning of the world from the point of view of quantum theory’, General Relativity and Gravitation, 43 (2011), 2911–28.

80 N. Bohr, ‘Atomic stability and conversation laws’, in Atti del Convegno di Fisica Nucleare (Rome: Reale Accademia d’Italia, 1932), pp. 119–30 (pp. 128, 130). Reproduced in BCW 9, 103–14.

81 Gennady E. Gorelik and V. Ya. Frenkel, Matvei Petrovich Bronstein and Soviet Theoretical Physics in the Thirties (Basel: Birkhäuser, 1994), p. 65.

82 Debye's address was not published in the proceedings volume. It is preserved in the archives of the Accademia dei Lincei in Rome and here cited from Guerra et al. 2014 (note 1), p. 1352. Goudsmit mentioned Pauli's recent proposal of the ‘neutron’ (neutrino) as a possible explanation of ‘the β–ray spectrum, in which it seems that the law of conservation of energy is not fulfilled’.

83 Bohr to Ellis, 31 August 1932 (BSC 2); Ellis to Bohr, 2 September 1932 (BSC 2).

84 Abstracts of session in Report, British Association for the Advancement of Science (London: J. Murray, 1932), pp. 306–08.

85 Chadwick concluded from his experimental data that the mass of the neutron was 1.0067 mass units, smaller than the sum of the proton and electron masses (1.0078 mass units). From this he concluded that he had discovered a tightly bound proton-electron system. It took more than a year until improved experiments resulted in a neutron mass larger than the total proton-electron mass (1.0085 versus 1.0081), demonstrating that the neutron is an unstable elementary particle. The discovery of the neutron was not an event but an extended process including several experiments, interpretations and negotiations.

86 L. Landau and R. Peierls, ’Erweiterung des Unbestimmtheitsprinzip für die relativistische Quantentheorie’, Zeitschrift für Physik, 69 (1931), 56–69 (p. 68). See also BCW 7, 7–12 and 229–35.

87 Pauli to Klein, 10 March 1930 (PBW 2, 7). For Heisenberg's remarkable theory, see Bromberg 1971 (note 1) and Darrigol 1988 (note 4). A detailed reconstruction is offered in Bruno Carazza and H. Kragh, ‘Heisenberg's lattice world: The 1930 theory sketch’, American Journal of Physics, 63 (1995), 595–605.

88 Whereas Gamow 1931 (note 2) did not refer to subjects of astrophysics, the much expanded second edition of 1937 included a section on nuclear matter and the interior of stars (234–38). At that time Bohr's speculation was forgotten and Gamow did not mention it.

89 R. C. Tolman, Relativity, Thermodynamics and Cosmology (Oxford: Oxford University Press, 1934), pp. 382, 486. Before turning to cosmology and general relativity Tolman had worked in areas of physical chemistry and atomic physics, including calculations of the electron structure in many-electron atoms based on Bohr's correspondence principle. See Kragh 2012 (note 11), pp. 214, 235–36.

90 R. C. Tolman, ‘Remarks on the possible failure of energy conservation’, Proceedings of the National Academy of Sciences, 20 (1934), 379–83. See also Tolman, ‘Suggestions as to the energy-momentum principle in a non-conservative mechanics’, Proceedings of the National Academy of Sciences, 20 (1934), 437–39, and Shahiv 2009 (note 27), 305–09.

91 K. Hufbauer, ‘Landau's youthful sallies into stellar theory: Their origins, claims, and receptions’, Historical Studies in the Physical and Biological Sciences, 37 (2007), 337–54 (p. 342).

92 Science News Letter, 25 (17 December 1932), 385–86.

93 G. Gamow, Thirty Years that Shook Physics (Garden City, NY: Doubleday & Company, 1966), 72–74. There is no documentary evidence that Gamow's account accurately reproduces Bohr's ideas.

94 Hufbauer 2007 (note 91), pp. 339–42; Dmitrii Yakovlev et al., ‘Lev Landau and the conception of neutron stars’, Physics-Uspekhi, 56 (2013), 289–95. Landau visited Bohr's institute from 8 April to 3 May 1930 and again from 20 September to 22 November 1930; he returned for a third visit from 25 February to 19 March 1931. According to Yakovlev et al. 2013 (this note) he discussed the paper with Bohr and his assistant Léon Rosenfeld during his third period in Copenhagen.

95 For the history of the mass limit of white dwarfs and evidence that priority belongs to neither Landau nor Chandrasekhar, but to the British physicist Edmond Stoner, see Michael Nauenberg, ‘Edmond C. Stoner and the discovery of the maximum mass of white dwarfs’, Journal for History of Astronomy, 39 (2008), 297–312.

96 L. D. Landau, ’On the theory of stars’, Physikalische Zeitschrift der Sowietunion, 1 (1932), 285–88. Reprinted in A Source Book in Astronomy and Astrophysics, 1900-1975, eds. Kenneth Lang and Owen Gingerich (Cambridge, MA: Harvard University Press, 1979), pp. 458–59. Landau included only a single reference, namely to the 1931 Landau-Peierls paper.

97 L. Biermann, Physikalische Berichte, 13 (1932), 1375–76.

98 Cited in Gorelik and Frenkel 1994 (note 81), p. 65.

99 M. Bronstein, ’The expanding universe‘, Physikalische Zeitschrift der Sowietunion, 3 (1933), 73–82 (p. 75–76). See also Kragh 1996 (note 78), pp. 36, 86–87, and G. E. Gorelik, ‘Matvei Bronstein and quantum gravity: 70th anniversary of the unsolved problem’, Physics-Uspekhi, 48 (2005), 1039–53.

100 After the discovery of dark energy in the late 1990s Bronstein's work became seen as a precursor of ‘quintessence’ theories of the vacuum energy based on a varying cosmological constant. Bronstein ended his short life in February 1938, executed by a military firing squad during Stalin's purges. Gorelik and Frenkel 1994 (note 81).

101 Pauli to Klein, 12 December (PWB 2, 45). See Jensen 2000 (note 1), p. 153.

102 Bronstein 1933 (note 99), pp. 81–82; note added on 18 January 1933. Gamow to Bohr, 31 December 1932 (BCW 9, 569). Radium E or tallium-206 is a beta emitter with half-life of 4 min.

103 Bohr to Gamow, 21 January 1993 (BCW 9, 571).

104 An English version of Bohr's Solvay address appears as ‘On the correspondence method in electron theory’ in BCW 7, 183–91.

105 G. Beck and K. Stille, ‘Zur Theorie des β–Zerfalls’, Zeitschrift für Physik, 86 (1936), 105–19 (p. 118). See Jensen 2000 (note 1), pp. 177–79 for details. Beck was well known to Bohr. He had visited the Copenhagen institute in 1930, participated in the Rome congress on nuclear physics, and from 15 April to 18 June 1932 and again from 31 July 1932 to 23 September 1933 he stayed with Bohr at his institute.

106 BCW 9, 140.

107 P. Dirac, ‘Does conservation of energy hold in atomic processes?’, Nature, 137 (1936), 298–99. R. Shankland, ‘An apparent failure in the photon theory of scattering’, Physical Review, 49 (1936), 8–13. See also ‘Atomic physics must discard conservation of energy’, Science News Letter, 29 (7 March 1936), 157. The case is described in Kragh 1990 (note 47), 169–74.

108 N. Bohr, ‘Conservation laws in quantum theory’, Nature, 138 (1936), 25–26. The only physicist who supported Dirac's proposal of energy non-conservation was Rudolf Peierls. See R. Peierls, ‘Interpretation of Shankland's experiment’, Nature, 137 (1936), 904.