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The Mind that Created the Bohr Atom

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Niels Bohr, 1913-2013

Part of the book series: Progress in Mathematical Physics ((PMP,volume 68))

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Abstract

Previously unavailable correspondence between Niels Bohr, his fiancée and his family, together with published yet unexploited Danish sources, now allows us to present a more detailed account than previously possible of the creation of the quantum atom. Owing to the undeveloped state of the psychology of invention, however, the account can only resemble an electron jump between well-defined states; the transition between them eludes description. The present attempt begins with an inventory of the “initial state”, that is, the relevant content of Bohr’s mind when he began working on the nuclear atom in the summer of 1912; continues with the inputs that stimulated the transition to his quantum atom early in 1913; and concludes with a description of the “end state”, the theory of the hydrogen spectrum and the remarkably revealing, contradictory justifications that Bohr initially offered to secure it. Observations on creativity in general round out the text.

Philosophari volo, sed paucis, siger den nordiske natur. (I want to philosophize, but in a few words, says the Nordic temperament.)

Møller, Skrifter (1930), 2, 364.

Invention is an Heroic thing, and plac’d above the reach of a low, and vulgar Genius. It requires an active, a bold, a nimble, a restless mind.

Spratt, History (1667), 392.

The following abbreviations are used: AH, Aaserud and Heilbron, Love, literature, and the quantum atom (2013); CW, Bohr, Collected works (1986–2008); DJH, Dansk jødisk historie; HK, Heilbron and Kuhn, Hist. stud. phys. sci. 1, 211–90 (1979); NBA, Niels Bohr Archive, Copenhagen; PM, London, Edinburgh and Dublin philosophical magazine. Full references are given under “Works Cited” below.

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Notes

  1. 1.

    AH, 76–80.

  2. 2.

    Niels to Margrethe, 21 Dec 11, in AH, 161.

  3. 3.

    AH, 73.

  4. 4.

    Pais, Bohr, 39 (1991).

  5. 5.

    Bamberger, Viking Jews 180 (1983); Hvidt, Jacobsen, 59 (2011).

  6. 6.

    Rerup, in Indenfor murene, 215 (1984); on Hanna Adler, Pais, Bohr, 38 (1991), AH, 20–4, and Margrethe Bohr, Interview (1963), session 1.

  7. 7.

    Rubin, Synsoplevede figurer (1915); Experimenta (1949), 9–11, 12–13 (quotes, text of 1927), 14–15, 79–81. Cf. Witt-Hansen, Dan. yearb. phil. 17, 45 (1980).

  8. 8.

    Witt-Hansen, Dan. yearb. phil. 17, 42 (1980); Rindom, Høffding, 65–6 (1913).

  9. 9.

    Hvidt, Jacobsen, 55–6 (2011).

  10. 10.

    Christensen, Rambam 20, 59–73 (2011).

  11. 11.

    Quoted from Klods-Hans by Rerup, in Indenfor murene (1984), 188–9.

  12. 12.

    AH, 9, 57.

  13. 13.

    Letter of 30 Jan 12, AH, 69, and ibid., 52–3.

  14. 14.

    Rerup, in Indenfor murene (1984), 196–7; AH, 94.

  15. 15.

    Pedersen, Erhvervhist. Årbog 20, 110–11 (1969); Roth, History (1964), 243–4.

  16. 16.

    Jacobsen, Rambam 16, 13–17 (2007); Trop, Jøderne (1907), 7–15, 19–20, 29.

  17. 17.

    Knudsen, Rambam 7, 6–8, 13–15 (1998).

  18. 18.

    Arnheim, DJH 30, 42–7 (1990); Lassen, DJH 25, 21–4 (1987).

  19. 19.

    Riis, Rambam 16, 34 (2007); Bille, DJH 21, 15 (1986).

  20. 20.

    M. Bohr, Interview, session 1.

  21. 21.

    Nathansen, Indenfor murene, 125 (1965).

  22. 22.

    Blüdnikow and Jørgensen, in Jørgensen, Indenfor murene, 134–6 (1984); Bamberger, Viking Jews, 98, 100, 105 (1983).

  23. 23.

    Thomsen, Rambam 11, 33, 38 (2002); Hvidt, Jacobsen, 22–3 (2011).

  24. 24.

    Hvidt, Jacobsen, 24–5, 37–9, 44–7, 70–1, 73 (quote) (2011).

  25. 25.

    Sandvad, Rambam 10, 78–9 (2001); Rerup, in Indenfor murene, 213–14 (1984); Hvidt, Jacobsen, 31 (2011).

  26. 26.

    Nathansen, Jude, 39–41, 46 (second quote), 78, 88, 94 (1931).

  27. 27.

    Quotes from, ibid., 42, 50, 60, resp.

  28. 28.

    Gibbons, in Hertel and Kristensen, Activist (1980), 61, 72, 94; Dahl and Mott, ibid., 325 (Brandes’ lecture).

  29. 29.

    Nathansen, Jude (1931), 103–4; cf. Knudsen, Rambam 7, 8, 16 (1998).

  30. 30.

    AH, 72–3.

  31. 31.

    M. Bohr, Interview (1963), session 1.

  32. 32.

    Hvidt, Jacobsen, 36 (2011); AH, 10.

  33. 33.

    AH, 134.

  34. 34.

    AH, 107.

  35. 35.

    AH, 157.

  36. 36.

    AH, 160.

  37. 37.

    AH, 134, 127, 12.

  38. 38.

    AH, 136, 155–6.

  39. 39.

    AH, 135–41.

  40. 40.

    Heilbron, Arch. hist. exact sci. 4, 269–80 (1968).

  41. 41.

    Niels to Margrethe, 16 and 19 Jul 12, in AH, 92–3, 166–7.

  42. 42.

    William James’ epitome of Høffding’s epistemology, in Høffding, Problems (1905), xi.

  43. 43.

    Jeans, in Théorie (1912), 62–71; Poincaré, ibid., 77; Nernst, re Rayleigh, ibid., 51.

  44. 44.

    Heilbron, in Lambert, Workshop (forthcoming).

  45. 45.

    Poincaré, Dernières pensées (1924), 166, 174 (quote), 185; cf. Gray, Poincaré, 150–2 (2013).

  46. 46.

    Poincaré, in Théorie, 451 (1912).

  47. 47.

    Poincaré, Dernières pensées, 179–80, 192 (quotes) (1924).

  48. 48.

    Niels to Margrethe, 12 and 17 Dec 11, in AH, 42–3.

  49. 49.

    Théorie, 377, 381 (1912); AH, 151; Poincaré, Dernières pensées, 190 (1924).

  50. 50.

    HK, 237–41.

  51. 51.

    HK, 237–8.

  52. 52.

    HK, 242.

  53. 53.

    Niels to Harald, 19 June 12, in HK, 238, and CW 2, 559.

  54. 54.

    Cf. Hevesy, Nature 131 (7 Jan 33), 4; Hevesy to Bohr, 15 Jan 13, in CW 2, 528.

  55. 55.

    “Rutherford Memorandum,” in CW 2, 136–58, on 147.

  56. 56.

    HK, 248–52.

  57. 57.

    HK, 245–6.

  58. 58.

    Bohr to Sophie Nørlund, 1 May 12, both quotes, in AH, 77.

  59. 59.

    Bohr, Interview, 21, 27 (1962): “I loved that [making things difficult] in some ways because it is a way to think over things” (21).

  60. 60.

    W. James, Pragmatism, 74 (1907); for descriptionism, Heilbron, in Bernhard et al., eds, Science, 52–7 (1982).

  61. 61.

    Høffding to Tönnies, 27 May 02, in Bickel and Fechner, Briefwechsel, 90 (1989); Aage Petersen, cited in Witt-Hansen, Dan. yearb. phil. 17, 48–9 (1980) (epistemology), 49–51 (logic).

  62. 62.

    Bohr, CW 10, 309, 319 (texts of 1928, 1932), and Høffding to Bohr, 22 Nov 06, ibid., 505; Rindom, Høffding, 84 (1913), and Samtaler, 56–7 (1918).

  63. 63.

    Høffding, Int. jl ethics 12:2, 137 (1902).

  64. 64.

    Fenger, in Hertel and Kristensen, Activist (1980), 50–2; Høffding, in Murchison, History 2, 197 (1932).

  65. 65.

    Andersen, in Møller, Skrifter (1930), 1, viii.

  66. 66.

    Feuer, Einstein, 111, 114–15, 122, 134–6, 139–44 (1974).

  67. 67.

    Holton, Daedalus, 1970, 1040–44.

  68. 68.

    Favrholdt, Filosoffen (2009), chap. 6

  69. 69.

    Favrholdt, Bohr’s philosophical background, 35–6 (1992), and (for Rosenfeld), Holton, Daedalus, 1970, 1052n24.

  70. 70.

    Favrholdt, in CW 10, 301–3, and, to overkill, in Favrholdt, Bohr’s philosophical background (1992), 22–31, 74–118.

  71. 71.

    Bohr, Interview, 76, 77 (1962).

  72. 72.

    Høffding, a great reader himself, complained that most students of Bohr’s generation did not know the great writers; Rindom, Samtaler, 52, 57 (1918), and Høffding, 84 (1913); AH, 106–9.

  73. 73.

    Niels to Margrethe, 12 Dec 11, AH, 39–40, 173.

  74. 74.

    Niels to Margrethe, 15 Jan 12, AH, 174.

  75. 75.

    James, Pragmatism, 92, 58 (1907).

  76. 76.

    The evaluation of James, after hearing Høffding lecture in 1904; James to F.C.S. Schiller, [1904], in James, Letters 2, 216 (1920).

  77. 77.

    Rubin, Experimenta, 20 (1949).

  78. 78.

    Jørgen Jørgensen, quoted by Witt-Hansen, Dan. yearb. phil. 17, 46 (1980); Rindom, Høffding, 86–7 (1913); AH, 61; Goethe, Gott und Welt: “Weite Welt und breites Leben / Langer Jahre redlich Streben / Stets geforscht und stets gegründet / Nie geschlossen, oft geründet.”

  79. 79.

    Høffding, Kierkegaard, 3–4 (1896); Rindom, Høffding, 21–31, 68–9 (1913).

  80. 80.

    Hansen, Høffding, 31 (1913).

  81. 81.

    Høffding, Problems, 180 (1905); cf. Rubin, Experimenta, 25 (1949), and Høffding, Int. jl ethics 22:2, 150 (1902).

  82. 82.

    James, in Høffding, Problems (1905), xiii; cf. ibid., 176–7, Rindom, Høffding, 85–6 (1913), and Hansen, Høffding, 31 (1923).

  83. 83.

    Bohr to Sophie Nørlund, 1 May 12, AH, 77.

  84. 84.

    Høffding, Problems, 186 (1905).

  85. 85.

    Niels to Margrethe, 1 May 12, AH, 78.

  86. 86.

    Høffding, Philosophy, 3 (1906).

  87. 87.

    Rindom, Høffding, 70, 79 (1913).

  88. 88.

    Niels to Margrethe, 19 Jul 12, AH, 92 (first quote); Rubin, Experimenta (1949), 27, 28, 22 (second and fourth quotes); James, in Høffding, Problems (1905), v (third quote); Rindom, Samtaler (1918), 64 (fifth quote).

  89. 89.

    Jacobsen and Brønsted, “Inledning,” in Relig. brevv. (1964), vi, xii, xvi, xviii; Jacobsen to Søren Alkaersig, 27 Feb 17, ibid., 214, and Niels Møller to Jacobsen, 3 Jan 18, ibid., 261.

  90. 90.

    Rubin, Experimenta (1949), “Preface.”

  91. 91.

    Niels to Harald, 26 June 10, in CW 1, 513.

  92. 92.

    Høffding to Meyerson, 12 Feb 24 (first quote), 23 Apr 26, 13 Apr 28 (second quote), 7 Oct 29, in Brandt et al., Correspondance (1939), 70, 123, 156, 169.

  93. 93.

    Høffding to Meyerson, 20 May 23, ibid., 51, re Høffding, Der Begriff der Analogie (1924); and 30 Mar 28, ibid.,149, re Bohr’s éloge on Høffding’s 85th birthday (CW 10, 308–9).

  94. 94.

    Høffding to Meyerson, 30 Dec 26, in Brandt et al., Correspondance, 131 (1939); the original has “physics” for the words in brackets. Høffding was second choice for the honor of first inhabitant of the Aeresbolig after Thomsen, the philologist in the Høffding-Bohr quartet, declined because of failing health. Rindom, Samtaler, 72–4 (1918).

  95. 95.

    Høffding, Problems, 90–2, 93–4 (1905) (first quotes), 94–106, 107 (third quote).

  96. 96.

    Ibid., 107–11, 112–13 (quote).

  97. 97.

    Ibid., 114–15, and Høffding, Int. jl ethics 22:2, 149 (1902), resp. Cf. Høffding, Jl phil. psych. sci. methods 2, 88–9 (1905).

  98. 98.

    Høffding, Problems, 112–13 (1905).

  99. 99.

    Møller, Skrifter 1, 292–3, 326 (1930).

  100. 100.

    AH, 107; Feuer, Einstein, 126–31 (1974).

  101. 101.

    Høffding, Jl phil. psych. sci. methods 2, 88 (1905).

  102. 102.

    Høffding, Kierkegaard (1896), 2 (quote), 63, 66.

  103. 103.

    E.g., CW 10, 143, 159–60, 200 (quote), 279.

  104. 104.

    Høffding, in Murchison, History 2, 203 (1932), with reference to complementarity.

  105. 105.

    Høffding, Kierkegaard, 57, 63 (1896).

  106. 106.

    AH, 128–9, 135, 154.

  107. 107.

    Niels to Harald, 20 Apr 09, CW 1, 501.

  108. 108.

    Niels to Harald, 20 Apr 09, CW 1, 501 (solitude); 17 and 27 Mar 09, ibid., 499 (logic); 26 Apr 09, 503 (notes); 26 June 10, 513 (cognition); 9 June 09, 505 (mother as amanuensis).

  109. 109.

    Remarks by Bohr in 1933 recorded by J. Rud Nielsen as quoted by Holton, Daedalus, 1970, 1053 n47. Cf. Feuer, Einstein (1974), 122, re quantum jumps and “Either/Or.”

  110. 110.

    Kierkegaard, Climacus, 103 (first quote) (1958), 116 (second quote), 126, 140 (third quote).

  111. 111.

    Ibid., 138, 115 (quote).

  112. 112.

    Bohr, Interview, 53 (1962); HK, 255.

  113. 113.

    HK, 255–6.

  114. 114.

    Nicholson, PM 22, 245, 263, 266 (Aug 1911); Bohr to Oseen, 1 Dec 11, in CW 1, 423, 427.

  115. 115.

    Heilbron, in Weiner, History, 46–7, 54–5 (1977).

  116. 116.

    Nicholson, PM 22, 865, 868 (Dec 1911). Nicholson published the details of the spectral matches in the Monthly notices of the Royal Astronomical Society; McCormmach, Arch. hist. exact sci. 3, 176–9 (1966), and HK, 258–62.

  117. 117.

    Nicholson, PM 22, 870, 873–4, 885 (Ra) (Dec 1911).

  118. 118.

    Ibid., 875. Rutherford and Royds, in Rutherford, Papers 2, 134–5 (1962).

  119. 119.

    Nicholson, PM 22, 867, 880–1, 883 (quote), 884, 888 (Dec 1911).

  120. 120.

    Bohr to Oseen, 1 Dec 1911, in CW, 1, 431.

  121. 121.

    HK, 255–6; McCormmach, Arch. hist. exact sci., 3, 169–70 (1966).

  122. 122.

    Nature 92, 424 (12 Dec 12).

  123. 123.

    Rayligh, ibid., 424, 423.

  124. 124.

    Rutherford, ibid., 423, 425, and (on beta and gamma rays), Papers 2, 286–7 (1962) (text of Aug 1912).

  125. 125.

    Bohr to Rutherford, 31 Jan 13, in CW 2, 579.

  126. 126.

    Niels to Harald, 23 Dec 12, in CW 1, 563, with the reading “classical” corrected to “chemical.”

  127. 127.

    Thomson, Corpuscular theory, 156–61 (1907), which suggests two clever implausible ways of establishing the shells.

  128. 128.

    Bohr to Rutherford, 31 Jan 13, in CW 2, 579–80.

  129. 129.

    HK, 264–6.

  130. 130.

    Bohr, Interview, 15–16 (quote), 44 (1962); PM 26, 6–7, 23–4 (1913), in CW 2, 166–7,183–4. Bohr took some time to work Nicholson out of his system; McCormmach, Arch. hist. exact sci. 3, 180–1 (1966); CW 2, 270, 315.

  131. 131.

    PM 26 (Jul 1913), 4–5, 7–8, in CW 2, 164–5, 167–8.

  132. 132.

    It might appear that the requirement that \(\nu _{n,n-1} \approx \omega _{n} \approx \omega _{n-1}\) conflicts with Eq. (5), from which, if \(\omega _{n} \approx \omega _{n-1},\nu _{n,n-1}\) would be ω n ∕2. However, \(\nu _{n,n-1} = [n\omega _{n} - (n - 1)\omega _{n-1}]/2 \approx [nd\omega _{n}/dn -\omega _{n}]/2 =\omega _{n}\) by Eq. (3).

  133. 133.

    Heilbron, Moseley, 102–5 (1974), and Isis 58, 451–70 (1967); Bohr, PM 26, 24–5 (1913) (CW 2, 184–5), and CW 2, 385.

  134. 134.

    CW 2, 294–6 (text of Dec 1913).

  135. 135.

    Bohr, PM 26, 15 (Jul 13), in CW 2, 175.

  136. 136.

    Bohr, PM 26, 25 (Jul 13), in CW 2, 185.

  137. 137.

    Bohr, Nature 92 (23 Oct 13), in CW 2, 275.

  138. 138.

    Hevesy to Bohr, in CW 2, 532 (23 Sep 13).

  139. 139.

    Rutherford to Bohr, in CW 2, 583 (20 Mar 13).

  140. 140.

    Hevesy to Bohr, in CW 2, 532 (23 Sep 13).

  141. 141.

    Einstein to Paul Ehrenfest, in Einstein, Papers 13, 202–3, 188 (22 and 15 Mar 22). On the Janusian method, Rothenberg, History of science 25, 2, 150, 155, 157–8; the remark about profound truths is Bohr’s.

  142. 142.

    Drachmann to Jacobsen, 24 Jul 14, in Jacobsen and Brønsted, Relig. brevv., 154 (1964).

  143. 143.

    AH, 36, 50, 67, 72, 74, 152.

  144. 144.

    Quotes from, resp., Niels to Harald, in CW 1, 519 (29 Sep 11), and to Ellen Bohr, in AH, 34 (4 Nov 11).

  145. 145.

    Bohr to Oseen, in CW 1, 427 (1 Dec 11).

  146. 146.

    Niels to Margrethe, AH 157, 51–2 (17 Dec 11 (quote), and 15 Jan 12).

  147. 147.

    Høffding to Bohr, in CW 10, 511–14 (20 Sep, and reply, 22 Sep 22); Bohr, ibid. 322 (text of 1931).

  148. 148.

    Quotes from, resp., Høffding, Jl phil. psych. sci. methods 2, 92 (1905), and Bohr, CW 1, 321.

  149. 149.

    Bohr, PM 26, 16–17 (1913), in CW 2, 166–7.

  150. 150.

    We have a similar list in Justice to the Jew (1910) by the Protestant theologian M.C. Peters: rationalism, studiousness, togetherness, industry, dedication to high ideals, love of liberty, passion for fairness, and, peculiarly, a fondness for taking baths. Quoted by Slezkine, Jewish century (2004), 56.

  151. 151.

    Veblen, Pol. sci. quarterly 34, 38–42, 39 quote (1919).

  152. 152.

    Quoted in Gray, Poincaré, 216–17 (1912), from Poincaré, Science and method, 51–2 (1914).

  153. 153.

    Hadamard, Essay, 12–14 (1945) (Poincaré), 15–16 (Helmholtz, Langevin, Ostwald).

  154. 154.

    Stewart, Elements, 323 (1802).

  155. 155.

    Simonton, Origins (1999), chap. 2, sets out the analogy between creativity and cut-and-try Darwinian selection.

  156. 156.

    James, Atlantic monthly 46, 456–7 (1880).

  157. 157.

    Høffding, in Feuer, Einstein, 115–16 (1974), the second quote coming from Høffding, Problems (1905), 8.

  158. 158.

    Mozart, quoted in Hadamard, Essay, 16 (1945).

  159. 159.

    James, Great men, 456 (1880), quoted from Simonton, Origins, 28–9, 44 (1999); Gauss, quoted in Hadamard, Essay, 15 (1945).

  160. 160.

    James, Atlantic monthly 46, 445 (1880).

  161. 161.

    Quoted by Maxwell, in Papers 1, 358 (1890).

  162. 162.

    Respectively, Ben Jonson, News, in Works, 435 (2012), and Faraday to Schönbein, 13 Nov 1845, in Kahlbaum and Derbyshire, Letters, 149 (1899).

  163. 163.

    Heilbron, Planck, 52 (2000).

  164. 164.

    Niels Møller to J.P. Jacobsen, 9 Jan 18, in Jacobsen and Brønsted, Relig. brevv., 262 (1964).

  165. 165.

    AH, 84 (second quote); boiling blood, passim, e.g., 23 Apr and 27 May 12 (AH, 74, 85).

  166. 166.

    Jonson, cited by Gordon, Jl Warb. Court. Institute 12, 158–9 (1959).

  167. 167.

    Høffding, Int. jl ethics 22:2, 143 (quote), 151, 141 (quote) (1902).

  168. 168.

    Maxwell, “Address,” in Papers 2, 220, quote (text of 1870).

  169. 169.

    Høffding, Int. jl ethics 22:2, 139, 147 (quote) (1902).

  170. 170.

    Maxwell, “Address,” in Papers 2, 227 (text of 1870).

  171. 171.

    Holton, in Mélanges 2, 261–4 (1964), Science, 95–8, 106 (1965), Daedalus, 1970, 1030–3, and Scientific imagination, 13–18 (1998).

  172. 172.

    CW 10, 265 (text of 1940).

  173. 173.

    Bohr, Interview, 61 (1962).

  174. 174.

    Ibid., 8, 57–9.

  175. 175.

    Høffding, Int. jl ethics 22:2, 138, 139 (1902), and Billings, Science 8, 544 (1886).

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  1. Berkeley and Oxford, April House, Shilton, Burford, OX18 4AB, England

    John L. Heilbron

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  1. Laboratoire Sphere, CNRS/Université Paris 7, Paris, cedex 13, Paris, France

    Olivier Darrigol

  2. Institut de Physique Théorique, CEA /Saclay, Gif-sur-Yvette Cedex, France

    Bertrand Duplantier

  3. Département de Physique de l´ENS, Laboratoire Kastler-Brossel, Paris cedex 05, Paris, France

    Jean-Michel Raimond

  4. Laboratoire de Physique Théorique, Université Paris-Sud, Orsay, France

    Vincent Rivasseau

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Heilbron, J.L. (2016). The Mind that Created the Bohr Atom. In: Darrigol, O., Duplantier, B., Raimond, JM., Rivasseau, V. (eds) Niels Bohr, 1913-2013. Progress in Mathematical Physics, vol 68. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-14316-3_4

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