Einstein's Clocks and Poincare's Maps

by Peter Galison

  109. Ibid., 141.

  110. Ibid., 159 and 180.

  111. On the history of the revolutionary calendar in France, see Baczko, “Le Calendrier républicain” (1992); Ozouf, “Calendrier” (1992).

  112. International Conference at Washington (1884), 183–88, on 184.

  CHAPTER 4

  1. Janssen, “Sur le Congrès” (1885), 716.

  2. At the Paris Telegraphic Conference of 1890, the assembled urged adoption of a universal time that would be set for all the world by the time of clocks at the prime meridian; cf. Documents de la Conférence Télégraphique (1891), 608–9.

  3. Howard, Franco-Prussian War (1979), quotation on 2, see also 43.

  4. Bucholz, Moltke (1991), ch. 2 and 3, esp. 146–47; also Bucholz, Moltke and the German Wars (2001), 72–73, 110–11, and 162–63.

  5. The establishment of uniform time is discussed in Kern, Culture (1983), 11–14; and in Howse, Greenwich (1980), 119–20. Simon Schaffer uses the Wells time machine as a guide through to the turn-of-the-century intersection of the mechanized workplace, literary and scientific engagement with time in “Time Machines” (in his “Metrology,” 1997).

  6. Moltke, “Dritte Berathung des Reichshaushaltsetats” (1892), 38–39 and 40; trans. Sandford Fleming, under the title “General von Moltke on Time Reform” (1891), 25–27.

  7. Fleming, “General von Moltke on Time Reform” (1891), 26.

  8. Newspaper clippings from the Cambridge University Library, including P.S.L, “Fireworks at the Royal Observatory,” Castle Review (n.d.); Nigel Hamilton, “Greenwich: Having a Go at Astronomy,” Illustrated London News (1975); and Philip Taylor, “Propaganda by Deed—the Greenwich Bomb of 1894” (n.d.). Conrad, Secret Agent (1953), 28–29.

  9. Lallemand, L’unification internationale des heures (1897), 5–6.

  10. Ibid., 7.

  11. Ibid., 8 and 12.

  12. Ibid., 17, 18, and 22–23.

  13. Poincaré, “Rapport sur la proposition des jours astronomique et civil” [1895].

  14. President of the Bureau of Longitude, 15 February 1897, Décimalisation du temps et de la circonférence, executing an order of the Minister of Public Instruction, 2 October 1896. From Archives Nationales, Paris.

  15. Commission de décimalisation du temps, 3 March 1897.

  16. Ibid., 3.

  17. Ibid., 3.

  18. Noblemaire to President Loewy, 6 March 1897; printed in Commission de décimalisation du temps, 3 March 1897, 5.

  19. Bernardières to Monsieur le Président du Bureau des Longitudes, 1 March 1897, printed in Commission de décimalisation du temps, 3 March 1897, 7.

  20. Bureau de la Société francaise de Physique to M. le Ministre du Commerce, approved by the Conseil de la Société on 22 April 1897; reproduced in Janet, “Rapport sur les projets de réforme” (1897), 10.

  21. In addition to the factor of 4 just mentioned, the division of the circle into 400 parts had a factor of 6 to convert 24 hours of time per day into the 400 grads that divided the circle (dividing 24 by 400 yielded a factor of 6); the final factor of 9 entered when one wanted to convert between old angles and new ones—multiplying by 360 and dividing by 400. The chart itself is reproduced in Poincaré, “Rapport sur les résolutions” (1897), 7.

  22. The Sarrauton system is presented in Sarrauton, Heure décimale (1897), with Sarrauton’s contribution dated April 1896.

  23. Commission de décimalisation du temps, 7 April 1897, 3.

  24. Cornu, “La Décimalisation de l’heure” (1897).

  25. Ibid., 390.

  26. Poincaré, “La décimalisation de l’heure” [1897], 678 and 679.

  27. Note pour Monsieur le Ministre, 29 November 1905, Archives Nationales, Paris, F/17/2921.

  28. Sarrauton, Deux Projets de loi, addressed to Loewy at the Bureau des Longitudes, 25 April 1899, Observatoire de Paris Archives, 1, 7, and 8.

  29. La Grye, Pujazon, and Driencourt, Différences de longitudes (1897), A3.

  30. Headrick, Tentacles (1988), 110–13.

  31. La Grye, Pujazon, and Driencourt, Différences de longitudes (1897), A6.

  32. Ibid., A13, citation on A84.

  33. La Grye, Pujazon, and Driencourt, Différences de longitudes (1897), A135–36.

  34. Headrick, Tentacles (1988), 115–16.

  35. A discussion of the Paris-London longitude campaign can be found in Christie, Telegraphic Determinations (1906), v–viii and 1–8, and further references therein. On the desirability of a redetermination, see the International Geodetic Conference, Paris, 1898.

  36. Lectures of 1892–93 reprinted in Poincaré, Oscillations Electriques (1894); idem, “Etude de la propagation” [1904], on submarine case, see 454.

  37. Report of the Superintendent of the Coast Survey (1869), 116.

  38. Loewy, Le Clerc, and de Bernardières, “Détermination des différences de longitude” (1882), A26 and A203.

  39. Rayet and Salats, “Détermination de la longitude” (1890), B100.

  40. La Grye, Pujazon, and Driencourt, Différences de longitudes (1897), A134.

  41. Calinon, Étude sur les diverses grandeurs (1897), 20–21.

  42. Calinon, Étude sur les diverses grandeurs (1897), 23 and 26. Former Polytechnician Jules Andrade said much the same thing (“there is an infinity of admissible clocks”) in his book on the foundations of physics, Leçons de méchanique physique (Paris, 1898), 2, which he finished on 4 September 1897. Poincaré cited this work too in “The Measure of Time” to support the contention that when we choose one clock over another it is a matter of convenience, not of one running true and the other wrong. Though Poincaré pursued the quantitative “scientific” notion of silmultaneity while Bergson attended principally to the qualitative experience of time, Bergson’s Time and Free Will ([1889], 2001) focused attention on the meaning of time.

  43. Note pour Monsieur le directeur, 20 March 1900. Archives Nationales, Paris, F/17/13026. Martina Schiavon tracks the role of the army, surveying, and the savant-officier in her richly documented study, “Savants officiers” (2001). For a textured study of colonialism and surveying (and many further references) see Burnett, Masters (2000).

  44. Comptes rendus de l’Association Géodésique Internationale (1899), 3–12 October 1898, 130–33, 143–44; Poincaré’s remark in Comptes rendus de l’Académie des Sciences 131 (1900), Monday, 23 July, 218.

  45. Headrick, Tentacles (1988), 116–17.

  46. Poincaré, “Rapport sur le projet de revision” (1900), 219.

  47. Ibid., 221–22.

  48. Ibid., 225–26.

  49. Comptes rendus de l’Association Géodésique Internationale (1901), 25 September—6 October 1900, session of 4 October; also Bassot, “Revision de l’arc” (1900), 1275.

  50. Comptes rendus de l’Académie des Sciences 134 (1902); 965–66, 968, 969, and 970.

  51. Comptes rendus de l’Académie des Sciences 136 (1903), 861.

  52. Comptes rendus de l’Académie des Sciences 136 (1903), 861–62.

  53. Comptes rendus de l’Académie des Sciences 136 (1903), 862 and 868; on the destruction, Comptes rendus de l’Académie des Sciences 138 (1904), 1014–15 (Monday 25 April 1904); native informants, Comptes rendus de l’Académie des Sciences 140 (1905), 998 and 999 (Monday 10 April 1905); quotation from Comptes rendus de l’Académie des Sciences 136 (1903), 871.

  54. Laurent Rollet, Henri Poincaré. Des Mathématiques à la Philosophie. Étude du parcours intellectuel, social et politique d’un mathématicien au début du siècle, unpublished doctoral dissertation, University of Nancy 2, 1999, 165.

  55. Poincaré, “Sur les Principes de la mécanique”; originally from Bibliothèque du Congrès international de philosophie III, Paris (1901), 457–94; modified and reprinted in Poincaré, Science and Hypothesis [1902], ch. 6, 90.

  56. Poincaré, “The Classic Mechanics,” in Science and Hypothesis [1902], ch. 6, 110, 104–05.

  57. Poincaré, “Hypotheses in Physics”; originally �
�Les relations entre la physique expérimentale et la physique mathématique” in Revue générale des sciences pures et appliquées 11 (1900), 1163–75; reprinted in Science and Hypothesis [1902], ch. 9, 144.

  58. Poincaré, “Intuition and Logic in Mathematics”; originally “Du rôle de l’intuition et de la logique en mathématiques,” in Comptes Rendus du deuxième Congrès international des mathématiciens tenu à Paris du 6–12 août 1900; reprinted in Poincaré, Foundations of Science (1982), 210–11.

  59. Poincaré, “La théorie de Lorentz” [1900], 464.

  60. Lorentz, Versuch einer Theorie [1895].

  61. Poincaré, Electricité et optique [1901], 530–32.

  62. Christie to Poincaré, 3 August 1899, accompanied by Christie to Loewy, 1 December 1898, and Christie to Colonel Bassot (Directeur du Service Géographique de l’armée), 9 February 1899. Observatoire de Paris, ref. X5, C6. Poincaré to Christie, 23 June 1899, 9 August 1899, and undated (but probably shortly after 9 August 1899), all from Christie Papers, Cambridge University Archives, MSS RGO 7/261.

  63. Poincaré, “La théorie de Lorentz” [1900], 483.

  64. Suppose B sends a signal to A at noon across the distance from A to B, AB. B should set his clock at noon plus the transmission time (the usual procedure). But the speed in the left-going direction is c + v, so the transmission speed in the headwind direction t(headwind) is AB/(c + v), and, conversely, transmission time in the tailwind direction is AB/(c – v). The “true” time of transmission from B to A is half the round-trip time, 1/2[t(headwind) + t(tailwind)], while the apparent time of transmission is just t(tailwind). So the error committed by using the apparent time of transmission is the difference between true and apparent transmission times, or

  Error = 1/2[t(headwind) + t(tailwind)] – t(tailwind)

  Using the definitions of t(tailwind) and t(headwind) above:

  Error = 1/2[AB/(c + v) – AB/(c – v)] = 1/2AB(c + v – c + v)/(c2 – v2 ) = ~ ABv/c2.

  Darrigol rightly points out that most historians of relativity have ignored this clock coordination interpretation of local time, Electrodynamics (2000), 359–60; also Miller’s wide-ranging Einstein, Picasso (2001), 200–15; for further references, see Stachel, Einstein’s Collected Papers, vol. 2 (1989), 308n.

  65. Poincaré et les Physiciens, unpubl. correspondence from the Henri Poincaré Archive: Annexe 3, document 205, 31 January 1902.

  66. Poincaré et les Physiciens, unpubl. correspondence from the Henri Poincaré Archive: Annexe 3, document 205, 31 January 1902.

  67. Poincaré, The Foundations of Science (1982), 352.

  68. See the excellent discussion in Henri Rollet, Henri Poincaré. Des Mathématiques à la Philosophie. Études du parcours intellectuel, social et politique d’un mathématicien au début du siècle, unpublished doctoral dissertation, University of Nancy 2, 1999, 249ff, quotation on 263; also Débarbat, “An Unusual Use” (1996).

  69. Poincaré, “Le Banquet du 11 Mai” (1903), 63.

  70. Ibid., 63–64.

  71. Débarbat, “An Unusual Use” (1996), 52.

  72. Darboux, Appell, and Poincaré, “Rapport” (1908), 538–49.

  73. Poincaré, “The Present State and Future of Mathematical Physics,” originally “L’État actuel et l’avenir de la physique mathématique” [24 September 1904, Congress of Arts and Science at St. Louis, Missouri], in Bulletin des Sciences Mathématiques 28 (1904), 302–24. Reprinted in Poincaré, Valeur de la Science (1904), 123–47, this quotation on 123.

  74. Poincaré, “The Present State” [1904], 128.

  75. Ibid.

  76. Ibid., 133. Translation modified: “en retard” should be “offset to a later time”—the clocks do not run “slow” in the sense of running at a slower rate. Italics added.

  77. Ibid., 142 and 146–47. Poincaré et les Physiciens, unpubl. correspondence from the Henri Poincaré Archive: document 124, 191–93, letter from Poincaré to Lorentz (n.d.) but sometime shortly after Poincaré’s return from Saint-Louis.

  78. Lorentz, “Electromagnetic phenomena” (1904).

  79. Poincaré, “Les Limites de la loi de Newton” (1953–54), 220 and 222.

  80. Poincaré, “La Dynamique de l’électron” [1908], 567.

  81. Poincaré, “Sur la Dynamique,” reprinted in his Mécanique Nouvelle (1906), 22; discussed by Miller, Einstein (1981).

  82. Poincaré et les Physiciens, unpubl. correspondence from the Henri Poincaré Archive: letter 127, Lorentz to Poincaré, 8 March 1906.

  CHAPTER 5

  1. See the excellent work on time in Switzerland, Messerli, Gleichmässig, pünktlich, schnell (1995), esp. ch. 5. For biographical details on Mathias Hipp, see de Mestral, Pionniers suisses (1960), 9–34; also Weber and Favre, “Matthäus Hipp” (1897); Kahlert, “Matthäus Hipp” (1989). On Hipp’s relation to the astronomer Hirsch, and the myriad ways in which the new technologies of time and simultaneity precision joined the history of experimental psychology to astronomy, see the excellent works by Canales, “Exit the Frog” (2001); Schmidgen, “Time and Noise” (2002); and Charlotte Bigg, Behind the Lines. Spectroscopic Enterprises in Early Twentieth Century Europe, unpublished doctoral dissertation, University of Cambridge, 2002.

  2. On Hipp, Kahlert, “Matthäus Hipp” (1989). Landes’s work, Revolution in Time (1983), 237–337, is excellent on the Swiss watch industry, though he focuses on clock production and not on networks.

  3. See Favarger, L’Électricité (1924), 408–09.

  4. “Die Zukunft der oeffentlichen Zeit-Angaben” (12 November 1890); Merle, “Tempo!” (1989), 166–78 cited in Dohrn-van Rossum, History of the Hour (1996), 350.

  5. Favarger, “Sur la Distribution de l’heure civile” (1902).

  6. Ibid., 199.

  7. Ibid., 200.

  8. Ibid., 201.

  9. Kropotkin, Memoirs (1989), 287.

  10. Favarger, “Sur la Distribution de l’heure civile” (1902), 202.

  11. Ibid., 203.

  12. Ibid. Newspaper quoted in Jakob Messerli, Gleichmässig Pünktlich Schnell (1995), 126.

  13. Einstein, “On the Investigation of the State of the Ether” [1895]; Einstein, “Autobiographical Notes” (1969), 53.

  14. Urner, “Vom Polytechnikum zur ETH,” 19–23.

  15. For example, Einstein’s notes on Weber’s lectures, in Collected Papers, vol. 1, 142. Weber’s own work ranged over a variety of topics in experimental and applied subjects: temperature dependence of specific heats, the energy distribution law for blackbody radiation, alternating current circuits, and carbon filaments. Editors’ note, Collected Papers 1, 62; Barkan, Nernst (1999), 114–17.

  16. Einstein’s notes on Weber’s lectures, in Collected Papers (Translation), vol. 1, 51–53.

  17. Einstein to Mileva Mari, 10 September 1899, item 52, in Collected Papers (Translation), vol. 1, 132–33.

  18. Einstein to Mileva Mari, August 1899; Letter 8 in Einstein, Love Letters (1992), 10–11; also in Collected Papers (Translation), vol. 1, 130–31. On Einstein’s specific knowledge of aspects of electrodynamics, see Holton, Thematic Origins (1973); Miller, Einstein’s Relativity (1981); and Darrigol, Electrodynamics (2000).

  19. On Einstein and the ether, see editors’ contribution, “Einstein on the Electrodynamics of Moving Bodies,” in Collected Papers, vol. 1, 223–25, and Darrigol, Electrodynamics (2000), 373–80. On Einstein’s early use of the relativity principle, ibid., 379.

  20. Einstein to Mileva Mari, May 1901, item 111, in Collected Papers (Translation), vol. 1, 174.

  21. Einstein to Mileva Mari, June 1901, item 112, in Collected Papers (Translation), vol. 1, 174–75.

  22. Einstein to Jost Winteler, 8 July 1901, item 115, in Collected Papers (Translation), vol. 1, 176–77. On Einstein’s battle, see Renn’s excellent article, “Controversy with Drude” (1997), 315–54.

  23. Department of Internal Affairs to Einstein, 31 July 1901, item 120, in Collected Papers (Translation), vol. 1, 179.

  24. Einstein to M
arcel Grossmann, September 1901, item 122, in Collected Papers (Translation), vol. 1, 180–81.

  25. Einstein to Swiss Patent Office, 18 December 1901, item 129, in Collected Papers (Translation), vol. 1, 188.

  26. Einstein to Mileva Mari, 19 December 1901, item 130, in Collected Papers (Translation), vol. 1, 188–89.

  27. Einstein to Mileva Mari, 17 December 1901, item 128, in Collected Papers (Translation), vol. 1, 186–87.

  28. Einstein to Mileva Mari, 19 December 1901, item 130, in Collected Papers (Translation), vol. 1, 188–89. Translation modified.

  29. Einstein to Mileva Mari, 28 December 1901, item131, in Collected Papers (Translation), vol. 1, 189–90.

  30. Einstein to Mileva Mari, 4 April 1901, item 96, in Collected Papers (Translation), vol. 1, 162–63.

  31. Einstein, advertisement for private lessons, 5 February 1902, item 135, in Collected Papers (Translation), vol. 1, 192.

  32. Einstein to Mileva Mari, February 1902, item 136, in Collected Papers (Translation), vol. 1, 192–93.

  33. Solovine, introduction to Einstein, Letters to Solovine (1993), 9.

  34. See Holton, Thematic Origins (1973), ch. 7.

  35. Mach, Science of Mechanics [1893], 272–73.

  36. Einstein, “Ernst Mach,” 1 April 1916, document 29, in Collected Papers, vol. 6, 280.

  37. Pearson, Grammar of Science [1892], 204, 226, and 227.

  38. Einstein, Letters to Solovine (1983), 8–9. Mill, System of Logic (1965), 322.

  39. Einstein, Letters to Solovine (1983), 8–9; On Einstein and Mach, see Holton, Thematic Origins (1973), ch. 7. Other works that Solovine recalls the group discussing were those by Ampère, Essai (1834); Mill, System of Logic (1965); and Pearson, Grammar of Science [1892]. Poincaré, Wissenschaft und Hypothese (1904).

  40. Poincaré, Wissenschaft und Hypothese (1904), 286–89.

  41. Einstein to Schlick, 14 December 1915, document 165, in Collected Papers, vol. 8a, 221; Collected Papers (Translation), 161.

  42. Most often the Lindemanns rendered Poincaré’s convention by Übereinkommen; but, for example, when Poincaré argued against the philosopher E. Le Roy in Science and Hypothesis (p. xxiii) that changed. Poincaré wrote, “Some people have been struck by this characteristic of free convention [French: “de libre convention,” Science et Hypothèse (24)] which may be recognized in certain fundamental principles of the sciences.” The Lindemanns put the relevant phrase as “ . . . den Charakter freier konventioneller Festsetzungen . . .” (Poincaré, Wissenschaft und Hypothese (1904), XIII).