Einstein's Clocks and Poincare's Maps

by Peter Galison

  43. Einstein to Solovine, 30 October 1924, in Einstein, Letters to Solovine, 63. One thinks (inter alia) of Max Planck, the first famous theorist-supporter of relativity, who disdained “convenience” talk in physics, celebrating instead that which was universal and invariant. See, for example, Heilbron, Dilemmas (1996), 48–52.

  44. Einstein, “Autobiographische Skizze,” in Seelig, ed., Helle Zeit, Dunkle Zeit (1956), 12. Einstein to Mileva Mari, February 1902, item 137, in Collected Papers (Translation), vol. 1, 193. On 2 June 1902 Einstein was notified officially that he had the job at the Patent Office at an annual salary of Sfr 3,500: item 140, in Collected Papers (Translation), vol. 1, 194–95; see also item 141, 19 June 1902, 195; and that he was to assume his duties on 1 July 1902: item 142, 196.

  45. On Poincaré’s views on dynamics and kinematics, see Miller, Frontiers (1986), parts I, III; Paty, Einstein Philosophe (1993), 264–76; and Darrigol, Electrodynamics (2000).

  46. Here is not the place to offer a full technical reconstruction of all aspects of Einstein’s path to special relativity. The reader is referred to an excellent short synthesis in Stachel et al., “Einstein on the Special Theory of Relativity,” editorial note in Collected Papers, vol. 2, 253–74, esp. 264–65. For further development of early history, see, for example, Miller, Einstein’s Relativity (1981); Darrigol, Electrodynamics (2000); and Pais, Subtle Is the Lord (1982).

  47. Flückiger, Albert Einstein (1974), 58.

  48. Einstein to Hans Wohlwend, 15 August–3 October 1902, item 2, in Collected Papers (Translation), vol. 5, 4–5.

  49. Flückiger, Albert Einstein (1974), 58.

  50. Flückiger, Albert Einstein (1974), 67; Einstein to Mileva Mari, September 1903, item 13, in Collected Papers (Translation), vol. 5, 14–15.

  51. References cited in Pais, Subtle Is the Lord (1982), 47–48, who cites Flückiger, Albert Einstein (1974).

  52. Nicolas Stoïcheff, patent 30224 submitted 6 January 1904 issued 1904; American Electrical Novelty, “Stromschliessvorrichtung an elektrischen Pendelwerken,” patent 31055 submitted 16 March 1904 and issued 1905.

  53. According to the lists of patents provided in Berner, Initiation (c. 1912), ch. 10.

  54. Hundreds of relevant patents are listed in the Journal Suisse d’horlogerie during the relevant years (1902–05). Sadly, the Swiss patent office dutifully destroyed all papers processed by Einstein 18 years after their creation; this was standard procedure on patent opinions, and even Einstein’s fame led to no exception. See Fölsing, Einstein (1997), 104.

  55. The most detailed linkage between Einstein’s patent work and his scientific work is on gyromagnetic compasses and Einstein’s production of the Einstein-de Haas effect, see Galison, How Experiments End (1987), ch. 2; in addition, see Hughes, “Einstein” (1993), and Pyenson, Young Einstein (1985). On Einstein’s assignment to evaluate electrical patents, see Flückiger, Albert Einstein (1974), 62.

  56. Flückiger, Albert Einstein (1974), 66.

  57. J. Einstein & Co. und Sebastian Kornprobst, “Vorrichtung zur Umwandlung der ungleichmässigen Zeigerausschläge von Elektrizitäts-Messern in eine gleichmässige, gradlinige Bewegung,” Kaiserliches Patentamt 53546, 26 February 1890; idem, “Neuerung an elektrischen Mess- und Anzeigervorrichtungen,” Kaiserliches Patentamt 53846, 21 November 1889; idem, “Federndes Reibrad”, 60361, 23 February 1890; “Elektrizitätszähler der Firma J. Einstein & Cie., München (System Kornprobst)” (1891), 949. Also see Frenkel and Yavelov, Einstein (in Russian) (1990), 75 ff., and Pyenson, Young Einstein (1985), 39–42. Further on the links between electric clocks and electricity measuring devices, see, for example, Max Moeller, “Stromschlussvorrichtung an elektrischen Antriebsvorrichtungen fuer elektrische Uhren, Elektrizitätszähler und dergl.” (Swiss patent 24342).

  58. Swiss Patent Office to Einstein, 11 December 1907, item 67, in Collected Papers (Translation), vol. 5, 46. On Einstein’s interest in dynamos, see Miller, Frontiers of Physics (1986), ch. 3. Einstein insisted that he only took up the role of expert witness if he judged the side he was defending to be in the right. For example, in 1928 he defended Siemens & Halske against Standard Telephones & Cables Ltd.—see Hughes, “Inventors” (1993), 34.

  59. Galison, How Experiments End (1987), ch. 2.

  60. Einstein to Heinrich Zangger, 29 July 1917, document 365, in Collected Papers, vol. 8a, 495–96.

  61. Paul Habicht to Einstein, 19 February 1908, item 86, in Collected Papers (Translation), vol. 5, 58–61, on 60.

  62. On “the little machine” see editors’ essay in Collected Papers, vol. 5, 51–54; Fölsing, Einstein (1997), 132, 241, and 267–78; Frenkel and Yavelov, Einstein (1990), ch. 4.

  63. Einstein to Albert Gockel, March 1909, item 144, in Collected Papers (Translation), vol. 5, 102.

  64. Einstein to Conrad Habicht, 24 December 1907, item 69 in Collected Papers (Translation), vol. 5, 47; Einstein to Jakob Laub, after 1 November 1908, item 125 in Collected Papers (Translation), vol. 5, 90. “I am presently carrying on an extremely interesting correspondence with H. A. Lorentz on the radiation problem. I admire this man like no other; I might say, I love him.” Einstein to Jakob Laub, 19 May 1909, item 161 in Collected Papers (Translation), vol. 5, 120–22, on 121.

  65. C. Vigreux and L. Brillié, “Pendule avec dispositif électro-magnétique pour le réglage de sa marche,” patent 33815.

  66. Einstein, “How I Created the Theory” (1982). Compare remarks that Einstein recorded on a discograph in 1924: “After seven years of reflection in vain (1898–1905), the solution came to me suddenly with the thought that our concepts and laws of space and time can only claim validity insofar as they stand in a clear relation to our experiences; and that experience could very well lead to the alteration of these concepts and laws. By a revision of the concept of simultaneity into a more malleable form, I thus arrived at the special theory of relativity.” Einstein, in Collected Papers (Translation), vol. 2, 264.

  67. Joseph Sauter, “Comment j’ai appris à connaître Einstein,” printed in Flückiger, Albert Einstein in Bern (1972), 156; Fölsing, Albert Einstein (1997), 155–56.

  68. Einstein to Habicht, May 1905, document 27, in Collected Papers (Translation), vol. 5, 19–20, on 20.

  69. Einstein, “Conservation of Motion” [1906] in Collected Papers (Translation), vol. 2, 200–206, on 200.

  70. Cohn, “Elektrodynamik” (1904).

  71. Einstein, “Relativity Principle” [1907], document 47, in Collected Papers, vol. 2, 432–88, on 435; Collected Papers (Translation), 252–311, on 254 (translation modified); also Einstein to Stark, 25 September 1907, document 59 in Collected Papers, vol. 5, 74–75. On Cohn’s physics, cf. Darrigol, Electrodynamics (2000), 368, 382, and 386–92.

  72. Abraham, Theorie der Elektrizität: Elektromagnetische Theorie der Strahlung (Leipzig, 1905), 366–79; cited in Darrigol, Electrodynamics (2000), 382.

  73. Warwick, “Cambridge Mathematics” (1992, 1993).

  74. Cited in Galison, “Minkowski” (1979), 98, 112–13.

  75. Galison, “Minkowski” (1979), 97.

  76. For an excellent overview of the reception of Minkowski’s ideas, see Walter, “The non-Euclidean style” (1999).

  77. Cited in Galison, “Minkowski” (1979), 95.

  78. Einstein, “The Principle of Relativity and Its Consequences in Modern Physics” [1910], document 2, in Collected Papers (Translation), vol. 3, 117–43, on 125.

  79. Einstein, “The Theory of Relativity” [1911], document 17, in Collected Papers (Translation), vol. 3, 340–50, on 348 and 350.

  80. “Discussion” Following Lecture Version of “The Theory of Relativity,” document 18, in Collected Papers (Translation), vol. 3, 351–58, on 351–52.

  81. “Discussion” Following Lecture Version of “The Theory of Relativity,” document 18, in Collected Papers (Translation), vol. 3, 351–58, on 356–58; see also the notes to the original version in Collected Papers, vol. 3, on 448–49. Poincaré, La Science (1905), on 165.


  82. Laue, Relativitätsprinzip (1913), 34.

  83. Planck, Eight Lectures (1998), 120; translation modified slightly following Walter, “Minkowski” (1999), 106. On Planck’s words and Einstein’s career, see Illy, “Albert Einstein,” 76.

  84. Einstein, “On the Principle of Relativity” [1914], document 1, in Collected Papers, vol. 6, 3–5, on 4; Collected Papers (Translation), vol. 6, 4.

  85. Cohn, “Physikalisches” (1913), 10; Einstein, “On the Principle of Relativity” [1914], document 1, in Collected Papers (Translation), vol. 6, 4.

  86. More precisely, this simple triangle shows quantitatively the relation between time measured in the two frames. Let Δt be the time it takes light to travel the distance h (so h = cΔt). We imagine the light clock moving to the right at a speed v, and the inclined path of the light pulse to cover a distance D in a time Δt' (so D = cΔt'). In the time Δt' that the beam takes to reach the top mirror, the launching point of the light beam has moved to the right an amount b which must be the speed of the clock multiplied by the time Δt', that is: b = vΔt'. So we have a right triangle (see 5.12b) with all the sides given. Apply Pythagorus’s theorem: D2 = b2 + h2. Substitute the values of D, b, and h, and we have: (cΔt')2 = (vΔt')2 + (cΔt)2. Subtracting (vΔt')2 from both sides and simplifying, we get: Δt' / Δt = 1/ √(1–v2/c 2). This is the crucial result. It says that a tick of the clock at rest that takes t in its rest frame (here light moving a distance h) is measured by an observer at rest to take a longer time (Δt') when the clock is moving at velocity v. For v/c = 4/5 the speed of light, this ratio 1/ √(1–v2/c2) is 5/3: a clock moving at four-fifths the speed of light would be measured by a stationary clock to run slow by a factor of 5/3. Of course “stationary” and “in motion” are, according to Einstein, entirely relative.

  87. Howeth, History (1963). Further on wireless time setting, see, for example, Roussel, Premier Livre (1922), esp. 150–52. Boulanger and Ferrié, La Télégraphie (1909), date the Eiffel Tower radio station to 1903. Ferrié, “Sur quelques nouvelles applications de la Télégraphie” (1911), esp. 178, indicates that planning for wireless time coordination began at the start of work on wireless; Rothé, Les Applications de la Télégraphie (1913), discusses the details of radio-communicated time coordination procedure.

  88. Max Reithoffer and Franz Morawetz, “Einrichtung zur Fernbetätigung von elektrischen Uhren mittels elektrischer Wellen,” Swiss patent 37912, submitted 20 August 1906.

  89. Depelley, Les Cables sous-marins (1896), 20.

  90. Poincaré, “Notice sur la télégraphie sans fil” [1902].

  91. Amoudry, Le Général Ferrié (1993), 83–95.

  92. Conférence Internationale de l’heure, in Annales du Bureau des Longitudes 9, D17.

  93. Commission Technique Interministérielle de Télégraphe sans Fil, 7th Meeting, 8 March 1909, MS 1060, II F1, Archives of the Paris Observatory.

  94. Poincaré “La Mécanique nouvelle” (1910), 4, 51, 53–54.

  95. (Approval) Ministre de l’Instruction publique et des Beaux-Arts, à Monsieur le Directeur de l’Observatoire de Paris, 17 July 1909; (Meeting minutes) Commission Technique Interministérielle de Télégraphe sans Fil, 10th Meeting, 26 June 1909, both documents MS 1060, II F1, Archives of the Paris Observatory.

  96. Poincaré, “La Mécanique Nouvelle” [1909], 9. Manuscript copy is dated 24 July 1909 (Archives de l’Académie des Sciences).

  97. Poincaré, “La Mécanique Nouvelle,” Tuesday 3 August 1909.

  98. Amoudry, Général Ferrié (1993), 109; see Comptes rendus de l’Académie des Sciences report 31 January [1910].

  99. Scientific American 109, 13 December 1913, 455; see also Joan Marie Mathys (unpubl. MA thesis, “The Right Place at the Right Time,” Marquette University, 30 September 1991).

  100. Lallemand, “Projet d’organisation d’un service international de l’heure” (1912). On the Eiffel Tower-Arlington exchange, see, for example, Amoudry, Général Ferrié (1993), 117; Joan Marie Mathys (unpublished MA thesis, 1991); and Scientific American 109, 13 December 1913, 445.

  101. Howse, Greenwich (1980), 155.

  102. See 11th and 13th meetings of the Commission Technique Interministérielle de Télégraphe sans Fil, 21 March 1911 and 21 November 1911, MS 1060, II F1, Archives of the Paris Observatory.

  103. Léon Bloch, Le Principe de la relativité (1922), 15–16. Dominique Pestre characterizes Bloch (and his brother) as physicists who were unusual for their time in France by writing textbooks that looked positively on the new physics of the early twentieth century and characteristically wrote using a series of progressive generalizations from the concrete to the abstract (no doubt to appeal to their more experimentally oriented colleagues). See Pestre, Physique et Physiciens (1984), 18, 56, and 117.

  104. See Bureau des Longitudes, Réception des signaux horaires: Renseignements météorologiques, seismologiques, etc., transmis par les postes de télégraphie sans fil de la Tour Eiffel, Lyon, Bordeaux, etc. (Bureau des Longitudes, Paris, 1924), 83–84.

  105. Corrections are of many sorts, and include effects due to the motion of satellites, the lower gravitational field at the height of the satellites, and the rotatory motion of the earth. The relativistic component of the Doppler shift is v2/2c2, which for satellite velocities is about seven millionths of a second per day. Because the speed of light is so much faster than the speed of the satellites, most of general relativity need not be taken into account, but the equivalence principle that is part of general relativity is significant. (The equivalence principle says that there is no way to distinguish the physics of a freely falling box from the same box without a gravitational field.) A more rigorous analysis would take into account (inter alia) that the satellites’ orbit is not always in the same gravitational field, that the earth observer may be moving on the surface of the earth, that the earth’s gravitational field is not the same everywhere on the earth’s surface, that the sun’s gravitational field affects the earth clock and the satellite clock differently, and that the apparent velocity of light is altered by the earth’s gravitational field.

  106. Neil Ashby, “General Relativity in the Global Positioning System,” www.phys.lsu.edu/mog/mog9/node9.html (accessed 28 June 2002).

  107. Chronology of activist actions, www.plowshares.se/aktioner/plowcron5.htm (accessed 19 February 2002); also see Los Angeles Times, 12 May 1992, “Men Arrested in Space Satellite Hacking Called Peace Activists,” Metro part B, 12.

  108. Taylor, “Propaganda by Deed” (n.d.), 5, in “Greenwich Park Bomb file,” Cambridge University archives. Serge F. Kovaleski, “1907 Conrad Novel May Have Inspired Unabomb Suspect,” Washington Post, 9 July 1996, A1.

  109. This has been pointed out many times: Infeld, Albert Einstein (1950), 23; Holton, Thematic Origins (1973); and Miller, Einstein’s Relativity (1981), and idem, “The Special Relativity Theory” (1982), 3–26. Einstein does refer to “Lorentz’s theory” in the text (but no footnote).

  110. Myers, “From Discovery to Invention” (1995), 77.

  111. By law, patent officers were taught to look for originality. In Switzerland that hunt for novelty had a specific meaning: “Discoveries do not count as new, if at the time of their registration in Switzerland, they are well enough known that their development by the technically adept is already possible.” The contrast with neighboring countries is worth noting. In France rejection for lack of originality is based on “publicity” given to prior work, while in Germany a similar refusal could be made if the invention had been either reported in an official publication of the last century or if its use was so well known that its employment by other technical people appeared possible. According to turn-of-the-century patent manuals, Swiss law lay closer to the French; originality in Switzerland meant that the invention was not actually known in Switzerland regardless of what might lie dormant in an obscure foreign publication.

  112. Schanze, Patentrecht (1903), 33.

  113. Ibid., 33–34.

  114. Einste
in, “The World as I See It,” in idem, Ideas and Opinions (1954), 10.

  CHAPTER 6

  1. Einstein, “On the Relativity Principle and the Conclusions Drawn From It” [1907], document 47, in Collected Papers, vol. 2, 432–88; in Collected Papers (Translation), vol. 2, 252–55.

  2. Einstein did cite Poincaré’s work on the inertia of energy in Einstein’s 1906 derivation of E = mc2 (“The Principle of Conservation of Motion of the Center of Gravity” [1906], document 35, in Collected Papers (Translation), vol. 2, 200–206); then in (“On the Inertia of energy” [1907], document 45, in Collected Papers (Translation), vol. 2, 238–50). Einstein re-omitted Poincaré when Einstein again wrote on the inertia of energy.

  3. Poincaré, “La Mécanique Nouvelle” [1909], 9. Manuscript copy is dated 24 July 1909 (Archives de l’Académie des Sciences).

  4. Faguet, Après l’Ecole (1927), 41.

  5. Einstein, “On the Development of our Views Concerning the Nature and Constitution of Radiation,” document 60, in Collected Papers (Translation), vol. 2, 379.

  6. “Discours du Duc M. de Broglie” in Poincaré, Livre du centenaire (1935), 71–78, on 76.

  7. General conclusions by Poincaré, in Langevin and de Broglie, Théorie du rayonnement (1912), 451.

  8. I have retranslated this quotation and also corrected a spurious insertion that seems to have crept into the secondary literature. The phrase gegen die Relativitaetstheorie simply does not appear in the original. Einstein to Heinrich Zangger, 15 November 1911, item 305, in Collected Papers, vol. 5, 249–50.

  9. Poincaré to Weiss, editors of Poincaré Papers date as ca. November 1911. Poincaré et les Physiciens, unpubl. correspondence from the Henri Poincaré Archive Zürich.