Einstein and Mach's Principle

  • Julian B. Barbour
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 250)

Einstein's attempt to realize Machian ideas in the construction of general relativity was undoubtedly a very major stimulus to the creation of that theory. Indeed, the very name of the theory derives from Einstein's conviction that a theory which does justice to Mach's critique of Newton's notion of absolute space must be generally relativis-tic, or covariant with respect to the most extensive possible transformations of the spacetime coordinates.

The extent to which general relativity is actually Machian is, however, the subject of great controversy. During the last six months, I have been examining closely all of Einstein's papers that concern the special and general theory of relativity together with a substantial proportion of his correspondence related to relativity. There were several things that I wished to establish: 1) What precisely was the defect (or defects) in the Newtonian scheme that Einstein sought to rectify in his general theory of relativity? 2) How did Einstein propose to rectify the perceived defect(s)? 3) What relation does Einstein's work on his Machian ideas bear to the other ideas and work of his predecessors and contemporaries on the problem of absolute and relative motion? 4) Finally, to what extent did general relativity solve that great and ancient problem of the connection between and status of absolute and relative motion?


Inertial Frame Inertial System Relativity Principle Absolute Space Reference Body 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Anderson, Edward and Julian B. Barbour. 2002. “Interacting Vector Fields in Relativity without Relativity.” Classical and Quantum Gravity 19: 3249–3261 (gr-qc 0201092).CrossRefGoogle Scholar
  2. Anderson, Edward, Julian B. Barbour, Brendan Z. Foster, and Niall Ó Murchadha. 2003. “Scale-Invariant Gravity: Geometrodynamics.” Classical and Quantum Gravity 20: 3217–3248 (gr-qc 0211022).CrossRefGoogle Scholar
  3. Barbour, Julian B. 1989. Absolute or Relative Motion, Vol. 1. The Discovery of Dynamics. Cambridge: Cambridge University Press. Reprinted 2001 as the paperback The Discovery of Dynamics. New York: Oxford University Press.Google Scholar
  4. ——. 1994. “The Timelessness of Quantum Gravity. I. The Evidence from the Classical Theory. II. The Appearance of Dynamics in Static Configurations.” Classical and Quantum Gravity 11: 2853–2897.CrossRefGoogle Scholar
  5. ——. 1995. “General relativity as a Perfectly Machian Theory.” In (Barbour and Pfister 1995).Google Scholar
  6. ——. 1997. “Nows Are All We Need.” In H. Atmanspacher and E. Ruhnau (eds.), Time, Temporality, Now. Berlin: Springer-Verlag.Google Scholar
  7. ——. 1999a. The End of Time. London: Weidenfeld & Nicholson: New York: Oxford University Press (2000).Google Scholar
  8. ——. 1999b. “The Development of Machian Themes in the Twentieth Century.” In J. Butterfield (ed.), The Arguments of Time. Oxford: Oxford University Press.Google Scholar
  9. ——. 2001. “On General Covariance and Best Matching.” In C. Callender and N. Huggett (eds.), Physics Meets Philosophy at the Planck Scale. Cambridge: Cambridge University Press.Google Scholar
  10. ——. 2003a. “Scale-Invariant Gravity: Particle Dynamics.” Classical and Quantum Gravity 20: 1543–1570 (gr-qc 0211021).CrossRefGoogle Scholar
  11. ——. 2003b. “Dynamics of Pure Shape, Relativity and the Problem of Time.” In H.-T. Elze (ed.), Deco-herence and Entropy in Complex Systems. Lecture Notes in Physics, Vol. 663. Berlin: Springer-Verlag (gr-qc 0308089).Google Scholar
  12. ——. (in preparation). Absolute or Relative Motion? Vol. 2: The Frame of the World. New York: Oxford University Press.Google Scholar
  13. Barbour, Julian B. and Bruno Bertotti. 1977. “Gravity and Inertia in A Machian Framework.” Nuovo Cimento 38B: 1–27.Google Scholar
  14. ——. 1982. “Mach's Principle and the Structure of Dynamical Theories.” Proceedings of the Royal Society of London, Series A 382: 295–306.CrossRefGoogle Scholar
  15. Barbour, Julian B., Brendan Z. Foster and Niall Ó Murchadha. 2002. “Relativity without Relativity.” Classical and Quantum Gravity 19: 3217–3248 (gr-qc 0012089).CrossRefGoogle Scholar
  16. Barbour, Julian B. and Herbert Pfister (eds.). 1995. Mach's Principle: From Newton's Bucket to Quantum Gravity. Einstein Studies, Vol. 6. Boston: Birkhäuser.Google Scholar
  17. Clemence, G.M. 1957. “Astronomical Time.” Reviews of Modern Physics 29, 2–8.CrossRefGoogle Scholar
  18. CPAE 1: John Stachel, David C. Cassidy, Robert Schulmann, and Jürgen Renn (eds.), The Collected Papers of Albert Einstein. Vol. 1. The Early Years, 1879–1902. Princeton: Princeton University Press, 1987.Google Scholar
  19. CPAE 2. 1989. John Stachel, David C. Cassidy, Jürgen Renn, and Robert Schulmann (eds.), The Collected Papers of Albert Einstein. Vol. 2. The Swiss Years: Writings, 1900–1909. Princeton: Princeton University Press.Google Scholar
  20. CPAE 4. 1995. Martin J. Klein, A. J. Kox, Jürgen Renn, and Robert Schulmann (eds.), The Collected Papers of Albert Einstein. Vol. 4. The Swiss Years: Writings, 1912–1914. Princeton: Princeton University Press.Google Scholar
  21. CPAE 5E: The Collected Papers of Albert Einstein. Vol. 5. The Swiss Years: Correspondence, 1902–1914. English edition translated by Anna Beck, consultant Don Howard. Princeton: Princeton University Press, 1995.Google Scholar
  22. CPAE 6. 1996. A. J. Kox, Martin J. Klein, and Robert Schulmann (eds.), The Collected Papers of Albert Einstein. Vol. 6. The Berlin Years: Writings, 1914–1917. Princeton: Princeton University Press.Google Scholar
  23. CPAE 7. 2002. Michel Janssen, Robert Schulmann, József Illy, Christoph Lehner, and Diana Kormos Buchwald (eds.), The Collected Papers of Albert Einstein. Vol. 7. The Berlin Years: Writings, 1918–1921. Princeton: Princeton University Press.Google Scholar
  24. Dziobek, Otto. 1888. Die mathematischen Theorien der Planeten-Bewegungen. Leipzig: J. A. Barth.Google Scholar
  25. ——. 1892. Mathematical Theories of Planetary Motions. Register Publishing Company. Reprinted by Dover in 1962.Google Scholar
  26. Einstein, Albert. 1905. “Zur Elektrodynamik bewegter Körper.” Annalen der Physik 17, 891–921, (CPAE 2, Doc. 23). English translation in (Lorentz et al. 1923).CrossRefGoogle Scholar
  27. ——. 1907. “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen.” V. §17. Jahr-buch der Radioaktivität und Elektronik 4: 411–462, (CPAE 2, Doc. 47).Google Scholar
  28. ——. 1912. “Gibt es eine Gravitationswirkung, die der elektrodynamischen Induktionswirkung analog ist?” Vierteljahrschrift für gerichtliche Medizin und öffentliches Sanitätswesen 44: 37–40, (CPAE 4, Doc. 7).Google Scholar
  29. ——. 1913a. “Zum gegenwärtigen Stande des Gravitationsproblems.” Physikalische Zeitschrift 14: 1249–1266, (CPAE 4, Doc. 17). (English translation in this volume.)Google Scholar
  30. ——. 1913b. “Physikalische Grundlagen einer Gravitationstheorie.” Vierteljahrsschrift der Naturfor-schenden Gesellschaft Zürich 58: 284–290, (CPAE 4, Doc. 16).Google Scholar
  31. ——. 1914. “Die formale Grundlage der allgemeinen Relativitätstheorie.” Sitzungsberichte der Preussi-schen Akademie der Wissenschaften, 1030–1085, Part 2, (CPAE 6, Doc. 9).Google Scholar
  32. ——. 1917. “Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie.” Sitzungsberichte der Preussischen Akademie der Wissenschaften: 142–145, (CPAE 6, Doc. 43).Google Scholar
  33. ——. 1918a. “Prinzipielles zur allgemeinen Relativitätstheorie.” Annalen der Physik 55: 241–244, (CPAE 7, Doc. 4).CrossRefGoogle Scholar
  34. ——. 1918b. “Dialog über Einwände gegen die Relativitätstheorie.” Die Naturwissenschaften 6: No. 48, 697–702, (CPAE 7, Doc. 13).CrossRefGoogle Scholar
  35. ——. 1919. “What is the Theory of Relativity?” The Times, 29 November 1919. Republished in (Einstein 1954).Google Scholar
  36. ——. 1921. “Geometrie und Erfahrung.” Sitzungsberichte der Preussischen Akademie der Wissenschaf-ten Vol. 1, 123–130.Google Scholar
  37. ——. 1923. “Grundgedanken und Probleme der Relativitätstheorie.” In Nobelstiftelsen, Les Prix Nobel en 1921–1922. Stockholm: Imprimerie Royale.Google Scholar
  38. ——. 1926. “Nichteuklidsche Geometrie in der Physik.” Neue Rundschau, January.Google Scholar
  39. ——. 1933. “Notes on the Origin of the General Theory of Relativity.” In Albert Einstein. Ideas and Opinions, 285–290. Translated by Sonja Bargmann. New York: Crown, 1954.Google Scholar
  40. ——. 1949. “Autobiographical Notes.” In P.A. Schilpp (ed.), Albert Einstein, Philosopher-Scientist. Evanston, Illinois: The Library of Living Philosophers, Inc., Illinois, 29.Google Scholar
  41. ——. 1954. Ideas and Opinions. New York: Crown Publishers.Google Scholar
  42. Frege, Gustav. 1891. “Über das Trägheitsgesetz.” Zeitschrift für Philosophie und philosophische Kritik 98, 145–161.Google Scholar
  43. Friedlaender, Benedict and Immanuel Friedlaender. 1896. Absolute oder relative Bewegung? Berlin: Leon-hard Simion. (English translation in this volume.)Google Scholar
  44. Hall, Alfred R. and Marie B. Hall. 1962. Unpublished Scientific Papers of Isaac Newton. Cambridge: Cambridge University Press.Google Scholar
  45. Helmholtz, Hermann L. F. 1968. “Über die Tatsachen, die der Geometrie zum Grunde liegen.” Nachrichte von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, No. 9, June 3rd.Google Scholar
  46. Hofmann, W. 1904. Kritische Beleuchtung der beiden Grundbegriffe der Mechanik: Bewegung und Träg-heit und daraus gezogene Folgerungen betreffs der Achsendrehung der Erde und des Foucault'schen Pendelversuchs. Wien und Leipzig: M. Kuppitsch.Google Scholar
  47. Kretschmann, Erich. 1917. “Über den physikalischen Sinn der Relativitätspostulate, A. Einsteins neue und seine ursprüngliche Relativitätstheorie.” Annalen der Physik 53: 575–614.Google Scholar
  48. Lagrange, Joseph-Louis. 1772. “Essai sur le problème des trois corps.” Republished in: Oeuvres de Lagrange, Vol. 6, Paris: Gauthier-Villars, 229 (1873).Google Scholar
  49. Lange, Ludwig. 1884. “Über die wissenschaftliche Fassung des Galilei'schen Beharrungsgesetz.” Philoso-phische Studien 2: 266–297.Google Scholar
  50. ——. 1885. “Über das Beharrungsgesetz.” Berichte der Königlichen Sächsischen Gesellschaft der Wis-senschaften, Math.-Physik. Klasse 333–351.Google Scholar
  51. ——. 1886. Die geschichtliche Entwicklung des Bewegungsbegriffs und ihr voraussichtliches Endergeb-nis. Ein Beitrag zur historischen Kritik der mechanischen Prinzipien. Leipzig: W. Engelmann.Google Scholar
  52. Laue, Max von. 1948. “Dr. Ludwig Lange. 1863–1936. (Ein zu unrecht Vergessener.)” Die Naturwissen-schaften 35, 193.CrossRefGoogle Scholar
  53. ——. 1955. Die Relativitätstheorie, Vol. 1. Die Spezielle Relativitätstheorie. Braunschweig: Vieweg.Google Scholar
  54. Lorentz, Hendrik Anton. 1895. Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern. Leiden: Brill.Google Scholar
  55. Lorentz, Hendrik Antoon et al. 1923. The Principle of Relativity. London: Methuen.Google Scholar
  56. Mach, Ernst. 1872. Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit. Prague: Calve.Google Scholar
  57. ——. 1883. Die Mechanik in ihrer Entwickelung. Historisch-kritisch dargestellt. Leipzig: F.A. Brock-haus.Google Scholar
  58. ——. 1911. History and Root of the Principle of the Conservation of Energy. Chicago: Open Court.Google Scholar
  59. ——. 1960. The Science of Mechanics. A Critical and Historical Account of Its Development. LaSalle: Open Court.Google Scholar
  60. Neumann, Carl. 1870. Ueber die Prinzipien der Galilei-Newtonschen Theorie. Leipzig: Teubner.Google Scholar
  61. Norton, John. 1995. “Mach's Principle before Einstein.” In (Barbour and Pfister 1995).Google Scholar
  62. Poincaré, Henri. 1898. “La Mesure du Temps.” Republished in Poincaré, Henri (1905). La Valeur de la Science. Google Scholar
  63. ——. 1902. La Science et l'Hypothèse. Paris: Flammarion.Google Scholar
  64. ——. 1905. Science and Hypothesis. London: Walter Scott Publ. Co.Google Scholar
  65. Reissner, Hans. 1914. “Über die Relativität der Beschleunigungen in der Mechanik.” Physikalische Zeit-schrift 15: 371–75.Google Scholar
  66. ——. 1915. “Über eine Möglichkeit die Gravitation als unmittelbare Folge der Relativität der Trägheit abzuleiten.” Physikalische Zeitschrift 16: 179–85.Google Scholar
  67. Riemann, Bernhard. 1867. “Über die Hypothesen, welche der Geometrie zu grunde liegen.” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 13.Google Scholar
  68. Tait. Peter G. 1883. “Note on Reference Frames.” Proceedings of the Royal Society of Edinburgh, Session 1883–84: 743–745.Google Scholar
  69. Thomson, James. 1883. “On the law of inertia; the principle of chronometry; and the principle of absolute clinural rest, and of absolute rotation.” In Proceedings of the Royal Society of Edinburgh, Session 1883–84, 568 and 730.Google Scholar
  70. Thomson, William and Peter G. Tait. 1867. Elements of Natural Philosophy. Cambridge: Cambridge University Press.Google Scholar

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