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Minkowski Spacetime: A Hundred Years Later pp 3–41Cite as

Hermann Minkowski, Relativity and the Axiomatic Approach to Physics

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 165))

Abstract

This article surveys the general background to Minkowski’s incursion into relativity, of which Einstein’s work represented just one side. Special attention is paid to the idiosyncratic, rich, and complex interaction between mathematics and physics, that stood at the center of attention of the Gttingen mathematicians since the turn of the twentieth century. In particular the article explains Minkowski’s formulation of special relativity in terms of space-time against the background of David Hilbert’s program for the axiomatization of physics. In addition, the article sheds light on the changing attitudes of Einstein towards mathematics, in the wake of Minkowski’s work, and his increasing willingness to attribute significance to mathematical formalism in developing physical theories.

This chapter is an adapted version of Chapter 4 of [5].

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References

  1. Born, M.:Die träge Masse und das Relativitätsprinzip. Ann. Phys. 28, 571–584 (1909)

    Article  Google Scholar 

  2. Born, M.: Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzip. Ann. Phys. 30, 1–56 (1909a)

    Article  Google Scholar 

  3. Born, M.: My Life: Recollections of a Nobel Laureate. Scribner’s, New York (1978)

    Google Scholar 

  4. Cohn, E.: Über die Gleichungen des electromagnetischen Feldes für bewegte Körper. Ann. Phys. 7, 29–56 (1902)

    Google Scholar 

  5. Corry, L.: Hilbert and the Axiomatization of Physics (1898–1918): From ‘Grundlagen der Geometrie’ to ‘Grundlagen der Physik’. Kluwer, Dordrecht (2004)

    Google Scholar 

  6. Darrigol, O.: The electrodynamic revolution in Germany as documented by early German expositions of ‘Maxwell’s Theory’. Arch. Hist. Ex. Sci. 45, 189–280 (1993)

    Article  MathSciNet  Google Scholar 

  7. Darrigol, O.: Electrodynamics form Ampère to Einstein.The University of Chicago Press, Chicago, IL (2000)

    Google Scholar 

  8. Einstein, A.: Bemerkungen zu der Notiz von Hrn. Paul Ehrenfest: ‘Die Translation deformierbarer Elektronen und der Flächensatz’. Ann. Phys. 23, 206–208 (1907) (CPAE 2, Doc. 44.)

    Article  Google Scholar 

  9. Einstein, A., Laub, K.: Über die elektromagnetischen Grundgleichungen für bewegte Körpern. Ann. Phys. 26, 532–540 (1908) (CPAE 2, Doc. 51.)

    Article  Google Scholar 

  10. Einstein, A., Laub, K.: Über die im elektromagnetischen Felde auf ruhende Körper ausgeübten ponderomotorischen Kräfte. Ann. Phys. 26, 541–550 (1908a) (CPAE 2, Doc. 52.)

    Article  Google Scholar 

  11. Frank, P.: Einstein. His Life and Times. New York, A. A. Knopf (1947)

    Google Scholar 

  12. Galison, P.:Minkowski’s space-time: From visual thinking to the absolute world. Hist. Stud. Phys. Sci. 10, 85–121 (1979)

    Article  Google Scholar 

  13. Giannetto, E.: The rise of special relativity: Henri Poincaré’s work before Einstein’s. In: Tucci, P. (ed.) Atti del XVIII Congresso Nazionale di Storia della Fisica e dell’Astronomia (Como 15–16 maggio 1998), pp. 171–207. Milano (1999)

    Google Scholar 

  14. Heilbron, J.: The Dilemmas of an Upright Man. Max Planck and the Fortunes of German Science. Harvard University Press, Cambridge, MA (2000)

    Google Scholar 

  15. Hentschel, K.: Interpretationen und Fehlinterpretationen der speziellen und der allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins. Birkhäuser, Basel/Boston (1990)

    MATH  Google Scholar 

  16. Hilbert, D.: Logische Principien des mathematischen Denkens (1905) (David Hilbert Nachlass, Göttingen 558a. Annotated by Max Born).

    Google Scholar 

  17. Hilbert, D.: Hermann Minkowski. Gött. Nach. 72–101 (1909) (Repr. in Math. Ann. 68, 445–471 (1910))

    Google Scholar 

  18. Holton, G.: Origins of Scientific Thought: Kepler to Einstein. Harvard University Press, Cambridge, MA (1988)

    Google Scholar 

  19. Jungnickel, C., McCormmach, R.: Intellectual Mastery of Nature – Theoretical Physics form Ohm to Einstein, 2 Vols. Chicago University Press, Chicago, IL (1986)

    Google Scholar 

  20. Katzir, S.:Poincaré’s relativistic Physics and its origins. Phys. Perspect. 7, 268–292 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  21. Kaufmann, W.: Über die Konstitution des Elektrons. Ann. Phys. 19, 487–553 (1906)

    Article  Google Scholar 

  22. Klein, F.: Über die geometrischen Grundlagen der Lorentzgruppe. Jahresb. DMV 19, 281–300 (1910)

    Google Scholar 

  23. Klein, F.: Vorlesungen über die Entwicklung der Mathematik im 19. In: Courant, R., Neugebauer, O. (eds.) Jahrhundert, 2 Vols. Springer, Berlin (1926) (Chelsea Repr., New York, 1948.)

    Google Scholar 

  24. Laue, M. v.:Das Relativitätsprinzip. Braunschweig, Vieweg (1911)

    Google Scholar 

  25. Lorentz, H.A.: Weiterbildung der Maxwellschen Theorie. Elektronentheorie. Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen V, 2–14, 145–280 (1904)

    Google Scholar 

  26. Maltese, G.,Orlando, L.: The definition of rigidity in the special theory of relativity and the genesis of the general theory of relativity. Stud. Hist. Phil. Mod. Phys. 26B, 263–306 (1995)

    Article  MathSciNet  Google Scholar 

  27. Miller, A.I.: Albert Einstein’s Special Theory of Relativity: Emergence (1905) and Early Interpretation, (1905–1911). Springer, New York (1997)

    Google Scholar 

  28. Minkowski, H.: (GA) Gesammelte Abhandlungen, ed. by D. Hilbert, 2 Vols. Leipzig 1911. (Chelsea reprint, New York 1967.)

    Google Scholar 

  29. Minkowski, H.: Ueber die Bewegung eines festes Körpers in einer Flüsigkeit. Berl. Ber., 1095–1110 (1888)

    Google Scholar 

  30. Minkowski, H.: Kapillarität. In: Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen V, 558–613 (1906)

    Google Scholar 

  31. Minkowski, H.: Wärmestrahlung, David Hilbert Nachlass, Göttingen 707 (1907)

    Google Scholar 

  32. Minkowski, H.: Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern. Gött. Nach., 53–111 (1908) [28, Vol. 2, 352–404]

    Google Scholar 

  33. Minkowski, H.: Raum und Zeit. Phys. Zeit. 10, 104–111 (1909) [28, Vol. 2, 431–444]

    Google Scholar 

  34. Minkowski, H.: Das Relativitätsprinzip. Ann. Phys. 47, 927–938 (1915)

    Article  Google Scholar 

  35. Minkowski, H.: Space and Time (Perrett, W., Jeffery, G.B. (English transl) of Minkowski 1909). In: Lorentz et al (eds.) The Principle of Relativity, pp. 73–91. Dover, New York (1952)

    Google Scholar 

  36. Norton, J.: Einstein, Nordström and the early demise of scalar, Lorentz-Covariant theories of gravitation. Arch. Hist. Ex. Sci. 45, 17–94 (1992)

    MATH  MathSciNet  Google Scholar 

  37. Norton, J.: General covariance and the foundations of general relativity. Rep. Prog. Phys. 56, 791–858 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  38. Pais, A.: Subtle is the Lord. The Science and the Life of Albert Einstein. Oxford University Press, New York (1982)

    Google Scholar 

  39. Planck, M.: Das Prinzip der Relativität und die Grundgleichungen der Mechanik. Ver. Deut. Phys. Ges. 8, 136–141 (1906)

    Google Scholar 

  40. Planck, M.: Zur Dynamik der bewegter Systeme. Berl. Ber. 13, 542–570 (1907) (Repr. in Ann. Phys. 26, 1–34 (1908))

    Google Scholar 

  41. Poincaré, H.: La valeur de la science. Paris (1905)

    Google Scholar 

  42. Poincaré, H.: Sur la dynamique de l’électron. Rendiconti del Circolo matimatico di Palermo 21, 129–176 (1906)

    Article  MATH  Google Scholar 

  43. Poincaré, H.: Science et méthode, Paris (1908) (English translation: Science and Method, New York, Dover – n.d.)

    Google Scholar 

  44. Pyenson, L.: Hermann Minkowski and Einstein’s Special Theory of Relativity. Arch. Hist. Ex. Sci. 17, 71–95 (1977) Repr. in [47, 80–100]

    MATH  MathSciNet  Google Scholar 

  45. Pyenson, L.: Physics in the shadows of Mathematics: The Göttingen Electron-theory seminar of 1905. Arch. Hist. Ex. Sci. 21, 55–89 (1979) Repr. in [47, 101–136]

    Article  MATH  MathSciNet  Google Scholar 

  46. Pyenson, L.: Relativity in late Wilhelmian Germany: The appeal to a pre-established harmony between Mathematics and Physics. Arch. Hist. Ex. Sci. 24 138–155 (1982) Repr. in [47, 137–157]

    MathSciNet  Google Scholar 

  47. Pyenson, L.: The Young Einstein – The Advent of Relativity. Adam Hilger Ltd, Bristol/Boston (1985)

    Google Scholar 

  48. Reich, K.: Die Entwicklung des Tensorkalküls. Vom absoluten Differentialkalkül zur Relativitätstheorie. Birkhäuser, Basel/Boston (1994)

    MATH  Google Scholar 

  49. Reid, C.:Hilbert. Springer, Berlin/New York (1970)

    Google Scholar 

  50. Schirrmacher, A.:Experimenting theory: The proofs of Kirchhoff’s radiation law before and after Planck. Hist. Stud. Phys. Sci. 33(2), 299–335 (2003)

    Google Scholar 

  51. Schwermer, J.: Räumliche Anschauung und Minima positiv definiter quadratischen Formen. Jahresb. DMV 93, 49–105 (1991)

    MATH  MathSciNet  Google Scholar 

  52. Seelig, C.: Albert Einstein. Europa Verlag, Zürich (1954)

    Google Scholar 

  53. Sommerfeld, A.: Zur Relativitätstheorie. I. Vierdimensionale Vektoralgebra. Ann. Phys. 32, 749–776 (1910); II. Vierdimensionale Vektoranalysis. Ann. Phys. 33, 649–689 (1910)

    Google Scholar 

  54. Stachel, J.: Einstein and Michelson: The context of discovery and the context of justification. Astronomische Nachrichten 303, 47–53 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  55. Staley, R.:On the histories of relativity: The propagation and elaboration of relativity theory in participant histories in Germany, 1905–1911. Isis 89, 263–299 (1998)

    Google Scholar 

  56. Walter, S.: Minkowski, mathematicians and the mathematical theory of relativity. In: Goenner, H. et al. (eds.) The Expanding Worlds of General Relativity, pp. 45–86. Birkhäuser, Boston (1999)

    Google Scholar 

  57. Walter, S.: The non-Euclidean style of Minkowskian relativity. In: Gray, J.J (ed.) The Symbolic Universe: Geometry and Physics (1990–1930), pp. 91–127. Oxford University Press, New York (1999a)

    Google Scholar 

  58. Walter, S.: Breaking in the 4-vectors: Lorentz-covariant gravitation theory, 1905–1910. In: Renn, J., Schemmel, M. (eds.) The genesis of general relativity, Vol. 3, Gravitation in the twilight of classical Physics: Between mechanics, field theory, and astronomy, pp. 193–152. Springer, Berlin (2007)

    Google Scholar 

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  1. Cohn Institute for History and Philosophy of Science, Tel-Aviv University, Tel Aviv, Israel

    Leo Corry

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  1. Liberal Arts College, Concordia University, de Maisonneuve Blvd. West 1455, Montreal, H3G 1M8, Canada

    Vesselin Petkov

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Corry, L. (2010). Hermann Minkowski, Relativity and the Axiomatic Approach to Physics. In: Petkov, V. (eds) Minkowski Spacetime: A Hundred Years Later. Fundamental Theories of Physics, vol 165. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3475-5_1

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