Conclusion
The advent of the general theory of relativity was so entirely the work of just one person — Albert Einstein — that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincaré and others. But where would the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordström to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordström's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordström see the most distant consequences of his own theory.
Similar content being viewed by others
References
Abraham, Max (1909) “Zur electromagnetischen Mechanik,” Physikalische Zeitschrift, 10, pp. 737–41.
Abraham, Max (1910) “Die Bewegungsgleichungen eines Massenteilchens in der Relativtheorie,” Physikalische Zeitschrift, 11, pp. 527–31.
Abraham, Max (1912a) “Zur Theorie der Gravitation,” Physikalische Zeitschrift, 13, pp. 1–4.
Abraham, Max (1912b) “Das Elementargesetz der Gravitation,” Physikalische Zeitschrift, 13, pp. 4–5.
Abraham, Max (1912c) “Relativität und Gravitation. Erwiderung auf eine Bemerkung des Hrn. A. Einstein,“ Annalen der Physik, 38, pp. 1056–58.
Abraham, Max (1912d) “Nochmals Relativität und Gravitation. Bemerkung zu A. Einsteins Erwiderung,” Annalen der Physik, 39, pp. 444–48.
Abraham, Max (1912e) “Eine neue Gravitationstheorie,” Archiv der Mathematik und Physik (3), XX, pp. 193–209.
Behacker, M. (1913) “Der freie Fall and die Planetenbewegung in Nordströms Gravitationstheorie,” Physikalische Zeitschrift, 14, pp. 989–992.
Corinaldesi, E., & Papapetrou, A. (1951) “Spinning Test Particles in General Relativity II,” Proceedings of the Royal Society, London, A209, pp. 259–68.
Ehrenfest, Paul (1907) “Die Translation deformierbarer Elektronen und der Flächensatz,” Annalen der Physik, 23, pp. 204–205.
Einstein, Albert (1907) “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen,” Jahrbuch der Radioaktivität und Elektronik, 4 (1907), pp. 411–462; 5 (1908), pp. 98–99.
Einstein, Albert (1907a) “Bemerkungen zu der Notiz von Hrn Paul Ehrenfest: ‘Die Translation deformierbarer Elektronen und der Flächensatz’,” Annalen der Physik, 23, pp. 206–208
Einstein, Albert (1907b) “Über die vom Relativitätsprinzip gefordete Trägheit der Energie,” Annalen der Physik, 23, pp. 371–384
Einstein, Albert (1911) “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes,” Annalen der Physik, 35, pp. 898–908
Einstein, Albert (1912a) “Lichtgeschwindigkeit und Statik des Gravitationsfeldes,” Annalen der Physik, 38, pp. 355–69
Einstein, Albert (1912b) “Zur Theorie des Statischen Gravitationsfeldes,” Annalen der Physik, 38, pp. 443–58
Einstein, Albert (1912c) “Gibt es eine Gravitationswirkung, die der elecktrodynamischen Induktionswirkung analog ist?” Vierteljahrsschrift für gerichtliche Medizin und öffentliches Sanitätswesen, 44, pp. 37–40
Einstein, Albert (1912d) “Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham,” Annalen der Physik, 38, pp. 1059–64
Einstein, Albert (1912e) “Bemerkung zu Abrahams vorangehender Auseinandersetzung ‘Nochmals Relativität und Gravitation’,” Annalen der Physik, 39, p. 704
Einstein, Albert (1913) “Zum gegenwärtigen Stande des Gravitationsproblems,” Physikalische Zeitschrift, 14, pp. 1249–1262.
Einstein, Albert (1915) “Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie,” Königlich Preussische Akademie der Wissenschaften (Berlin). Sitzungsberichte, 1915, pp. 831–39.
Einstein, Albert (1933) “Notes on the Origin of the General Theory of Relativity,” pp. 285–290 in Ideas and Opinions, trans. Sonja Bargmann, New York: Crown, 1954.
Einstein, Albert (1949) Autobiographical Notes. Open Court, 1979
Einstein, Albert, & Fokker, Adriaan D. (1914) “Die Nordströmsche Gravitationstheorie vom Standpunkt des absoluten Differentialkalküls,” Annalen der Physik, 44, pp. 321–28.
Einstein, Albert, & Grossmann, Marcel (1913) Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. Leibzig: B. G. Teubner (separatum); with addendum by Einstein in Zeitschrift für Mathemaik und Physik, 63 (1913), pp. 225–61.
Holton, Gerald (1975) “Finding favor with the Angel of the Lord. Notes towards the Psychobiographical Study of Scientific Genius,” in Y. Elkana, ed., The Interaction between Science and Philosophy. Humanities Press, 1975.
Isaksson, Eva (1985) “Der finnische Physiker Gunnar Nordström und sein Beitrag zur Entstehung der allgemeinen Relativitätstheorie Albert Einsteins,” NTM-Schriftenr., Gesch. Naturwiss., Technik, Med., Leipzig, 22, 1, pp. 29–52.
Janssen, Michel (manuscript) “Larmor, Lorentz and Laue on the Trouton and Trouton-Noble Experiments.” Klein, Martin, et al. (forthcoming) The Collected Papers of Albert Einstein, Vol. 4, Princeton Univ. Press.
Laue, Max (1911a) “Zur Dynamik der Relativitätstheorie,” Annalen der Physik, 35, pp. 524–542.
Laue, Max (1911b) Das Relativitätsprinzip. Braunschweig: Friedrich Vieweg und Sohn.
Laue, Max (1911c) “Ein Beispiel zur Dynamik der Relativitätstheorie,” Verhandlungen der Deutschen Physikalischen Gesellschaft, 1911, pp. 513–518.
Laue, Max (1912) “Zur Theorie des Versuches von Trouton und Noble,” Annalen der Physik, 38, pp. 370–84
Laue, Max (1917) “Die Nordströmsche Gravitationstheorie,” Jahrbuch der Radioaktivität und Elektronik, 14, pp. 263–313.
Laue, Max (1921) Die Relativitätstheorie. Vol. 2: Die allgemeine Relativitätstheorie und Einsteins Lehre von der Schwerkraft. Braunschweig: Freidrich Vieweg und Sohn.
Laue, Max (1949) “Zu Albert Einsteins 70-tem Geburstag,” Rev. Mod. Phys., 21, pp. 348–49
Lewis, Gilbert N., & Tolman, Richard, C. (1909) “The Principle of Relativity, and Non-Newtonian Mechanics,” Philosophical Magazine, 18, pp. 510–523.
Liu, Chuang (1991) Relativistic Thermodynamics: Its History and Foundation. Ph.D. Dissertation, University of Pittsburgh.
Maxwell, James C. “A dynamical theory of the electromagnetic field,” pp. 526–597 in W. D. Niven, (ed.) The Scientific Papers of James Clerk Maxwell, Cambridge at the University Press, 1890, reprinted New York: Dover, 1965
Mie, Gustav (1914) “Bemerkungen zu der Einsteinschen Gravitationstheorie. I and II,” Physikalische Zeitschrift, 14, pp. 115–122, 169–176.
Minkowski, Hermann (1908) “Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern,” Königliche Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, Nachrichten 1908, pp. 53–111; pp. 352–404 in Gesammelte Abhandlung von Hermann Minkowski Vol. 2. Leipzig, 1911, reprinted New York: Chelsea. Page citations from this edition.
Minkowski, Hermann (1909) “Raum und Zeit,” Physikalische Zeitschrift, 10, pp. 104–111; pp. 431–444 in Gesammelte Abhandlungen von Hermann Minkowski, Vol. 2. Leipzig, 1911, reprinted New York: Chelsea (page citations from this edition); translated as “Space and Time,” pp. 75–91 in H. A. Lorentz et al, Principle of Relativity. 1923; reprinted New York: Dover, 1952.
Misner, Charles, W., Thorne, Kip, S., & Wheeler, John A. (1973) Gravitation. San Francisco: Freeman.
Nordström, Gunnar (1909) “Zur Elektrodynamik Minkowskis,” Physikalische Zeitschrift, 10, pp. 681–87.
Nordström, Gunnar (1910) “Zur elektromagnetischen Mechanik,” Physikalische Zeitschrift, 11, pp. 440–45
Nordström, Gunnar (1911) “Zur Relativitätsmechanik deformierbar Körper,” Physikalische Zeitschrift, 12, pp. 854–57
Nordström, Gunnar (1912) “Relativitätsprinzip und Gravitation,” Physikalische Zeitschrift, 13, pp. 1126–29
Nordström, Gunnar (1913a) “Träge und schwere Masse in der Relativitätsmechanik,” Annalen der Physik, 40, pp. 856–78
Nordström, Gunnar (1913b) “Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzips,” Annalen der Physik, 42, pp. 533–54
Nordström, Gunnar (1914) “Die Fallgesetze und Planetenbewegungen in der Relativitätstheorie,” Annalen der Physik, 43, pp. 1101–10
Nordström, Gunnar (1914a) “Über den Energiesatz in der Gravitationstheorie,” Physikalische Zeitschrift, 14, pp. 375–80
Nordström, Gunnar (1914b) “Über die Möglichkeit. das elektromagnetische Feld und das Gravitationsfeld zu vereinigen,” Physikalische Zeitschrift, 15, pp. 504–506
Nordström, Gunnar (1914c) “Zur Elektrizitätsund Gravitationstheorie,” Ofversigt af Finska Vetenskaps-Societetens Förhandlingar, 57, (1914–1915), Afd. A, N:o. 4, pp. 1–15.
Nordström, Gunnar (1915) “Über eine Mögliche Grundlage einer Theorie der Materie,” Ofversigt af Finska Vetenskaps-Societetens Förhandlingar, 57, (1914–1915), Afd. A, N:o. 28, pp. 1–21.
Norton, John D. (1984) “How Einstein found his Field Equations: 1912–1915,” Historical Studies in the Physical Sciences, 14, pp. 253–316; reprinted in Don Howard & John Stachel (eds.) Einstein and the History of General Relativity: Einstein Studies, Vol. 1 Boston: Birkhäuser, 1989, pp. 101–159.
Norton, John D. (1985) “What was Einstein's Principle of Equivalence?” Studies in History and Philosophy of Science, 16, pp. 203–246; reprinted in Don Howard & John Stachel (eds.) Einstein and the History of General Relativity: Einstein Studies, Vol. 1 Boston: Birkhäuser, 1989, pp. 3–47. (Page citations from the former.)
Norton, John D. (1992) “The Physical Content of General Covariance” in J. Eisenstaedt & A. Kox eds, Studies in the History of General Relativity: Einstein Studies, Vol. 3, Boston: Birkhauser.
Norton, John D. (forthcoming) “Eliminative Induction as a Method of Discovery: How Einstein Discovered General Relativity.”
Pais, A. (1982) Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford: Clarendon.
Papapetrou, A. (1951) “Spinning Test Particle in General Relativity I,” Proceedings of the Royal Society, London, A209, pp. 248–58.
Pauli, Wolfgang (1921) “Relativitätstheorie,” in Encyklopädie der mathematischen Wissenschaften, mit Einschluss an ihrer Anwendung. Vol. 5, Physik, Part 2. Arnold Sommerfeld, ed., Leipzig: B. G. Teubner, 1904–1922, pp. 539–775. [Issued November 15, 1921] English translation Theory of Relativity. With supplementary notes by the author. G. Field, trans. London: Pergamon, 1958. (Citations from the Pergamon edition.)
Planck, Max (1908) “Zur Dynamik Bewegter Körper,” Annalen der Physik, 26, pp. 1–34
Poincaré, Henri (1905) “Sur la Dynamique de l'Électron,” Comptes Rendus des Seances de l'Académie des Sciences, 140, pp. 1504–1508
Poincaré, Henri (1906) “Sur la Dynamique de l'Électron,” Rendiconti del Circolo Matematico di Palermo, 21, pp. 129–75
Ricci, Gregorio & Levi-Civita, Tullio (1901) “Méthodes de Calcul Différentiel Absolu et leurs Application,” Math. Ann., 54, pp. 125–201; reprinted in T. LeviCivita, Opere Matematiche, Vol. 1, Bologna, 1954, pp. 479–559
Rohrlich, Fritz (1960) “Self-Energy and Stability of the Classical Electron,” American Journal of Physics, 28, pp. 639–43
Sommerfeld, Arnold (1910), “Zur Relativitätstheorie I. Vierdimensionale Vektoralgebra,” Annalen der Physik, 32, pp. 749–776; “Zur Relativitätstheorie II. Vierdimensionale Vektoranalysis,” Annalen der Physik, 33, pp. 649–89.
Speziali, Pierre, ed., (1972) Albert Einstein — Michele Besso: Correspondance 1903–1955. Paris: Hermann.
Stachel, John, ed., (1989) Collected Papers of Albert Einstein, Volume 2. The Swiss Years: Writings, 1900–1909. Princeton: Princeton Univ. Press.
Tolman, Richard C. (1934) Relativity, Thermodynamics and Cosmology. Oxford: Oxford University Press; Dover reprint, 1987
Trouton, Frederick T., & Noble, H. R. (1903) “The Mechanical Forces Acting on a Charged Condensor moving through Space,” Philosophical Transactions of the Royal Society of London, 202, pp. 165–181
Weyl, Hermann (1918) “Reine Infinitesimal Geometrie,” Mathematische Zeitschrift, 2, pp. 384–411.
Wheeler, John A. (1979) “Einstein's Last Lecture,” pp. 187–190 in G. E. Tauber (ed.), Albert Einstein's Theory of General Relativity. New York: Crown.
Author information
Authors and Affiliations
Additional information
Communicated by J. Buchwald
Rights and permissions
About this article
Cite this article
Norton, J.D. Einstein, Nordström and the early demise of scalar, Lorentz-covariant theories of gravitation. Arch. Hist. Exact Sci. 45, 17–94 (1992). https://doi.org/10.1007/BF00375886
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00375886