Skip to main content
SpringerLink
Log in

Einstein, Nordström, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation

  • Chapter
The Genesis of General Relativity

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 250))

The advent of the special theory of relativity in 1905 brought many problems for the physics community. One, it seemed, would not be a great source of trouble. It was the problem of reconciling Newtonian gravitation theory with the new theory of space and time. Indeed it seemed that Newtonian theory could be rendered compatible with special relativity by any number of small modifications, each of which would be unlikely to lead to any significant deviations from the empirically testable consequences of Newtonian theory.1 Einstein's response to this problem is now legend. He decided almost immediately to abandon the search for a Lorentz covariant gravitation theory, for he had failed to construct such a theory that was compatible with the equality of inertial and gravitational mass. Positing what he later called the principle of equivalence, he decided that gravitation theory held the key to repairing what he perceived as the defect of the special theory of relativity—its relativity principle failed to apply to accelerated motion. He advanced a novel gravitation theory in which the gravitational potential was the now variable speed of light and in which special relativity held only as a limiting case.

It is almost impossible for modern readers to view this story with their vision unclouded by the knowledge that Einstein's fantastic 1907 speculations would lead to his greatest scientific success, the general theory of relativity. Yet, as we shall see, in 1907 Einstein had only the slenderest of grounds for judging all Lorentz covariant gravitation theories unacceptable. His 1907 judgement was clearly overly hasty. It was found quite soon that one could construct Lorentz covariant gravitation theories satisfying the equality of inertial and gravitational mass without great difficulty. Nonetheless we now do believe that Einstein was right in so far as a thorough pursuit of Lorentz covariant gravitation theories does lead us inexorably to abandon special relativity. In the picturesque wording of Misner et al. (1973, Ch.7) “gravity bursts out of special relativity.”

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 749.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 949.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abraham, Max. 1909. “Zur elektromagnetischen Mechanik.”Physikalische Zeitschrift, 10: 737–41.

    Google Scholar 

  • ——1910. “Die Bewegungsgleichungen eines Massenteilchens in der Relativtheorie.”Physikalische Zeitschrift, 11: 527–31.

    Google Scholar 

  • ——. 1912a. “Zur Theorie der Gravitation.”Physikalische Zeitschrift, 13: 1–4. (English translation in this volume.)

    Google Scholar 

  • ——. 1912b. “Das Elementargesetz der Gravitation.”Physikalische Zeitschrift, 13: 4–5.

    Google Scholar 

  • ——. 1912c. “Relativität und Gravitation. Erwiderung auf einer Bemerkung des Hrn. A. Einstein.”Annalen der Physik, 38: 1056–58.

    Article  Google Scholar 

  • ——. 1912d. “Nochmals Relativität und Gravitation. Bemerkung zu A. Einsteins Erwiderung.”Annalen der Physik, 39: 444–48.

    Article  Google Scholar 

  • ——. 1912e. “Eine neue Gravitationstheorie.”Archiv der Mathematik und Physik(3), XX: 193–209. (English translation in this volume.)

    Google Scholar 

  • Behacker, M. 1913. “Der freie Fall and die Planetenbewegung in Nordströms Gravitationstheorie.”Physikalische Zeitschrift, 14: 989–992.

    Google Scholar 

  • Corinaldesi, E. and A. Papapetrou, A. 1951. “Spinning Test Particles in General Relativity II.”Proceedings of the Royal Society, London, A209: 259–68.

    Google Scholar 

  • 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 

  • CPAE 3. 1993. Martin J. Klein, A. J. Kox, Jürgen Renn, and Robert Schulmann (eds.),The Collected Papers of Albert Einstein. Vol. 3.The Swiss Years: Writings, 1909–1911. Princeton: Princeton University Press.

    Google Scholar 

  • 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 

  • 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 

  • Ehrenfest, Paul. 1907. “Die Translation deformierbarer Elektronen und der Flächensatz.”Annalen der Physik, 23: 204–205.

    Article  Google Scholar 

  • Einstein, Albert. 1907a. “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen.”Jahrbuch der Radioaktivität und Elektronik, (1907) 4: 411–462; (1908) 5: 98–99, (CPAE 2, Doc. 47).

    Google Scholar 

  • ——. 1907b. “Bemerkungen zu der Notiz von Hrn Paul Ehrenfest: ‘Die Translation deformierbarer Elektronen und der Flächensatz’.” Annalen der Physik, 23: 206–208, (CPAE 2, Doc. 44).

    Article  Google Scholar 

  • ——. 1907c. “Über die vom Relativitätsprinzip gefordete Trägheit der Energie.”Annalen der Physik, 23: 371–384.

    Article  Google Scholar 

  • ——. 1911. “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes.”Annalen der Physik, 35: 898–908, (CPAE 3, Doc. 23).

    Article  Google Scholar 

  • ——. 1912a. “Lichtgeschwindigkeit und Statik des Gravitationsfeldes.”Annalen der Physik, 38: 355–69, (CPAE 4, Doc. 3).

    Article  Google Scholar 

  • ——. 1912b. “Zur Theorie des Statischen Gravitationsfeldes.”Annalen der Physik, 38: 443–58, (CPAE 4, Doc. 4).

    Article  Google Scholar 

  • ——. 1912c. “Gibt es eine Gravitationswirkung die der elektrodynamischen Induktionswirkung analog ist?”Vierteljahrsschrift für gerichtliche Medizin und öffentliches Sanitätswesen, 44: 37–40, (CPAE 4, Doc. 7).

    Google Scholar 

  • ——. 1912d. “Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham.”Annalen der Physik, 38: 1059–64, (CPAE 4, Doc. 8).

    Article  Google Scholar 

  • ——. 1912e. “Bemerkung zu Abrahams vorangehender Auseinandersetzung ‘Nochmals Relativität und Gravitation’.”Annalen der Physik, 39: 704, (CPAE 4, Doc. 9).

    Article  Google Scholar 

  • ——. 1913. “Zum gegenwärtigen Stande des Gravitationsproblems.”Physikalische Zeitschrift, 14: 1249–1262, (CPAE 4, Doc. 17). (English translation in this volume.)

    Google Scholar 

  • ——. 1915. “Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie.”Königlich Preussische Akademie der Wissenschaften(Berlin).Sitzungsberichte. 1915: 831–39, (CPAE 6, Doc. 24).

    Google Scholar 

  • ——. 1933. “Notes on the Origin of the General Theory of Relativity.” InIdeas and Opinions, 285–290. Translated by Sonja Bargmann. New York: Crown, 1954.

    Google Scholar 

  • ——. 1949.Autobiographical Notes. Open Court, 1979.

    Google Scholar 

  • Einstein, Albert and Adriaan D. Fokker. 1914. “Die Nordströmsche Gravitationstheorie vom Standpunkt des absoluten Differentialkalküls.”Annalen der Physik, 44: 321–28, (CPAE 4, Doc. 28).

    Google Scholar 

  • Einstein, Albert and Marcel Grossmann. 1913.Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. Leipzig: B.G.Teubner (separatum); with addendum by Einstein inZeitschrift für Mathematik und Physik, 63(1913): 225–61, (CPAE 4, Doc. 13).

    Google Scholar 

  • Holton, Gerald. 1975. “Finding Favor with the Angel of the Lord. Notes towards the Psychobiographical Study of Scientific Genius.” In Yehuda Elkana (ed.),The Interaction between Science and Philosophy. Humanities Press.

    Google Scholar 

  • Isaksson, Eva. 1985. “Der finnische Physiker Gunnar Nordström und sein Beitrag zur Entstehung der allgemeinen Relativitätstheorie Albert Einsteins.”NTM-Schriftennr. Gesch. Naturwiss., Technik, Med.Leipzig, 22, 1: 29–52.

    Google Scholar 

  • Janssen, Michel. 1995. “A Comparison between Lorentz's Ether Theory and Einstein's Special Theory of Relativity in the Light of the Experiments of Trouton and Noble.” PhD dissertation, University of Pittsburgh.

    Google Scholar 

  • Laue, Max. 1911a. “Zur Dynamik der Relativitätstheorie.”Annalen der Physik, 35: 524–542.

    Article  Google Scholar 

  • ——. 1911b.Das Relativitätsprinzip. Braunschweig: Friedrich Vieweg und Sohn.

    Google Scholar 

  • ——. 1911c. “Ein Beispiel zur Dynamik der Relativitätstheorie.”Verhandlungen der Deutschen Physikalischen Gesellschaft, 1911: 513–518.

    Google Scholar 

  • ——. 1912. “Zur Theorie des Versuches von Trouton und Noble.”Annalen der Physik, 38: 370–84.

    Article  Google Scholar 

  • ——. 1917. “Die Nordströmsche Gravitationstheorie.”Jahrbuch der Radioaktivität und Elektronik, 14: 263–313.

    Google Scholar 

  • ——. 1921.Die Relativitätstheorie. Vol. 2:Die allgemeine Relativitätstheorie und Einsteins Lehre von der Schwerkraft. Braunschweig: Friedrich Vieweg und Sohn.

    Google Scholar 

  • ——. 1949. “Zu Albert Einsteins 70-tem Geburtstag.”Rev. Mod. Phys., 21: 348–49.

    Article  Google Scholar 

  • Lewis, Gilbert N. and Richard C. Tolman. 1909. “The Principle of Relativity, and Non-Newtonian Mechanics.”Philosophical Magazine, 18: 510–523.

    Google Scholar 

  • Liu, Chuang. 1991.Relativistic Thermodynamics: Its History and Foundation. Ph.D. Dissertation, University of Pittsburgh.

    Google Scholar 

  • Maxwell, James C. 1864. “A dynamical theory of the electromagnetic field.” In W. D. Niven (ed.),The Scientific Papers of James Clerk Maxwell. Cambridge University Press, 1890. Reprinted 1965, New York: Dover, 526–597.

    Google Scholar 

  • Mie, Gustav. 1914. “Bemerkungen zu der Einsteinschen Gravitationstheorie. I and II.”Physikalische Zeitschrift, 14: 115–122; 169–176.

    Google Scholar 

  • Minkowski, Hermann. 1908. “Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern.”Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, Nachrichten1908: 53–111; InGesammelte Abhandlung von Hermann MinkowskiVol.2, Leipzig, 1911, 352–404. Reprinted New York: Chelsea. Page citations from this edition. (English translation of the appendix “Mechanics and the Relativity Postulate” in this volume.)

    Google Scholar 

  • ——. 1909. “Raum und Zeit.”Physikalische Zeitschrift, 10: 104–111. InGesammelte Abhandlung von Hermann MinkowskiVol.2, Leipzig, 1911, 431–444. Reprinted New York: Chelsea (page citations from this edition). Translated as “Space and Time,” in H.A.Lorentz et al.,Principle of Relativity, 1923, 75–91. Reprinted in 1952, New York: Dover.

    Google Scholar 

  • Misner, Charles W., Kip S. Thorne, and John A. Wheeler. 1973.Gravitation. San Francisco: Freeman.

    Google Scholar 

  • Nordström, Gunnar. 1909. “Zur Elektrodynamik Minkowskis.”Physikalische Zeitschrift, 10: 681–87.

    Google Scholar 

  • ——. 1910. “Zur elektromagnetischen Mechanik.”Physikalische Zeitschrift, 11: 440–45.

    Google Scholar 

  • ——. 1911. “Zur Relativitätsmechanik deformierbar Körper.”Physikalische Zeitschrift, 12: 854–57.

    Google Scholar 

  • ——. 1912. “Relativitätsprinzip und Gravitation.”Physikalische Zeitschrift, 13: 1126–29. (English translation in this volume.)

    Google Scholar 

  • ——. 1913a. “Träge und schwere Masse in der Relativitätsmechanik.”Annalen der Physik, 40: 856–78. (English translation in this volume.)

    Article  Google Scholar 

  • ——. 1913b. “Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzips.”Annalen der Physik, 42: 533–54. (English translation in this volume.)

    Article  Google Scholar 

  • ——. 1914a. “Die Fallgesetze und Planetenbewegungen in der Relativitätstheorie.”Annalen der Physik, 43: 1101–10.

    Article  Google Scholar 

  • ——. 1914b. “Über den Energiesatz in der Gravitationstheorie.”Physikalische Zeitschrift, 14: 375–80.

    Google Scholar 

  • ——. 1914c. “Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu vereinigen.”Physikalische Zeitschrift, 15: 504–506.

    Google Scholar 

  • ——. 1914d. “Zur Elektrizitäts- und Gravitationstheorie.”Ofversigt af Finska Vetenskaps-Societetens Förhandlingar, 57, (1914–1915), Afd. A, N:o.4: 1–15.

    Google Scholar 

  • ——. 1915. “Über eine Mögliche Grundlage einer Theorie der Materie,”Ofversigt af Finska Vetenskaps-Societetens Förhandlingar, 57, (1914–1915), Afd. A, N:o.28: 1–21.

    Google Scholar 

  • Norton, John D. 1984. “How Einstein found his Field Equations: 1912–1915.”Historical Studies in the Physical Sciences, 14: 253–316. Reprinted 1989 in Don Howard and John Stachel (eds.),Einstein and the History of General Relativity(Einstein Studies.vol. 1). Boston/Basel/Berlin: Birkhäuser, 101–159.

    Google Scholar 

  • ——. 1985. “What was Einstein's Principle of Equivalence?”Studies in History and Philosophy of Science, 16, 203–246. Reprinted 1989 in Don Howard and John Stachel (eds.),Einstein and the History of General Relativity. (Einstein Studiesvol. 1.) Boston/Basel/Berlin: Birkhäuser, 3–47. (Page citations from the former.)

    Article  Google Scholar 

  • ——. 1992a. “The Physical Content of General Covariance.” In J. Eisenstaedt and A. Kox (eds.),Studies in the History of General Relativity. (Einstein Studies, vol. 3.) Boston/Basel/Berlin: Birkhäuser.

    Google Scholar 

  • ——. 1992b. “Einstein, Nordström and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation.”Archive for History of Exact Sciences45: 17–94.

    Article  Google Scholar 

  • ——. 1993. “Einstein and Nordström: Some Lesser-Known Thought Experiments in Gravitation.” In J. Earman, M. Janssen and J. D. Norton (eds.),The Attraction of Gravitation: New Studies in the History of General Relativity. (Einstein Studies, vol. 5.) Boston/Basel/Berlin: Birkhäuser, 3–29.

    Google Scholar 

  • ——. 1995. “Eliminative Induction as a Method of Discovery: How Einstein Discovered General Relativity.” In J. Leplin (ed.),The Creation of Ideas in Physics: Studies for a Methodology of Theory Construction. Dordrecht: Kluwer, 29–69.

    Google Scholar 

  • Pais, Abraham. 1982.Subtle is the Lord … The Science and the Life of Albert Einstein. Oxford: Clarendon.

    Google Scholar 

  • Papapetrou, Achilles. 1951. “Spinning Test Particle in General Relativity I.”Proceedings of the Royal Society,London, A209, 248–58.

    Google Scholar 

  • Pauli, Wolfgang. 1921. “Relativitätstheorie.” InEncyklopädie der mathematischen Wissenschaften, mit Einschluss an ihrer Anwendung. Vol. 5,Physik, Part 2. Arnold Sommerfeld (ed.). Leipzig: B.G. Teubner, 1904–1922, 539–775. [Issued November 15, 1921.] English translationTheory of Relativity. With supplementary notes by the author. G. Field. Translated in 1958, London: Pergamon. (Citations from the Pergamon edition.)

    Google Scholar 

  • Planck, Max. 1908. “Zur Dynamik bewegter Körper.”Annalen der Physik, 26: 1–34.

    Article  Google Scholar 

  • Poincaré, Henri. 1905. “Sur la Dynamique de l' Électron.”Comptes Rendus des Séances de l' Academie des Sciences, 140: 1504–1508.

    Google Scholar 

  • ——. 1906. “Sur la Dynamique de l' Électron,”Rendiconti del Circolo Matematico di Palermo, 21: 129–75.

    Article  Google Scholar 

  • Ricci, Gregorio and Tullio Levi-Civita. 1901. “Méthodes de Calcul Différentiel Absolu et leurs Application.”Math. Ann., 54: 125–201. Reprinted 1954 in T. Levi-Civita,Opere Matematiche, vol. 1, Bologna, 479–559.

    Article  Google Scholar 

  • Rohrlich, Fritz. 1960. “Self-Energy and Stability of the Classical Electron.”American Journal of Physics, 28: 639–43.

    Article  Google Scholar 

  • Sommerfeld, Arnold. 1910. “Zur Relativitätstheorie I. Vierdimensionale Vektoralgebra.”Annalen der Physik, 32: 749–776; “Zur Relativitätstheorie II. Vierdimensionale Vektoranalysis.”Annalen der Physik, 33: 649–89.

    Article  Google Scholar 

  • Speziali, Pierre (ed.). 1972.Albert Einstein-Michele Besso: Correspondance 1903–1955. Paris: Hermann.

    Google Scholar 

  • Tolman, Richard C. 1934.Relativity, Thermodynamics and Cosmology. Oxford: Oxford University Press; Dover reprint, 1987.

    Google Scholar 

  • Trouton, Frederick T. and Henry R. Noble. 1903. “The Mechanical Forces Acting on a Charged Condensor moving through Space.”Philosophical Transactions of the Royal Society of London, 202: 165–181.

    Google Scholar 

  • Weyl, Hermann. 1918. “Reine Infinitesimal Geometrie.”Mathematische Zeitschrift, 2: 384–411.

    Article  Google Scholar 

  • Wheeler, John A. 1979. “Einstein's Last Lecture.” In G. E. Tauber (ed.),Albert Einstein's Theory of General Relativity. New York: Crown, 187–190.

    Google Scholar 

Download references

Authors
  1. John D. Norton
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Minnesota, USA

    Michel Janssen

  2. University of Pittsburgh, USA

    John D. Norton

  3. Max Planck Institute for the History of Science, Germany

    Jürgen Renn

  4. Einstein Papers Project, Caltech, USA

    Tilman Sauer

  5. Boston University, USA

    John Stachel

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Norton, J.D. (2007). Einstein, Nordström, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation. In: Janssen, M., Norton, J.D., Renn, J., Sauer, T., Stachel, J. (eds) The Genesis of General Relativity. Boston Studies in the Philosophy of Science, vol 250. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4000-9_27

Download citation

Publish with us

Policies and ethics

Search

Navigation