Abstract
The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of “general relativistic quantum mechanics” Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called ‘quantum phenomena’, represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld’s work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr’s correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.
Similar content being viewed by others
References
Ashtekar, Abhay and Robert Geroch. 1974. Quantum theory of gravitation, Reports on Progress in Physics, 37: 1211–56.
Bacciagaluppi, Guido and Antony Valentini. 2009. Quantum Theory at the Crossroads. Reconsidering the 1927 Solvay Conference. Cambridge: Cambridge University Press.
Bahrami, Mohammad, André Grossardt, Sandro Donadi and Angelo Bassi. 2014. The Schrödinger-Newton equation and its foundations, New Journal of Physics, 16: 115007.
Berestetskii, Valdimir, Evgenij M. Lifšhitz and Lev Pitaevskii. 1971. Relativistic Quantum Theory. Oxford: Pergamon Press.
Birrel, Nicholas D. and Paul C. W. Davies. 1982. Quantum fields in Curved Space. Cambridge: Cambridge University Press.
Blum, Alexander, Martin Jähnert, Christoph Lehner and Jürgen Renn. 2017. Translation as heuristics: Heisenber’s turn to matrix mechanics, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 60: 3–22.
Bronstein, Matvei P. 1935. Quantentheorie schwacher Gravitationsfelder. Physikalische Zeitschrift der Sowjetunion, 9: 140–157 (1936).
Carlip, Steven. 2008. Is Quantum Gravity necessary? Classical and Quantum Gravity, 25: 154010.
Chadwick, James. 1932. Possible existence of a neutron. Nature, 129: 312 1932.
Darrigol, Olivier. 1992. From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory. Berkeley: University of California Press.
de Broglie, Louis. 1927a. La mécanique ondulatoire et la structure atomique de la matière et du rayonnement. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 185: 380–382.
de Broglie, Louis. 1927b. L’univers à cinq dimensions et la mécanique ondulatoire. Le Journal de Physique et le Radium, Tome VIII: 65–73. Série VI.
De Donder, Theophile. 1926a. Application de la relativité aux le systèmes atomiques et moléculaires. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 182: 1380–1382.
De Donder, Theophile. 1926b. Application de la quantification déduite de la Gravifique einsteinienne. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 183: 594–595
De Donder,Theophile. 1927a. The Mathematical Theory of Relativity. Cambridge, MA: MIT.
De Donder, Théophile. 1927b. Le Principe de Correspondance déduit de la Gravifique et la Mécanique ondulatoire. (Quatrième communication). Bulletin de l’Académie royale de Belgique [Classe des Sciences], 13: 504–509. Serie 5.
De Donder, Théophile. 1930. Einsteinian gravity. Annales de l’Institut Henri Poincaré, 1: 77–116.
De Donder Théophile. 1930. Théorie invariantive du calcul des variations. Paris: Gauthier-Villars.
De Donder, Theophile and Frans H. van den Dungen. 1926. La quantification déduite de la Gravifique einsteinienne. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 183: 22–24.
Dirac, Paul A. M. 1928. The Quantum Theory of the Electron. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 117: 610–624.
Duff, Michael J. 1973. Quantum Tree Graphs and the Schwarzschild Solution. Physical Review D, 7: 2317–2326.
Duff, Michael J., B.E.W. Nilsson and C.E. Pope. 1986. Kaluza-Klein Supergravity. Physics Reports, 130: 1–142.
Eddington, Arthur S. 1923. The Mathematical Theory of Relativity. Cambridge: Cambridge University Press.
Einstein, Albert. 1916. Näherungsweise Integration der Feldgleichungen der Gravitation. Sitzungsberichte der Königlich Preussische Akademieder Wissenschaften, part 1: pp. 688–696.
Giulini, Domenico and André Grossardt. 2012. The Schrödinger–Newton equation as a non-relativistic limit of self-gravitating Klein–Gordon and Dirac fields. Classical and Quantum Gravity, 29: 215010.
Gordon, Walter. 1927. Der Comptoneffekt nach der Schrd¨ingerschen Theorie. Zeitschrift für Physik, 40: 117–133.
Gorelik, Gennady E. and Viktor Frenkel. 1994. Matvei Petrovich Bronstein and Sovjet Theoretical Physics in the Thirties. Basel: Birkhäuser.
Hagar, Amit. 2014. Discrete or Continuous? The Quest for Fundamental Length in Modern Physics. Cambridge: Cambridge University Press.
Hawking, Stephen W. 1975. Particle Creation by Black Holes. Communications in Mathematical Physics, 43: 199–220.
Heisenberg, Werner. 1927. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik, 43: 172–198.
Hilbert, David. 1900. Mathematische Probleme – Vortrag, gehalten auf dem internationalen Mathematiker-Kongreß zu Paris 1900. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 3: 253–297.
Jacobsen, Anja S. 2012. Léon Rosenfeld. Physics, Philosophy, and Politics in the Twentieth Century. Singapore: World Scientific.
Jaffé, George. 1922. Bemerkungen über die relativistischen Keplerellipsen. Annalen der Physik, 372: 212.
Jeffery, George B. 1921. The Field of an Electron on Einstein’s Theory of Gravitation. Proceedings of the Royal Society of London A, 99: 123–134.
Jordan, Pascual. 1947. Erweiterung der projektiven Relativitätstheorie. Annalen der Physik, 1: 219–228.
Jordan, Pascual and Oslar Klein. 1927. Zum Mehrkörperproblem der Quantentheorie. Zeitschrift für Physik, 45: 751–765.
Kaluza, Theodore. 1921. Zum Unitätsproblem in der Physik. Sitzungsberichte der KoniglichAkademieder Preussischen Akademie der Wissenschaften, 1: 966–972.
Kaluza, Theodor. 1984. On the Unification Problem in Physics. In: Lee, H. C., editor, An Introduction to Kaluza-Klein Theories – Workshop on Kaluza-Klein Theories, p. 1. Chalk River, Ontario, Canada: World Scientific. Translated by Taizo Muta.
Kanatchikov, Igor V. 1998. From the De Donder-Weyl Hamiltonian Formalism to Quantization of Gravity. In: Rainer, Martin and Schmidt, Hans-Jurgen, editors, Current topics in mathematical cosmology. Proceedings, International Seminar, ISMC’98, Potsdam, Germany, March 30–April 4, 1998: 457–467. Singapore: World Scientific.
Kanatchikov, Igor V. 2014. On precanonical quantization of gravity. Nonlinear Phenomena in Complex Systems, 17: 372–376.
Kiefer, Claus. 2004. Quantum Gravity. Oxford: Claredon Press.
Klein, Oskar. 1926a. Quantentheorie und fünfdimensionale Relativitätstheorie. Zeitschrift für Physik, 37: 895–906.
Klein, Oskar. 1926b. The atomicity of electricity as a quantum theory law. Nature, 118: 516.
Klein, Oskar. 1927a. Sur l’article de M. L. de Broglie: L’univers à cinq dimensions et la mécanique ondulatoire. Le Journal de Physique et le Radium, Tome VIII: 242–243. Série VI.
Klein, Oskar. 1927b. Zur fünfdimensionalen Darstellung der Relativitätstheorie. Zeitschrift für Physik, 46: 188–208.
Klein, Oskar. 1927c. Elektrodynamik und Wellenmechanik vom Standpunkt des Korrespondenzprinzip, Zeitschrift für Physik, 41: 407–442.
Klein, Oskar. 1984. “Quantum Theory and five-dimensional Relativity” by Oskar Klein. In: Lee, H. C., editor, An Introduction to Kaluza-Klein Theories – Workshop on Kaluza-Klein Theories: 10–21. Chalk River, Ontario, Canada: World Scientific. Traduzione a cura di Taizo Muta.
Klein, Oskar. 1991. From my Life of Physics. In: The Oskar Klein Memorial Lectures. Vol. 1: Lectures by C. N. Yang and S. Weinberg with translated reprints by O. Klein. Editor: Gösta Ekspong. Singapore: World Scientific Publishing Co. Pte. Ltd.
Kramers, Hendrik A. 1922. On the application of Einstein’s theory of gravitation to a stationary field of gravitation, Proceedings Koninklijke Akademie van Wetenschappen, 23: 1052–1073.
Kuhn, Thomas S. and John L. Heilbron. 1963. Interview with Dr. Leon Rosenfeld by Thomas S. Kuhn and John L. Heilbron At Carlsberg. July 1, 1963. College Park, MD USA: Niels Bohr Library & Archives, American Institute of Physics. Session I.
Landau, Lev D. and Evgenij M. Lifšhitz. 1951. The Classical Theory of Fields. Cambridge: Addison-Wesley.
Lodge, Oliver. 1921. The Gravitational Field of an Electron. Nature, 107: 392.
Mehra, Jagdish and Helmut Rechenberg. 2001. The Historical Development of Quantum Theory 1–6. New York: Springer-Verlag.
Mehra, Jagdish and Helmut Rechenberg. 2001. The Probability Interpretation and the Statistical Transformation Theory, the Physical Interpretation, and the Empirical and Mathematical Foundations of Quantum Mechanics 1926–1932. The Historical Development of Quantum Theory, Vol. 6, The Completion of Quantum Mechanics 1926–1941, Part I. New York: Springer-Verlag.
Misner, Charles W., Kip S. Thorne and John A. Wheeler. 1973. Gravitation. San Francisco: W.H. Freeman and Company.
M∅ller, Christian. 1962. The energy-momentum complex in general relativity and related problems. In Les théories relativistes de la gravitation. (ed. A. Lichnerowicz and M. A. Tonnelat), Paris: Editions du Centre National de la Recherche Scientifique.
Nordström, Gunnar. 1914. Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu Vereinigen. Physlische Zeitschrift, 15: 504–506.
O’Raifeartaigh, Lochlain and Norbert Straumann. 2000. Gauge theory: Historical origins and some modern developments. Reviews of Modern Physics, 72: 1–23.
Overduin, James M. and Paul S. Wesson. 1997. Kaluza-Klein Gravity. Physics Reports, 283: 303–380.
Pais, Abraham. 1982. “Subtle is the Lord ...”. The Science and Life of Albert Einstein. Oxford: Oxford University Press.
Pais, Abraham. 2000. The Genius of Science: A Portrait Gallery. Oxford: Oxford University Press.
Pauli, Wolfgang. 1927. Zur Quantenmechanik des magnetischen Elektrons. Zeitschrift für Physik, 43: 601–623.
Pauli, Wolfgang. 1993. Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a. Band III: 1940–1949/Scientific Correspondence with Bohr, Einstein, Heisenberg a.o. Volume III: 1940–1949. Edited by Karl von Meyenn. Berlin, Heidelberg: Springer-Verlag.
Penrose, Roger. 1996. On gravity’s role in quantum state reduction. General Relativity and Gravitation, 28: 581–600.
Rickles, Dean. 2005. “Pioneers of Quantum Gravity”. Talk presented at the Third Conference on History of Quantum Physics (HQ3).
Rickles, Dean. 2013. “Pourparlers for Amalgamation: Some Early Sources of Quantum Gravity Research”. In: Shaul Katzir, Christoph Lehner and Renn Jürgen, editors, Traditions and Transformations in the History of Quantum Physics, Chapter 6. Max Planck Research Library for the History and Development of Knoledge. Proceedings 5. Third International Conference on the History of Quantum Physics, Berlin, June 28–July 2, 2010; http://www.edition-open-access.de/proceedings/5/index.html.
Robertson, Baldwin. 1972. Introduction to field operators in quantum mechanics. American Journal of Physics, 41 :678–690.
Rocci, Alessio. 2013. On first attempts to reconcile quantum principles with gravity. Journal of Physics: Conference Series, 470: 12004.
Rocci, Alessio. 2015a. Oliver in Quantum-Gravity-land. http://www.oliverlodge.org/oliver-in-quantum-gravity-land/. Based on talk given at 3rd Making Waves Workshop. October, 31 Liverpool.
Rocci, Alessio. 2015b. History of Quantum Gravity: from the birth of General Relativity to the end of WWII 1915–1945. http://paduaresearch.cab.unipd.it/8916, Language: Italian.
Rosenfeld, Léon. 1927a. L’Univers à cinq dimensions et la Mécanique ondulatoire. Bulletin de l’Académie royale de Belgique [Classe des Sciences], 13: 304–325. Serie 5.
Rosenfeld, Léon. 1927b. L’Univers à cinq dimensions et la Mécanique ondulatoire. (Deuxième communication). Bulletin de l’Académie royale de Belgique [Classe des Sciences], 13: 447–458. Serie 5.
Rosenfeld, Léon. 1927c. L’Univers à cinq dimensions et la Mécanique ondulatoire. (Troisième communication). Bulletin de l’Académie royale de Belgique [Classe des Sciences], 13: 573–579. Serie 5.
Rosenfeld, Léon. 1927d. L’électron magnétique et la mécanique ondulatoire. Comptes rendus hebdomadaires des séances de l’Académie des sciences, T184: 1540–1541.
Rosenfeld, Léon. 1927e. L’Univers à cinq dimensions et la Mécanique ondulatoire. (Quatrième communication). Bulletin de l’Académie royale de Belgique [Classe des Sciences], 13: 661–682. Serie 5.
Rosenfeld, Léon. 1930a. Über die Gravitationswirkungen des Lichtes. Zeitschrift für Physik, 65: 589–599.
Rosenfeld, Léon. 1930b. Zur Quantelung der Wellenfelder. Annalen der Physik, 5: 113–152.
Rosenfeld, Léon. 1963. On quantization of fields. Nuclear Physics, 40: 353–356.
Rosenfeld, Léon. 2017. On the quantization of wave fields. European Physical Journal H, 42: 63–94.
Salisbury, Donald and Kurt Sundermeyer. 2017. Léon Rosenfeld’s general theory of constrained Hamiltonian dynamics. European Physical Journal H, 42: 23–61.
Schrödinger, Erwin. 1926. Quantisierung als Eigenwertproblem. (Erste Mitteilung). Annalen der Physik, 79: 361–376.
Schrödinger, Erwin. 1927. Der Energieimpulssatz der Materiewellen. Annalen der Physik, 82: 265–272.
Solomon, Jacques. 1938. Gravitation et quanta. Journal de Physique et le Radium, 9: 479–485.
Stachel, John. 1999. Introduction. In: Tian Yu Cao, editor, Conceptual foundations of quantum field theory, Chapter V, Quantum field theory and space-time. Cambridge: Cambridge University Press. pp. 166–175.
Rickles, Dean, and Steven Weinstein. 2016. “Quantum Gravity”, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2016/entries/quantum-gravity/.
Thiry, Yves. 1948. Les équations de la théorie unitaire de Kaluza. Comptes rendus hebdomadaires des séances de l’Académie des sciences, T226: 216–218.
Vallarta, Manuel Sandoval. 1924. Bohr’s Atomic Model from the Standpoint of the General Theory of Relativity and of the Calculus Of Perturbations. Ph.D. thesis, Cambridge, MA, USA: Massachusetts Institute of Technology.
von Borzeszkowski, Horst-Heino and Hans J. Treder. 1988. The Meaning of Quantum Gravity. Dordrecht: D. Reidel Publishing Company.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Peruzzi, G., Rocci, A. Tales from the prehistory of Quantum Gravity. EPJ H 43, 185–241 (2018). https://doi.org/10.1140/epjh/e2018-80018-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjh/e2018-80018-6