Skip to main content Accessibility help
  • Cited by 1
  • Print publication year: 2003
  • Online publication date: March 2008

14 - Theories of space-time in modern physics

from 4 - Philosophy and the new physics



Among the most important events of twentieth-century physics, we must surely count the development of the special and the general theories of relativity by Einstein in 1905 and 1916, and that of quantum mechanics, which was worked out about ten years later by Bohr, Heisenberg, Schrödinger, and de Broglie. Owing to these theories, the physicist’s conception of space-time underwent two major upheavals.

Although they apply on different scales, the general theory of relativity and the quantum field theory play a fundamental role in describing the natural world, so a complete description of nature must encompass both of them. The formal attempt to quantise general relativity, however, leads to nonsensical infinite formulas. In the sixties non-Abelian gauge theory emerged as a framework for describing all natural forces except gravity; however, at the same time, the inconsistency between general relativity and quantum field theory emerged clearly as the limitation of twentieth-century physics. The resulting problem is a theorists’ problem par excellence: experiments provide little help, and the inconsistency illustrates the intermingling of philosophical, mathematical, and physical thought.

It is a fact of great significance that every physical theory of some generality and scope, whether it is a classical or a quantum theory, a particle or a field theory, presupposes a space-time geometry for the formulation of its laws and for its interpretation, and the choice of this geometry predetermines to some extent the laws which are taken to govern the behaviour of matter. Thus Newton’s classical mechanics (and especially its law of gravitation) is based on the assumption of an absolute simultaneity relation between events and a Euclidean geometry; similarly, the physical principle of the universal proportionality of inertial and gravitational mass, as recognised by Einstein between 1907 and 1915, requires the assignment of a non-integrable, that is, path-dependent, linear connection with non-vanishing curvature to space-time (the law of parallel displacement).

Adler, R., Bazin, M., and Schiffer, M. (1965). Introduction to General Relativity, San Francisco: McGraw-Hill.
Barbour, J. B. (1982). ‘Relational Concepts of Space and Time’, The British Journal for the Philosophy of Science 33.
Bergman, P. G. (1942). Introduction to the Theory of Relativity, Englewood Cliffs, NJ: Prentice-Hall.
Bohm, D. (1965). The Special Theory of Relativity, New York: W. A. Benjamin.
Boi, L. (1995). Le problème mathématique de l espace. Une quête de l'intelligible, Berlin: Springer.
Boi, L. (1999). ‘Some Mathematical, Epistemological and Historical Reflections on the Relationship between Geometry and Reality, Spacetime Theory and the Geometrization of Theoretical Physics, from B. Riemann to H. Weyl and Beyond’, Preprint C.A.M.S. (EHESS, Paris) no. 176.
Cao, T. Yu (1997). Conceptual Developments of 20th Century Field Theories, Cambridge: Cambridge University Press.
Cartan, E. (1923). ‘Sur les variétés à connexion affine et la théorie de la relativité généralisée’, Annales de l Ecole Normale Supérieure 40.
Clifford, W. K. (1876). ‘On the Space-Theory of Matter’, Cambridge Philosophical Society Proceedings 2.
Cohen-Tannoudji, G. and Spiro, M. (1986). La matière-espace-temps, Paris: Fayard.
Coleman, R. A. and Kort, H. (1995). ‘A New Semantics for the Epistemology of Geometry. I: Modeling Spacetime Structure’, Erkenntnis 2, 42. (Special Issue on ‘Reflections on Spacetime: Foundations, Philosophy, History’, ed. Majer, U. and Schmidt, H.-J..)
Damour, Th. (1995). ‘General Relativity and Experiment’ in Iagolnitzer, D. (ed.), Proceedings of the XIth International Congress of Mathematical Physics, Boston: International Press.
Earman, J., Glymour, C., and Stachel, J. (eds.) (1977). Foundations of Space-Time Theories, Minneapolis: University of Minnesota Press.
Eddington, A. (1924). The Mathematical Theory of Relativity, Cambridge: Cambridge University Press.
Ehlers, J. (1973). ‘The Nature and Structure of Spacetime’ in Mehra, J. (ed.), The Physicist’s Conception of Nature, Dordrecht: Reidel.
Einstein, A. and Infeld, L. (1938). The Evolution of Physics, New York: Simon and Schuster.
Einstein, A. (1905). ‘Zur Elektrodynamik bewegter Körper’, Annalen der Physik 17.
Einstein, A. (1916). ‘Die Grundlagen der allgemeinen Relativitätstheorie’, Annalen der Physik 4, 49.
Einstein, A. (1956). The Meaning of Relativity, Princeton, NJ: Princeton University Press.
Ellis, G. F. R. and Williams, R. M. (1988). Flat and Curved Space-Times, Oxford: Clarendon Press.
Feynman, R. (1967). The Character of Physical Laws, Cambridge, MA: The MIT Press.
Fock, V. (1959). The Theory of Space, Time and Gravitation, London: Pergamon Press.
Friedman, M. (1983). Foundations of Space-Time Theories: Relativistic Physics and the Philosophy of Science, Princeton, NJ: Princeton University Press.
Geroch, R. P. and Horowitz, G. T. (1979). ‘Global structures of spacetimes’ in Hawking, S. W. and Israel, W. (eds.), General Relativity. An Einstein Centenary Survey, Cambridge: Cambridge University Press.
Graves, J. C. (1971). The Conceptual Foundations of Contemporary Relativity Theory, Cambridge, MA: The MIT Press.
Grünbaum, A. (1973). Philosophical Problems of Space and Time, 2nd, enlarged edn. Dordrecht: Reidel.
Hawking, S. W. and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time, Cambridge: Cambridge University Press.
Holton, G. (1960). ‘On the Origins of the Special Theory of Relativity’, American Journal of Physics 28.
Kanitscheider, B. (1972). ‘Die Rolle der Geometrie innerhalb physikalischer Theorien’, Zeitschrift für Philosophische Forschung 26.
Kobayashi, S. and Nomizu, K. (1962). Foundations of Differential Geometry, 2 vols. New York: Wiley.
Lichnerowicz, A. (1955). Théories relativistes de la gravitation et de l'électromagnétisme, Paris: Masson.
Lindsay, R. B. and Margenau, H. (1957). Foundations of Physics, New York: Dover.
Lorentz, H. A., Einstein, A., Minkowski, H., and Weyl, H. (1923). The Principle of Relativity. A Collection of Original Memoirs on the Special and General Theory of Relativity, London: Methuen.
Lorentz, H. A. (1905). Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern, Leiden: Brill.
Mach, E. (1883). Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt, Leipzig: Brockhaus. Trans. 1893 McCormack, T., The Science of Mechanics, Chicago: Open Court.
Mainzer, K. (1994). ‘Philosophie und Geschichte von Raum und Zeit’, in Ausdretsch, J. and Mainzer, K. (eds.), Philosophie und Physik der Raum-Zeit, Zurich: Bibliographische Institut.
Malamet, D. (1997). ‘Causal theories of time and the conventionality of simultaneity’, Noûs 11.
Minkowski, H. (1909). ‘Raum und Zeit’, Physikalische Zeitschrift 10.
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973), Gravitation, San Francisco: Freeman.
Paty, M. (1993). Einstein Philosophe, Paris: Presses Universitaires de France.
Pauli, W. (1981). Theory of Relativity, New York: Dover. 1st German edn 1921.
Penrose, R. (1968). ‘Structure of Space-Time’, in DeWitt, C. M. and Wheeler, J. A. (eds.), Battelle Rencontres. 1967 Lectures in Mathematics and Physics, New York: Benjamin.
Petitot, J. (1992). ‘Actuality of Transcendental Aesthetics for Modern Physics’, in Boi, L. et al. (eds.), A Century of Geometry: Epistemology, History and Mathematics, Heidelberg: Springer Verlag.
Poincaré, H. (1902). La Science et l'Hypothèse, Paris: Flammarion.
Poincaré, H. (1906). ‘Sur la dynamique de l'électron’, Rend. Circ. Mat. Palermo 21.
Regge, T. (1961). ‘General relativity without coordinates’, Rivista del Nuovo Cimento 19.
Reichenbach, H. (1958). The Philosophy of Space and Time, transl. Reichenbach, M. and Freund, J., New York: Dover.
Ricci, G. and Levi-Civita, T. (1901). ‘Méthodes de calcul différentiel absolu et leurs applications’, Mathematische Annalen 54.
Riemann, B. (1867). ‘Über die Hypothesen, welche der Geometrie zu Grunde liegen’, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zur Göttingen 13.
Rindler, W. (1960). Special Relativity, Edinburgh: Oliver & Boyd.
Schilpp, P. A. (ed.) (1949). Albert Einstein: Philosopher-Scientist, Evanston, IL: The Library of Living Philosophers.
Schrödinger, E. (1954). Space-Time Structure, Cambridge: Cambridge University Press.
Souriau, J.-M. (1964). Géométrie et Relativité, Paris: Hermann.
Spivak, M. (1979). A Comprehensive Introduction to Differential Geometry, Berkeley, CA: Publish or Perish.
Stachel, J. (1995). ‘History of Relativity’ in Brown, L. M., Pais, A., and Pippard, B.Sir (eds.), Twentieth Century Physics, vol. I, Bristol: Institute of Physics Publ..
Stamatescu, I.-O. (1994). ‘Quantum Field Theory and the Structure of Space-Time’ in Stamatescu, I.-O. (ed.), Philosophy, Mathematics and Modern Physics, Heidelberg: Springer Verlag.
Synge, J. L. (1955). Relativity: The Special Theory, Amsterdam: North-Holland.
Synge, J. L. (1964). The Petrov Classification of Gravitational Fields, Dublin: Dublin Institute for Advanced Studies.
Torretti, R. (1996), Relativity and Geometry, New York: Dover (1st edn Pergamon, 1983).
Trautman, A., Pirani, F. A. E., and Bondi, H. (1965). Lectures on General Relativity, Englewood Cliffs, NJ: Prentice-Hall.
Trautman, A. (1973). ‘Theory of Gravitation’ in Mehra, J. (ed.), The Physicist’s Conception of Nature, Dordrecht: Reidel.
Weinberg, S. (1918). Raum-Zeit-Materie, Berlin: Springer Verlag. 4th edn (1921).
Weinberg, S. (1973). Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity, New York: Wiley.
Weyl, H. (1918). Transl. Brose, H. L., Space-Time-Matter, London: Methuen.
Wheeler, J. A. (1962). Geometrodynamics, New York and London: Academic Press.
Zahar, E. (1989). Einstein’s Revolution: A Study in Heuristic, La Salle, IL: Open Court.
Zeeman, E. C. (1967). ‘The Topology of Minkowski space’, Topology 6.