Advertisement

Approximative Reduction by Completion of Empirical Uniformities

Kepler’s theory of planetary motion and Newton’s theory of gravitation

Abstract

In physics almost all important examples of theory reduction are of an approximative nature, for instance the reductions of nonrelativistic to relativistic theories of spacetime and dynamics, or of classical to corresponding quantum theories. To formalize the idea of theory approximation one needs a mathematical structure with a certain type of convergence — the Cauchy convergence, which is defined on a uniform structure (comp. [9], [10], [11]). This convergence type reflects the general fact that the approximated structures or models of the reduced theory are not models of the reducing theory, i.e. the approximation process takes you out of the approximating theory, as it were. For instance in the wellknown reduction example of Kepler’s theory of planetary motion to Newton’s theory of gravitation, Keplerian orbits are not solutions of Newton’s differential equations.

Keywords

Particle System Physical Theory Theory Reduction Keplerian Orbit Planetary Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. [1]
    M. Born, Optik, Springer; Berlin 1933.Google Scholar
  2. [2]
    N. Bourbaki, General Topology; Herman, Paris 1966.Google Scholar
  3. [3]
    N. Bourbaki, Theory of Sets; Herman, Paris 1968.MATHGoogle Scholar
  4. [4]
    R. Breuer, J. Ehlers, Propagation of high-frequency electromagnetic waves through a magnetized plasma in curved spacetime I, II; Proc. R. Soc. Lond. A 370 (1980).Google Scholar
  5. [5]
    E. Cech, Topological spaces; Interscience, London 1966.MATHGoogle Scholar
  6. [6]
    J. Ehlers, Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie, to appear in Festschrift für Mittelstaedt (1981).Google Scholar
  7. [7]
    K. Hepp, The classical limit for quantum mechanical correlation functions; Commun. math. Phys. 35, 265–277 (1974).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    H.W. Knobloch, F. Kappel, Gewöhnliche Differentialgleichungen; Teubner, Stuttgart 1974.MATHGoogle Scholar
  9. [9]
    G. Ludwig, Die Grundstrukturen einer physikalischen Theorie, Springer, Berlin 1978.MATHGoogle Scholar
  10. [10]
    D. Mayr, Investigations of the concept of reduction II; Erkenntnis 16 (1981).Google Scholar
  11. [11]
    C.-U. Moulines, Approximative explanation of empirical theories: a general explication; Erkenntnis 10, 201–229 (1976).CrossRefGoogle Scholar
  12. [12]
    D. Ruelle, Statistical Mechanics, Rigorous Results; Benjamin, New York 1969.MATHGoogle Scholar
  13. [13]
    E. Scheibe, Die Erklärung der Keplersehen Gesetze durch Newtons Gravitationsgleichung; in E. Scheibe und G. Süßmann (eds), Einheit und Vielheit, Festschrift für Carl Friedrich von Weizsäcker, Vandenhoeck & Ruprecht, Göttingen, 1973.Google Scholar
  14. [14]
    W. Stegmüller, The Structuralist View of Theories; Springer, Berlin 1979.MATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • D. Mayr
    • 1
  1. 1.Fachbereich PhysikPhilipps-Universität MarburgMarburgFederal Republic of Germany

Personalised recommendations