Advertisement

Foundations of Physics

, Volume 19, Issue 10, pp 1151–1170 | Cite as

The logic of reduction: The case of gravitation

  • Fritz Rohrlich
Article

Abstract

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be derived directly from the superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T′.

Keywords

Dimensional Reduction Physical Theory Intermediate Step Mathematical Structure Central Concept 
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.

References

  1. 1.
    E. Nagel,The Structure of Science (Harcourt, Brace & World, New York, 1961).Google Scholar
  2. 2.
    R. M. Yoshida,Reduction in the Physical Sciences (Dalhousie University Press, Halifax, 1977).Google Scholar
  3. 3.
    P. K. Feyerabend, “Explanation, Reduction, and Empiricism,” inMinnesota Studies in the Philosophy of Science, Vol. III, H. Feigl and G. Maxwell, eds. (University of Minnesota, Minneapolis, 1962), pp. 28–97.Google Scholar
  4. 4.
    T. S. Kuhn,The Structure of Scientific Revolutions (University of Chicago Press, Chicago, 19709), 2nd edn.Google Scholar
  5. 5.
    R. M. Wald,General Relativity (University of Chicago Press, Chicago, 1984).Google Scholar
  6. 6.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Fransisco, 1973).Google Scholar
  7. 7.
    W. Rindler,Essential Relativity (Springer, New York, 1977), 2nd edn.Google Scholar
  8. 8.
    T. Damour, “The Problem of Motion in Newtonian and Einsteinian Gravity,” in300 Years of Gravitation. S. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge, 1987), pp. 128–198.Google Scholar
  9. 9.
    R. Geroch,Comm. Math. Phys. 13, 180–193 (1969).Google Scholar
  10. 10.
    M. Fierz and W. Pauli,Proc. R. Soc. London A 173, 211–232 (1939).Google Scholar
  11. 11.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973), p. 186.Google Scholar
  12. 12.
    P. Havas and J. N. Goldberg,Phys. Rev. 128, 398 (1962).Google Scholar
  13. 13.
    S. Deser,Gen. Relativ. Gravit. 1, 9 (1970).Google Scholar
  14. 14.
    T. Biswas,Am. J. Phys. 56, 1032 (1988).Google Scholar
  15. 15.
    E. Cartan,Ann. Ecole Norm. 40, 325–412 (1923);41, 1–25 (1924).Google Scholar
  16. 16.
    K. Friedrichs,Math. Ann. 98, 566–575 (1927).Google Scholar
  17. 17.
    E. Inönü and E. P. Wigner,Proc. Natl. Acad. Sci. USA 39, 510 (1953).Google Scholar
  18. 18.
    P. Havas,Rev. Mod. Phys. 36, 938–965 (1964).Google Scholar
  19. 19.
    D. B. Malament, “Newtonian Gravity, Limits, and the Geometry of Space and Time,” inFrom Quarks to Quasars, R. G. Colodny, ed. (University of Pittsburgh Press, 1986), pp. 181–201.Google Scholar
  20. 20.
    J. Ehlers, “Uber den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie,” inGrundprobleme der modernen Physik, J. Nitschet al., eds. (Bibliographisches Institut, 1981).Google Scholar
  21. 21.
    E. Ehlers, “On limit relations between, and approximative explanations of, physical theories,” inLogic, Methodology, and Philosophy of Science, Vol. VII, R. Marcuset al., eds. (Elsevier Science Publishers, New York, 1986), pp. 387–403.Google Scholar
  22. 22.
    E. J. Moniz and D. H. Sharp,Phys. Rev. D 15, 2850 (1977); see also Sec. 3 in F. Rohrlich, “Fundamental Physical Problems of Quantum Electrodynamics,” inFoundations of Radiation Theory and Quantum Electrodynamics, A. O. Barut, ed. (Plenum Press, New York, 1980).Google Scholar
  23. 23.
    C. G. Hempel, “On the ‘standard Conception’ of Scientific Theories,” inMinnesota Studies in the Philosophy of Science, Vol. IV, M. Radner and S. Winokur, eds. (University of Minnesota Press, Minneapolis, 1970), pp. 142–163.Google Scholar
  24. 24.
    C. G. Hempel and P. Oppenheim,Philos. Sci. 15, 135–175 (1948).Google Scholar
  25. 25.
    C. A. Hooker,Dialogue 20, 38, 201, 496 (1981).Google Scholar
  26. 26.
    F. Rohrlich,Br. J. Philos. Sci. 39, 295 (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Fritz Rohrlich
    • 1
  1. 1.Department of PhysicsSyracuse UniversitySyracuse

Personalised recommendations