, Volume 141, Issue 3, pp 417–429

The Newtonian Limit of Relativity Theory and the Rationality of Theory Change

  • Ardnés Rivadulla


The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c→∞ in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In this paper I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics.


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  1. Adler, C.: 1987, 'Does Mass Really Depend on Velocity, Dad?', Am. J. Phys. 55(8), 739–743Google Scholar
  2. Born, M.: 1962, Einstein's Theory of Relativity, Dover, New York. First German edition, 1920.Google Scholar
  3. Dalla Chiara, M. L. and G. Toraldo di Francia: 1999, Introduzione alla filosofia della scienza, Roma-Bari, Laterza & Figli Spa. Spanish edition Confines: Introducción a la filosofaa de la ciencia, Crítica, Barcelona, 2001.Google Scholar
  4. Earman, J. and A. Fine: 1977, 'Against Indeterminacy', The Journal of Philosophy 74(9), 535–539.Google Scholar
  5. Eddington, A. S.: 1923, The Mathematical Theory of Relativity, Cambridge University Press.Google Scholar
  6. Einstein, A.:1917,Über die spezielle und allgemeine Relativitätstheorie, (Reprinted in A.J. Fox, M. J. Klein and R. Schulmann (eds.),The Collected Papers of Albert Einstein,Vol.6, The Berlin Years, 1914-1917, Princeton University Press, 1996.)Google Scholar
  7. Feyerabend, P. K.:1978,'Kuhns "Struktur wissenschaftlicher Revolutionen". Ein Trost-büchlein für Spezialisten?', in P. K. Feyerabend(ed.),Der wissenschaftliche Realismus und die Autorität der Wissenschaften, Ausgewählte Schriften, Band 1. Vieweg & Sohn, Braunschweig.Google Scholar
  8. Feyerabend, P. K.: 1981a, 'Explanation, Reduction and Empiricism', in P. K. Feye-rabend (ed.), Realism, Rationalism and Scientific Method, Philosophical Papers,Vol. 1, Cambridge University Press.Google Scholar
  9. Feyerabend, P. K.: 1981b, 'Consolations for the Specialist', in P. K. Feyerabend (ed.), Problems of Empiricism, Philosophical Papers, Vol. 2. Cambridge University Press.Google Scholar
  10. Field, H.: 1973, 'Theory Change and the Indeterminacy of Reference', The Journal of Philosophy LXX(14), 462–481.Google Scholar
  11. Goldstein, H.: 1950, Classical Mechanics, Addison-Wesley, Reading, Mass. Second edition 1980.Google Scholar
  12. Goldstein, H., C. Poole and J. Safko: 2002, Classical Mechanics, Addison Wesley, San Francisco. Third edition.Google Scholar
  13. Jammer, M.: 1961, Concepts of Mass in Classical and Modern Physics, Harvard University Press, Cambridge, Mass.Google Scholar
  14. Jammer, M.: 2000, Concepts of Mass in Contemporary Physics and Philosophy, Princeton University Press, Princeton, New Jersey.Google Scholar
  15. Kant, I.: 1936, Gesammelte Schriften, Hrsg. von der Preussischen Akademie der Wis-senschaften. Band XXI. Dritte Abtheilung: Handschriftlicher Nachlass, Achter Band, Opus Postumum, Walter de Gruyter & Co., Berlin und Leipzig.Google Scholar
  16. Kuhn, T. S.: 1970, The Structure of Scientific Revolutions, Second enlarged edition, University of Chicago Press.Google Scholar
  17. Kuhn, T. S.: 1977, 'Theory-Change as Structure-Change', in R. E. Butts and J. Hintikka (eds.), Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science, D. Reidel, Dordrecht.Google Scholar
  18. Kuhn, T. S.: 1990, 'The Road Since Structure', in A. Fine, et al. (eds.), PSA 1990, 2, 3–13.Google Scholar
  19. Landau, L. and E. Lifshitz: 1951, The Classical Theory of Fields, Addison-Wesley Press, Cambridge, Mass.Google Scholar
  20. Misner, CH. W., K. S. Thorne, and J. A. Wheeler: 1973, Gravitation, W. H. Freeman and Co., San Francisco.Google Scholar
  21. Newton, I.: 1704, Optics, Encyclopaedia Britannica, INC, Chicago 1952, 4th printing 1993.Google Scholar
  22. Okun, L. B.: 1989, 'The Concept of Mass', Physics Today, pp. 31–36Google Scholar
  23. Okun, L. B.: 1990, 'Replies', in Putting to Rest Mass Misconceptions, Physics Today, Letters, pp. 114–117Google Scholar
  24. Popper, K.: 1935, Logik der Forschung, Springer, Wien. (The Logic of Scientific Discovery, Hutchinson, London 1959).Google Scholar
  25. Popper, K.: 1979, Die beiden Grundprobleme der Erkenntnistheorie,J.C.B. Mohr, Tübingen. Edited by Troels Eggers Hansen on the basis of manuscripts from the years 1930-1933.Google Scholar
  26. Popper, K.: 1994, 'The Rationality of Scientific Revolutions', in K. Popper, The Myth of the Framework, Routledge, London. Appeared in R. Harré (ed.), Problems of Scientific Revolution, 1975.Google Scholar
  27. Sandin, T. R.: 1991, 'In Defense of Relativistic Mass', Am. J. Phys. 59(11), 1032–1036.Google Scholar
  28. Sneed, J.: 1971, The Logical Structure of Mathematical Physics, D. Reidel, Dordrecht.Google Scholar
  29. Sneed, J.: 1977, 'Describing Revolutionary Scientific Change: A Formal Approach', in R. E. Butts and J. Hintikka (eds.), Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science, D. Reidel, Dordrecht.Google Scholar
  30. Stegmüller, W.: 1980, Neue Wege der Wissenschaftsphilosophie, Springer-Verlag, Berlin.Google Scholar
  31. Taylor, E. and J. A. Wheeler: 1992, Spacetime Physics. Introduction to Special Relativity, 2nd edn, Freeman and Co., New York.Google Scholar
  32. Torretti, R.: 1999, The Philosophy of Physics, Cambridge University Press.Google Scholar
  33. Weinberg, S.: 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York.Google Scholar
  34. Weinberg, S.: 1989, 'Newtonianism and Today's Physics', in S. W. Hawking and W. Israel (eds.), 300 Years of Gravitation, Cambridge University Press.Google Scholar
  35. Weinberg, S.: 1998, 'The Revolution That Didn't Happen', The New York Review of Books XLV(15), 48–52.Google Scholar

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  • Ardnés Rivadulla

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