The logic of reduction: The case of gravitation

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 The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be derived directly from the superseding theory T; it is severely constrained by the mathematical structure, and it can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′.

[1]  W. Pauli,et al.  On relativistic wave equations for particles of arbitrary spin in an electromagnetic field , 1939 .

[2]  R. Geroch.  Limits of spacetimes , 1969 .

[3]  J. Ehlers.  On limit relations between and approximate explanations of physical theories , 1986 .

[4]  J. Ehlers.  Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie , 1981 .

[5]  David H. Sharp,et al.  Radiation Reaction in Nonrelativistic Quantum Electrodynamics , 1977 .

[6]  Paul K. Feyerabend,et al.  Explanation, reduction, and empiricism , 1962 .

[7]  Ernest Nagel,et al.  The Structure of Science , 1962 .

[8]  P. Havas.  Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity , 1964 .

[9]  K. Friedrichs,et al.  Eine invariante Formulierung des Newtonschen Gravitationsgesetzes und des Grenzüberganges vom Einsteinschen zum Newtonschen Gesetz , 1928 .

[10]  F. Rohrlich.  Pluralistic Ontology and Theory Reduction in the Physical Sciences , 1988, The British Journal for the Philosophy of Science.

[11]  F. Rohrlich.  Fundamental Physical Problems of Quantum Electrodynamics , 1980 .

[12]  D. Raine.  General relativity , 1980, Nature.

[13]  J. Goldberg,et al.  Lorentz-Invariant Equations of Motion of Point Masses in the General Theory of Relativity , 1962 .

[14]  C. Hempel,et al.  Studies in the Logic of Explanation , 1948, Philosophy of Science.

[15]  E. Wigner,et al.  On the Contraction of Groups and Their Representations. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Carl G. Hempel,et al.  On the "standard conception" of scientific theories , 1970 .

[17]  Cliff Hooker,et al.  Towards a General Theory of Reduction. Part I: Historical and Scientific Setting , 1981, Dialogue.

[18]  Self-interaction and gauge invariance , 2004, gr-qc/0411023.

[19]  T. Kuhn,et al.  The Structure of Scientific Revolutions. , 1964 .

[20]  E. Cartan.  Sur les variétés à connexion affine et la théorie de la relativité généralisée. (première partie) , 1923 .

[21]  生出 勝宣.  W. Rindler: Essential Relativity, 2nd ed., Springer-Verlag, New York, 1977, xiv+284ページ, 24×16cm, 10,840円. , 1978 .

[22]  Thibault Damour,et al.  THE PROBLEM OF MOTION IN NEWTONIAN AND EINSTEINIAN GRAVITY , 1986 .