On limit relations between, and approximative explanations of, physical theories

Studies in Logic and the Foundations of Mathematics

Volumn 114, Issue C, 1986, Pages 387-403

  Ehlers, Jürgen ^a  

^a Werner Heisenberg Institut für Physik   (Germany)

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[No Author keywords available]

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EID: 77956976796     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(09)70702-5     Document Type: Article

References (35)

1. Popper, K., Normal science and its dangers 57. Lakatos, J., Musgrave, (eds.) Criticism and the Growth of Knowledge, 1970, Cambridge Univ. Press, London.
2. Bourbaki, N. 1968 Theory of Sets (Paris).
3. Ludwig, G., Die Grundstrukturen einer physikalischen Theorie, 1978, Springer, Berlin.
4. Balzer, W., Erkenntnis 15 (1980), 291–408.
5. Scheibe, E., 1983 371–383, in: Epistemology and Philosophy of Science Proc. 7th Intern. Wittgenstein Symposium, eds., Hölder-Pichler-Tempsky (Wien).
6. Scheibe, E., Zeitschr. f. allgem. Wissenschaftstheorie 14 (1983), 68–80.
7. Mayr, D., Hartkämper, A., Schmidt, H.J., (eds.) Structure and Approximation in Physical Theories, 1981, Plenum Press, New York, 55–70 See ref. 3 and.
8. Ashtekar, A., Commun. Math. Phys., 71, 1980, 59.
9. Emch, G.G., Intern. J. Theor. Physics 22 (1983), 397–420.
10. Emch, G.G., J. Math. Phys. 23 (1982), 1785–1791.
11. In his famous address delivered at the 80th assembly of German Natural Scientists and Physicians in Cologne (1908), H. Minkowski already described geometrically how the metric of special relativity degenerates into the Newtonian one if “c → ∞”.
12. Ehlers, J., Penrose, R., Rindler, W., Am. J. Phys. 33 (1965), 995–997 This section is based on.
13. Ehlers, J., Relations between the Galilei-invariant and the Lorentz-invariant theories of collisions. Mayr, D., Süssmann, G., (eds.) Space, Time and Mechanics, 1983, Reidel, Dordrecht, 21–37.
14. The index of inertia of a real symmetric two-tensor, or equivalently of a real quadratic form is (here) defined as the number of positive terms in its normal (diagonal) form.
15. Künzle, H.P., Ann. Inst. Henri Poincaré 17 (1972), 337–362.
16. An event is “a process without parts”. A spacetime axiomatics which begins with “finite, extended” processes and introduces events as idealized limits of sequences of processes has been given by D. Mayer (Dissertation, University of Munich, 1979). See also Mayr's Habilationsschrift (University of Marburg, 1984).
17. In the domain of molecules (atoms, ions), e.g., one can take M to be the sum of the masses of the nucleons and electrons contained in a molecule. Then U is the sum of the nuclear and atomic binding energies.
18. Segal, J.E., Duke Math. J., 18, 1951, 221 A representation is indecomposable if it is not equivalent to a direct sum of representations. A Lie algebra A' is said to be a contraction of another one, A if there exists a one-parameter family of bases of A such that the corresponding family of structure constants converges to the set of structure constants belonging to some basis of A'. This notion can be extended in several ways to Lie groups and to representations of Lie algebras and Lie groups and is basic for the “Galilean limits” of relativistic theories. The original papers are.
19. Inõnü, E., Wigner, E.P., Proc. Nat. Acad. Sci., 39, 1953, 510.
20. Hermann, R., Lie Groups for Physicists, 1966, Benjamin, New York See also and the references therein.
21. Sufficient conditions are stated in the second reference given in note 11.
22. Ludwig, Foundations of Quantum Mechanics I, 1983, Springer, New York A formulation of such “constraints” (Sneed) requires the use of pretheories (“Vor-theorien” in the sense of ref. 3) or a theory of “preparing procedures” as given by.
23. Rindler, W., Introduction to Special Relativity, 1982, Clarendon Press, Oxford section 29.
24. This section is based primarily on ref. 13.
25. Ehlers, J., Nitsch, J., et al. (eds.) Grundlagenprobleme der modernen Physik, 1981, Bibliogr. Inst., Mannheim, 65–84.
26. ab..
27. Trautman, A., Held, A., (eds.) General Relativity and Gravitation, 1, 1980, Plenum Press, New York See, e.g., the contribution of.
28. Hawking, S.W., Ellis, G.F.R., The Large Scale Structure of Space-Time, 1973, Cambridge Univ. Press, London.
29. Will, C.M., Hawking, S.W., Israel, W., (eds.) General Relativity, 1979, Cambridge Univ. Press, London See, e.g., the review article by.
30. Künzle, H.P. and Nester, J.M., Hamiltonian formulation of gravitating perfect fluids and the Newtonian limit, to appear in J. Math. Phys.;.
31. Futamase, T., Schutz, B.F., Phys. Rev. D., 1983, 2363–2381.
32. Futamase, T., Phys. Rev. D., 1983, 2373–2381 (The last two papers contain an interesting approach, but I think their claims have not been mathematically established yet.).
33. Trautman, A., Comptes Rendus Paris, 257, 1983, 617.
34. Geroch, R.P., Esposito, F.P., Witten, L., (eds.) Asymptotic Structure of Space-Time, 1977, Plenum Press, New York.
35. Ashtekar, A., Ch. 2. Held, A., (eds.) General Relativity and Gravitation, 2, 1980, Plenum Press, New York.