Skip to main content

Causality Requirements and the Theory of Relativity

  • Chapter
Boston Studies in the Philosophy of Science

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 5))

Abstract

As pointed out first by Felix Klein1, the concept of ‘theory of relativity’ should always be understood with reference to a particular group. In this sense, we shall be concerned here with three theories of relativity, the one associated with Newtonian physics, and Einstein’s special and general theory. The groups to be considered are those associated with transformations of the space-time coordinates, and thus the physics underlying them is that of the respective space-time concepts.

Work supported by the National Science Foundation. — Paper based on a lecture given at the Boston Colloquium for the Philosophy of Science, November 29, 1965 (to appear in Boston Studies in the Philosophy of Science, Vol. 5).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Springer-Verlag, Berlin, 1927, Vol. 2, Ch. 2.

    Google Scholar 

  2. See e.g. C. Møller, The Theory of Relativity, Oxford University Press, Oxford, 1952, or D. Bohm, The Special Theory of Relativity, W. A. Benjamin, Inc., New York, 1965.

    Google Scholar 

  3. The space-time structure of the special theory of relativity is discussed in all textbooks of this theory; a particularly detailed account is given in H. Arzeliès, La cinématique relativiste, Gauthier-Villars, Paris, 1955 [English translation: Relativistic Kinematics, Pergamon Press, Oxford, 1966].

    Google Scholar 

  4. H. Minkowski, Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl. (1908) 53; Math. Ann. 68 (1910) 742.

    Google Scholar 

  5. A detailed exposition of this problem is given in P. Havas, Rev. Mod. Phys. 36 (1964) 938, with references to earlier literature.

    Article  Google Scholar 

  6. For a detailed discussion of the foundation problems of general relativity see P. Havas, in Delaware Seminar in the Foundations of Physics (ed. by M. Bunge), Springer-Verlag, New York, 1967, p. 124.

    Google Scholar 

  7. A. Einstein, Ann. Physik 49 (1916) 769.

    Article  Google Scholar 

  8. E. Kretschmann, Ann.Physik 53 (1917) 575.

    Google Scholar 

  9. A. Einstein, Ann. Physik 55 (1918) 241.

    Article  Google Scholar 

  10. A. Einstein, Ann. Physik 35 (1911) 898.

    Article  Google Scholar 

  11. The case of gravitational fields without sources was treated by E. Cartan, Ann. Ec. Norm. 40 (1923) 325, and 41 (1924) 1 [reprinted in Oeuvres Complètes, Gauthier-Villars, Paris, 1955, Vol. III/1, pp. 659 and 789] in a formulation somewhat different from that of Einstein’s theory, and by K. Friedrichs, Math. Ann. 98 (1927) 566 in a formulation very close to Einstein’s.

    Google Scholar 

  12. For a particularly detailed discussion see C. Møller (Reference 2), and H. Arzeliès, Relativité généralisée. Gravitation, Gauthier-Villars, Paris, 1961, Fasc. 1.

    Google Scholar 

  13. Of the enormous literature on causality, we only mention the following books which offer a good introduction to problems relevant for physics in general, and for relativity in particular; as well as to some of the numerous meanings of causality suggested by various authors: V. F. Lenzen, Causality in Natural Science, C. C. Thomas Publisher, Springfield, 1954; H. Weyl, The Open World, Yale University Press, New Haven, 1932; P. Frank, Das Kausalgesetz und seine Grenzen, Springer-Verlag, Wien, 1932; M. Bunge, Causality, Harvard University Press, Cambridge, Mass., 1959.

    Google Scholar 

  14. P. Havas, in Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science (ed. by Y. Bar-Hillel), North-Holland Publ. Co., Amsterdam, 1965, p. 347. is M. Laue, Phys. Zeits. 12 (1911) 48.

    Google Scholar 

  15. M. Born, Ann. Physik 30 (1909) 1; for references to later work see H. D. Wahlquist and F. B. Estabrook, J. Math. Phys. 7 (1966) 894.

    Article  Google Scholar 

  16. For a review of this work see P. Havas, in Statistical Mechanics of Equilibrium and Non-Equilibrium (ed. by J. Meixner), North-Holland Publ. Co., Amsterdam, 1965, p. 1.

    Google Scholar 

  17. E. C. G. Stückelberg, Helv. Phys. Acta 14 (1941) 588 and 15 (1942) 23.

    Google Scholar 

  18. R. P. Feynman, Phys. Rev. 74 (1948) 939. so p. Havas, Acta Phys. Austr. 3 (1949) 342.

    Article  Google Scholar 

  19. H. Schmidt, Zeits. Phys. 151 (1958) 365, 408; S. Tanaka, Prog. Theor. Phys. 24(1960) 171.

    Article  Google Scholar 

  20. Ya. P. Terletskii, Dokl. Akad. Nauk SSRS 133 (1960) 329 [English translation: Soviet Physics-Doklady 5 (1960) 782].

    Google Scholar 

  21. O. M. P. Bilaniak, V. K. Deshpande, and E. C. G. Sudarshan, Am. J. Phys. 30 (1962) 718.

    Article  Google Scholar 

  22. G. Feinberg, Phys. Rev. 159 (1967) 1089.

    Article  Google Scholar 

  23. For a review see M. Born, Ann. Inst. H. Poincaré 7 (1937) 155.

    Google Scholar 

  24. D. I. Blokhintsev, Usp. Fiz. Nauk 89 (1966) 185 [English translation: Sov. Phys. Uspekhi 9 (1966) 405]. It should be noted that Blokhintsev’s interpretation of the implications of the theory of relativity for causality does not agree with the one presented here.

    Google Scholar 

  25. J. Plebanski, ‘Non-Linear Electrodynamics’, Mexico, 1966, unpublished; this paper contains some considerations on signals similar to those presented here.

    Google Scholar 

  26. G. Boillat, C. R. Ac. Sc. 262 (1966) 1285, and references given there.

    Google Scholar 

  27. H. Ekstein (to be published).

    Google Scholar 

  28. B. Ferretti, N. Cim. 27 (1963) 1503; 43A (1966) 507, 516.

    Article  Google Scholar 

  29. Principally by Stückelberg and his collaborators; this work is reviewed by G. Wanders, Fortschr. Phys. 4 (1956) 611. Also A. Peres, Ann. Phys (N. Y.) 37 (1966) 179.

    Article  Google Scholar 

  30. Indeed, it is well known that there are an infinite number of interpolation models which lead to exactly the same scattering amplitudes; in particular, it is possible to have an infinity of interactions for which the condition of microcausality is not satisfied which give the same scattering amplitudes as one which does satisfy this conditions, as shown by S. Gasiorowicz and M. A. Ruderman, Phys. Rev. 110 (1958) 261.

    Article  Google Scholar 

  31. G. Wanders, N. Cim. 14 (1959) 168.

    Article  Google Scholar 

  32. G. Wanders, Helv. Phys. Acta 38 (1965) 142.

    Google Scholar 

  33. J. H. Crichton and E. H. Wichman, Phys. Rev. 132 (1963) 2788; F. Coester, Helv. Phys. Acta 38 (1965) 7.

    Article  Google Scholar 

  34. H. S. Snyder, Phys. Rev. 71 (1947) 38; H. T. Flint, Phys. Rev. 74 (1948) 209, and Nature 163(1949) 131.

    Article  Google Scholar 

  35. W. Heisenberg, Ann. Phys. 32 (1938) 20.

    Article  Google Scholar 

  36. A. Schild, Can. J. Math. 1 (1938) 29.

    Article  Google Scholar 

  37. B. T. Darling, Phys. Rev. 80 (1950) 460.

    Article  Google Scholar 

  38. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Proc. Roy. Soc. A269 (1962) 21.

    Google Scholar 

  39. See e.g. the reports and discussion at the International Meeting in Florence 1964 on ‘Problems of Energy and Gravitational Waves’, Pubblicazioni del comitato nazionale per le manifestazione celebrative del IV centenario delia nascità de Galileo Galilei, G. Barbèra, Florence, 1965, Vol. II, tomo 1.

    Google Scholar 

  40. W. B. Bonnor, J. Math. Mech. 9 (1960) 439.

    Google Scholar 

  41. L. Infeld, Quest, Doubleday, Doran & Co., Inc., New York, 1941, p. 93.

    Google Scholar 

  42. R. Serini, Atti Acc. Lincei 27 (1919) 235; A. Einstein and W. Pauli, Ann. Math. 44 (1943) 131.

    Google Scholar 

  43. J. A. Wheeler, Geometrodynamics, Academic Press, New York, 1962; R. W. Fuller and J. A. Wheeler, Phys. Rev. 128 (1962) 919.

    Google Scholar 

  44. H. J. Treder, Reference 41, p. 248, and references given there. In this connection, it might also be mentioned that C. Lanczos has suggested to consider space-time to possess a periodic microstructure of very high curvature, with signature—4, the usual structure corresponding to signature —2 appearing only as a macroscopic average; see J. Math. Phys. 4 (1963) 951.

    Google Scholar 

  45. This is by no means necessary, however, although almost universally implied. For a concise discussion of this problem see L. Rosenfeld, Nucl. Phys. 40 (1963) 353, and Einstein Symposium, Akademie-Verlag, Berlin, 1966, p. 185. For a survey of some recent work on quantization and the problems involved see e.g. B. de Witt in Gravitation (ed. by L. Witten), John Wiley and Sons, Inc., New York, 1962, Ch. 5.

    Article  Google Scholar 

  46. R. Penrose, Phys. Rev. Letters 14 (1965) 57; S. W. Hawking, ibid. 17 (1966) 444; R. P. Geroch, ibid. 17 (1966) 445.

    Article  Google Scholar 

  47. K. Gödel, Rev. Mod. Phys. 21 (1949) 447.

    Article  Google Scholar 

  48. S. Chandrasekhar and J. P. Wright, Proc. Nat. Ac. Sc. 47 (1961) 341.

    Article  Google Scholar 

  49. K. Schwarzschild, Sitzber. preuss. Akad. Wiss. Physik-math. Kl. (1916) 189; J. Droste, Versl. Kon. Akad. Wet. Amsterdam 25 (1916) 163.

    Google Scholar 

  50. G. E. Lemaître, Ann. Soc. Sc. Bruxelles A53 (1933) 51.

    Google Scholar 

  51. M. D. Kruskal, Phys. Rev. 119 (1960) 1743; G. Szekeres, Publ. Math. (Debrecen) 7 (1960) 285.

    Article  Google Scholar 

  52. J. L. Synge, Proc. Roy. Irish Ac. 53 A (1950) 83, and 59 A (1957) 1; C. Fronsdal, Phys. Rev. 116(1959) 778.

    Google Scholar 

  53. W. Israel, Phys. Rev. 143 (1966) 1016.

    Article  Google Scholar 

  54. W. Rindler, Phys. Rev. Letters 15 (1965) 1001; J. L. Anderson and R. Gautreau, Phys. Letters 20 (1966) 24; F. J. Belinfante, ibid. 20 (1966) 25; W. Israel, Nature 211 (1966) 466.

    Article  Google Scholar 

  55. W. Israel, Nature 209 (1966) 66; Phys. Letters 21 (1966) 47; Phys. Rev. 153 (1967) 1388.

    Article  Google Scholar 

  56. L. Mysak and G. Szekeres, Can. J. Phys. 44 (1966) 617.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Robert S. Cohen Marx W. Wartofsky

Rights and permissions

Reprints and permissions

Copyright information

© 1969 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Havas, P. (1969). Causality Requirements and the Theory of Relativity. In: Cohen, R.S., Wartofsky, M.W. (eds) Boston Studies in the Philosophy of Science. Boston Studies in the Philosophy of Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3381-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-3381-7_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3383-1

  • Online ISBN: 978-94-010-3381-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics