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The Role of Newton’s Constant in Einstein’s Gravity

  • Vittorio de Alfaro
Part of the The Subnuclear Series book series (SUS, volume 18)

Abstract

The purpose of this lecture is to develop some remarks about the Einstein theory of gravity, called General Relativity after its invariance transformations. In particular I will address my attention to the role of the Newton constant according to the point of view that has been developed by Sergio Fubini, Giuseppe Furlan and myself 1,2, and to the consequences of this point of view.

Keywords

Scalar Field Quantum Gravity Spontaneous Symmetry Breaking Flat Space Newton Constant 
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References and Footnotes

  1. 1.
    V. de Alfaro, S. Fubini and G. Furlan, Nuovo Cim. A 50, 523 (1979).CrossRefGoogle Scholar
  2. 2.
    V. de Alfaro, S. Fubini and G. Furlan, Nuovo Cim. B 57, 227 (1980).CrossRefGoogle Scholar
  3. 3.
    For a review see ‘Quantum Gravity, an Oxford Symposium’ eds. C. Isham, R. Penrose and D.W. Sciama, Oxford Univ. PressGoogle Scholar
  4. 4.
    J. Ellis, M.K. Gaillard, L. Maiani and B. Zumino, ‘Attempts at Superunification’, CERN Th-2841.Google Scholar
  5. 5.
    S. Weinberg, contribution to the Einstein Centenary Volume ‘Gravitational Theories since Einstein’, eds. S.W. Hawking and W. Israel, Cambridge University Press 1978.Google Scholar
  6. 6.
    The proposal of general relativity was formulated in ‘Die Grundlagen der Allgemeinen Relativitätstheorie’, Annalen der Physik 49, 769 (1916). The cosmological constant was introduced in ‘Kosmologische Betrachtungen zu? allgemeiner Relativitätstheorie’, Sitz. Preuss. Akad. d. Wiss., Berlin 1917, p. 142.Google Scholar
  7. 7.
    S. Coleman and F. De Luccia, ‘Gravitational Effects on and of Vacuum Decay’, SLAC-PUB 2463, Jan. 1980.Google Scholar
  8. 8.
    I. Newton, ‘Philosophiae Naturalis Principia Mathematica’ London 1687 (facsimile published by W. Dawson and Sons, London), Liber Tertius, Props. VII and VIII; see also ‘The Mathematical Principles of Natural Philosophy, by sir Isaac Newton, translated into English by Andrew Motte’, London 1729 (facsimile published by W. Dawson and Sons, London 1968 ), pp. 225, 226.Google Scholar
  9. 9.
    Prof. H. Rechenberg, Max-Planck Institut für Physik und Astrophysik, Muenchen, private communication.[lt is a pleasure to thank prof. Rechenberg for the information about the work of Planck from which the above lines have been extracted.]Google Scholar
  10. 10.
    See e.g. M. Jammer, “The Conceptual Development of Quantum Mechanics”, Mc Graw-Hill, New York, N.Y. 1966.Google Scholar
  11. 11.
    M. Planck, Sitz. Preuss. Akad. d. Wissenschaften,Berlin 1899, pp. 440–470.Google Scholar
  12. 12.
    The definitions are as in S. Weinberg’s Gravitation and Cosmology’ J. Wiley, New York N.Y. 1972 (except that we work with x4= it).Google Scholar
  13. 13.
    See for instance V. de Alfaro, S. Fubini, G. Furlan and C. Rossetti, ‘Currents in Hadron Physics’, Amsterdam 1973 P. 699.Google Scholar
  14. 14.
    See ref. 1 and V. de Alfaro, S. Fubini and G. Furlan, lectures given at the XIX Universitätswochen, Schladming February 1980.Google Scholar
  15. 15.
    This definition differs by the factor (4π)1/2 from the Planck length as defined in eq. (5). Numerically, ℓ= 5.72 x 10-33 cm.Google Scholar
  16. 16.
    See e.g. ref. 13, ch. 5.Google Scholar
  17. 17.
    S. Coleman, in “Laws of the Hadronic Matter”, A. Zichichi ed., Academic Press 1975, p. 165.Google Scholar
  18. 18.
    Long before the achievements of renormalization W. Heisenberg pointed out that coupling constants with dimension of positive power of a length pose problems for the theory at small distances, and believed that the associated mass could set a limit to the applicability of the theory (as it happened to be true for beta-decay). See W. Heisenberg, Z. Physik 101, 251 (1938) and 113, 61 (1939).CrossRefGoogle Scholar
  19. 19.
    The idea that the small distance behaviour of quantum gravity could be better than what is indicated by standard perturbation theory has been strongly advocated by A. Salam; see ‘Impact of Quantum Gravity in Particle Physics’ in ref. 3, and the papers quoted there.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Vittorio de Alfaro
    • 1
  1. 1.Istituto di Fisica TeoricaUniversità di TorinoTorinoItaly

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