Skip to main content
SpringerLink
Log in

Quantum gravity, the origin of time and time's arrow

  • Part II. Invited Papers Dedicated To Asim Orhan Barut
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature Tc below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T<Tc, allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T>Tc, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. S. DeWitt,Phys. Rev. 160, 1113 (1967); J. A. Wheeler,Battelle Rencontres, C. deWitt and J. A. Wheeler, eds. (Benjamin, New York, 1968).

    Google Scholar 

  2. T. Banks,Nucl. Phys. B 249, 332 (1985).

    Google Scholar 

  3. J. J. Halliwell and S. W. Hawking,Phys. Rev. D 31, 1777 (1985).

    Google Scholar 

  4. R. Brout, G. Horowitz, and D. Weil,Phys. Lett. B 192, 318 (1987); R. Brout and G. Venturi,Phys. Rev. D 39, 2436 (1989).

    Google Scholar 

  5. A. Vilenkin,Phys. Rev. D 39, 1116 (1989).

    Google Scholar 

  6. J. J. Halliwell,Conceptual Problems in Quantum Cosmology, A. Ashtekar and J. Stachel, eds. (Birkhäser, Boston, 1991), p. 204.

    Google Scholar 

  7. W. G. Unruh,Phys. Rev. D 40, 1048 (1989).

    Google Scholar 

  8. M. Henneaux and C. Teitelboim,Phys. Lett. B 222, 195 (1989).

    Google Scholar 

  9. K. V. Kuchař,Phys. Rev. D 43, 3332 (1991).

    Google Scholar 

  10. J. B. Hartle and S. W. Hawking,Phys. Rev. D 28, 2960 (1983).

    Google Scholar 

  11. G. Gibbons, S. W. Hawking, and M. Perry,Nucl. Phys. B 138, 141 (1978).

    Google Scholar 

  12. F. David,Nucl. Phys. B 348, 507 (1991);Mod. Phys. Lett. A 5, 1019 (1990); P. Silvestrov and A. Yelkhovsky,Phys. Lett. B 251, 525 (1990).

    Google Scholar 

  13. S. Caracciolo and A. Pelisseto,Phys. Lett. B 207, 468 (1988).

    Google Scholar 

  14. H. Hamber and R. Williams,Nucl. Phys. B 269, 712 (1986).

    Google Scholar 

  15. J. Greensite,Nucl. Phys. B 361, 729 (1991).

    Google Scholar 

  16. T. Regge,Nuovo Cimento 19, 558 (1961); P. Menotti and A. Pelissetto,Phys. Rev. D 35, 1194 (1987); J. Ambjørn and J. Jurkiewicz,Phys. Lett. B 278, 42 (1992).

    Google Scholar 

  17. A. Ashtekar,Phys. Rev. D 36, 1587 (1987).

    Google Scholar 

  18. L. Smolin,Conceptual Problems of Quantum Gravity, A. Ashtekar and J. Stachel, eds. (Birkhäuser, Boston, 1991), p. 228.

    Google Scholar 

  19. S. W. Hawking, D. N. Page, and C. N. Pope,Nucl. Phys. B 170, 283 (1980); S. W. Hawking,Commun. Math. Phys. 87, 395 (1982).

    Google Scholar 

  20. K. V. Kuchař,J. Math. Phys. 22, 2640 (1981).

    Google Scholar 

  21. A. Strominger,Phys. Rev. Lett. 52, 1733 (1984).

    Google Scholar 

  22. D. Gross,Nucl. Phys. B 236, 349 (1984).

    Google Scholar 

  23. A. Hosoya and M. Morikawa,Phys. Rev. D 39, 1123 (1989).

    Google Scholar 

  24. S. Coleman,Nucl. Phys. B 307, 867 (1988);Nucl. Phys. B 310, 643 (1988).

    Google Scholar 

  25. T. Banks,Nucl. Phys. B 309, 493 (1988).

    Google Scholar 

  26. S. Giddings and A. Strominger,Nucl. Phys. B 307, 854 (1988).

    Google Scholar 

  27. R. Utiyama,Phys. Rev. 101, 1597 (1956); T. W. Kibble,J. Math. Phys. 2, 212 (1960); C. N. Yang,Phys. Rev. Lett. 33, 143 (1974); E. E. Fairchild, Jr.,Phys. Rev. D 14, 384 (1976); 2833(E) (1976).

    Article  Google Scholar 

  28. S. W. MacDowell and F. Mansouri,Phys. Rev. Lett. 38, 739 (1977); L. N. Chang and F. Mansouri,Phys. Rev. D 17, 3168 (1978).

    Google Scholar 

  29. F. W. Hehl, inSpin, Rotation and Supergravity (Proceedings of the 6th Course of the International School of Cosmology and Gravitation, Erice, Sicily, 1979), P. G. Bergmann and V. Sabbata, eds. (Plenum, New York, 1980); Y. Ne'eman and T. Regge,Nuovo Cimento 1, N5 (1978).

    Google Scholar 

  30. A. A. Tseytlin,Phys. Rev. D 26, 3327 (1982).

    Google Scholar 

  31. M. Kaku, P. K. Townsend, and P. van Nieuwenhuizen,Phys. Lett. B 69, 304 (1977).

    Google Scholar 

  32. B. Julia and J. F. Luciani,Phys. Lett. B 90, 270 (1980).

    Google Scholar 

  33. J. P. Hsu and M. D. Xin,Phys. Rev. D 24, 471 (1981).

    Google Scholar 

  34. S. Deser, H. S. Tsao, and P. van Nieuwenhuizen,Phys. Rev. D 10, 3337 (1974).

    Google Scholar 

  35. K. S. Stelle,Phys. Rev. D 16, 953 (1977).

    Google Scholar 

  36. L. D. Landau and E. M. Lifshitz,Statistical Physics, translated by J. B. Sykes and M. J. Kearsley (Addison-Wesley, Reading, Massachusetts), p. 427.

  37. S. Weinberg,Phys. Rev. D 9, 3320 (1974).

    Google Scholar 

  38. R. Mohapatra and G. Senjanovic,Phys. Rev. D 20, 3390 (1979).

    Google Scholar 

  39. P. Langacker and So-Young Pi,Phys. Rev. Lett. 45, 1 (1980).

    Google Scholar 

  40. V. Kuzmin, M. Shaposhnikov, and I. Tkachev,Nucl. Phys. B 196, 29 (1982).

    Google Scholar 

  41. T. W. Kephart, T. J. Weiler, and T. C. Yuan,Nucl. Phys. B 330, 705 (1990).

    Google Scholar 

  42. S. Dodelson and L. M. Widrow,Phys. Rev. D 42, 326 (1990).

    Google Scholar 

  43. P. Salomonson and B. K. Skagerstam,Phys. Lett. B 155, 98 (1985).

    Google Scholar 

  44. Ling-Fong Li,Phys. Rev. D 9, 1723 (1974).

    Google Scholar 

  45. E. W. Kolb and M. S. Turner,The Early Universe (Addison-Wesley, Reading, Massachusetts, 1990).

    Google Scholar 

  46. A. D. Linde,Rep. Prog. Phys. 47, 925 (1984).

    Google Scholar 

  47. For a recent review of inflationary models, see E. W. Kolb, Fermi National Laboratory preprint FNAL-Conf-90/195A, to be published in the proceedings of the Nobel Symposium No. 79,The Birth and Early Evolution of the Universe, Symposium held at Östersund, Sweden, June 1990.

  48. J. W. Moffat and D. C. Tatarski, University of Toronto preprint, UTPT-91-26, 1991.

  49. R. Penrose,General Relativity, An Einstein Centenary Survey, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge, 1979), p. 581;The Emperor's New Mind (Vintage Press, New York, 1990), p. 391.

    Google Scholar 

  50. S. Weinberg,Gravitation and Cosmology (Wiley, New York, 1972), p. 370.

    Google Scholar 

  51. G. Lüders,Ann. Phys. (Leipzig) 2, 1 (1957); J. S. Bell,Proc. R. Soc. London A 231, 79 (1955).

    Google Scholar 

  52. Violation of Lorentz invariance has been considered previously by: H. B. Nielsen and I. Picek,Nucl. Phys. B 211, 269 (1983); M. Gasperin,Phys. Lett. B 163, 84 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Toronto, M5S 1A7, Toronto, Ontario, Canada

    J. W. Moffat

Authors
  1. J. W. Moffat
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moffat, J.W. Quantum gravity, the origin of time and time's arrow. Found Phys 23, 411–437 (1993). https://doi.org/10.1007/BF01883721

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01883721

Keywords

Search

Navigation