Communications in Mathematical Physics

, Volume 87, Issue 3, pp 395–415 | Cite as

The unpredictability of quantum gravity

  • S. W. Hawking
Article

Abstract

Quantum gravity seems to introduce a new level of unpredictability into physics over and above that normally associated with the uncertainty principle. This is because the metric of spacetime can fluctuate from being globally hyperbolic. In other words, the evolution is not completely determined by Cauchy data at past or future infinity. I present a number of axioms that the asymptotic Green functions should obey in any reasonable theory of quantum gravity. These axioms are the same as for ordinary quantum field theory in flat spacetime, except that one axiom, that of asymptotic completeness, is omitted. This allows pure quantum states to decay into mixed states. Calculations with simple models of topologically non-trivial spacetime indicate that such loss of quantum coherence will occur but that the effect will be very small except for fundamental scalar particles, if any such exist.

Keywords

Coherence Quantum Field Theory Quantum State Green Function Quantum Gravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys.43, 199–220 (1975)Google Scholar
  2. 2.
    Gross, D.J., Perry, M.J., Jaffe, L.G.: Instability of flat space at finite temperature. Phys. Rev. D25, 330–355 (1982)Google Scholar
  3. 3.
    Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D14, 2460 (1976)Google Scholar
  4. 4.
    Page, D.N.: Is black-hole evaporation predictable. Phys. Rev. Lett.44, 301 (1980)Google Scholar
  5. 5.
    Wald, R.M.: Black holes, thermodynamics, and time reversibility. In: Quantum gravity. 2. Isham, C.J., Penrose, R., Sciama, D.W., Oxford, Clarendon Press 1981Google Scholar
  6. 6.
    Penrose, R.: Zero rest-mass fields including gravitation, asymptotic behaviour. Proc. R. Soc. Lond. A284, 159–203 (1965)Google Scholar
  7. 7.
    Sachs, R.K.: Asymptotic symmetries in gravitational theory. Phys. Rev.128, 2851 (1962)Google Scholar
  8. 8.
    Penrose, R.: Asymptotic properties of fields and space-times. Phys. Rev. Lett.10, 66–68 (1963)Google Scholar
  9. 9.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: Cambridge University Press 1973Google Scholar
  10. 10.
    Streater, R.F., Wightman, A.S.: PCT, spin and statistics, and all that, New York: Benjamin 1964Google Scholar
  11. 11.
    Hawking, S.W., Page, D.N., Pope, C.N.: Quantum gravitational bubbles. Nucl. Phys. B.170, 283 (1980)Google Scholar
  12. 12.
    Warner, N.P.: The scattering of spin-1 particles by quantum gravitational bubbles. Commun. Math. Phys.86, 419–436 (1982)Google Scholar
  13. 13.
    Page, D.N.: Is quantum gravity time symmetric and/or deterministic? GRG14, 299–302 (1982)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • S. W. Hawking
    • 1
  1. 1.D.A.M.T.P.University of CambridgeCambridgeEngland

Personalised recommendations