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Coupling of Quantum Fields to Classical Gravity

  • Michael J. W. HallEmail author
  • Marcel Reginatto
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 184)

Abstract

We consider ensembles on configuration space that consist of quantum fields which interact with and are the source of a classical gravitational field. These are hybrid systems where gravity remains classical while matter is described by quantized fields. There are some well known arguments in the literature which claim that such models are not possible. However, an examination of the most prominent ones, that are detailed enough to allow scrutiny, indicates that the hybrid models considered here are not excluded by any of the consistency arguments. We illustrate the approach with two examples. Our first example is a cosmological model. We consider the case of a closed Robertson–Walker universe with a massive quantum scalar field and solve the equations using a particular ansatz which selects a highly non-classical solution, one in which the scale factor of the Robertson–Walker universe is restricted to discrete values as a consequence of the interaction of the classical gravitational field with the quantized scalar field. We discuss this cosmological model in two approximations, that of a minisuperspace model and that of a midisuperspace model. Our second example concerns black holes. We consider CGHS black holes and show that we recover Hawking radiation from the equations that describe a hybrid system consisting of a classical CGHS black hole in a collapsing geometry interacting with a quantized scalar field. We also show that the hybrid model provides a natural resolution to the well known problem of time in quantum gravity.

Keywords

Black Hole Scalar Field Quantum Gravity Gravitational Field Momentum Constraint 
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.

References

  1. 1.
    Albers, M., Kiefer, C., Reginatto, M.: Measurement analysis and quantum gravity. Phys. Rev. D 78, 064051 (2008)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Rosenfeld, L.: On quantization of fields. Nucl. Phys. 40, 353–356 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Carlip, S.: Is quantum gravity necessary? Class. Q. Grav. 25, 154010 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boughn, S.: Nonquantum gravity. Found. Phys. 39, 331–351 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Butterfield, J., Isham, C.: In: Callender, C., Huggett, N. (eds.) Spacetime and the Philosphical Challenge of Quantum Gravity. Physics meets philosophy at the Planck scale. Cambridge University Press, Cambridge (2001)Google Scholar
  6. 6.
    Dyson, F.: Is a graviton detectable? Int. J. Mod. Phys. A 28, 1330041 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    Dyson, F.: The world on a string. N. Y. Rev. Books 51(8), 16–19 (2004)Google Scholar
  8. 8.
    Rothman, T., Boughn, S.: Can gravitons be detected? Found. Phys. 36, 1801–1825 (2006)ADSCrossRefzbMATHGoogle Scholar
  9. 9.
    Boughn, S., Rothman, T.: Aspects of graviton detection: graviton emission and absorption by atomic hydrogen. Class. Quantum Grav. 23, 5839–5852 (2006)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    Parker, L., Toms, D.: Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity. Cambridge University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  11. 11.
    Diósi, L.: Gravitation and quantum-mechanical localization of macro-objects. Phys. Lett. A 105, 199–202 (1984)ADSCrossRefGoogle Scholar
  12. 12.
    DeWitt, B.S.: The Quantization of Geometry. In: Witten, L. (ed.) Gravitation: an introduction to current research, pp. 266–381. Wiley, New York (1962)Google Scholar
  13. 13.
    Eppley, K., Hannah, E.: The necessity of quantizing the gravitational field. Found. Phys. 7, 51–68 (1977)ADSCrossRefGoogle Scholar
  14. 14.
    Page, D.N., Geilker, C.D.: Indirect evidence for quantum gravity. Phys. Rev. Lett. 47, 979–982 (1981)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Feynman, R.P.: The Feynman Lectures on Gravitation. Addison-Wesley, Boston (1995). ReadingGoogle Scholar
  16. 16.
    Mattingly, J.: Why Eppley and Hannah’s thought experiment fails. Phys. Rev. D 73, 064025 (2006)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Huggett, N., Callender, C.: Why quantize gravity (or any other field for that matter)? Philos. Sci. 68, S382–S394 (2001)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Mattingly, J.: Is quantum gravity necessary? In: Kox, A.J., Eisenstaedt, J. (eds.) The universe of general relativity (Einstein Studies Volume 11), pp. 327–338. Birkhäuser, Boston (2005)CrossRefGoogle Scholar
  19. 19.
    Kiefer, C.: Quantum Gravity. Oxford University Press, Oxford (2012)zbMATHGoogle Scholar
  20. 20.
    Kiefer, C.: Conceptual problems in quantum gravity and quantum cosmology. ISRN Math. Phys. 2013, 509316 (2013)ADSCrossRefzbMATHGoogle Scholar
  21. 21.
    Hall, M.J.W., Reginatto, M.: Interacting classical and quantum ensembles. Phys. Rev. A 72, 062109 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    Reginatto, M.: Cosmology with quantum matter and a classical gravitational field: the approach of configuration-space ensembles. J. Phys.: Conf. Ser. 442, 012009 (2013)ADSGoogle Scholar
  23. 23.
    Jackiw, R.: Diverse Topics in Theoretical and Mathematical Physics. World Scientific, Singapore (1995)CrossRefzbMATHGoogle Scholar
  24. 24.
    Hatfield, B.: Quantum Field Theory of Point Particles and Strings. Perseus Books, Cambridge (1992)zbMATHGoogle Scholar
  25. 25.
    Long, D.V., Shore, G.M.: The Schrödinger wave functional and vacuum states in curved spacetime. Nucl. Phys. B 530, 247–278 (1998)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Herdeiro, C.A.R., Ribeiro, R.H.: Sampaio. M.: Scalar Casimir effect on a D-dimensional Einstein static universe. Class. Quantum Grav. 25, 165010 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Kiefer, C., Zeh, H.D.: Arrow of time in a recollapsing quantum universe. Phys. Rev. D 51, 4145–4153 (1995)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Zeh, H.D.: The Physical Basis of the Direction of Time. Springer, Berlin (1992)CrossRefzbMATHGoogle Scholar
  29. 29.
    Callan, C.G., Giddings, S.B., Harvey, J.A., Strominger, A.: Evanescent black holes. Phys. Rev. D 45, R1005–R1009 (1992)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Strominger, A.: Les Houches lectures on black holes. arXiv:hep-th/9501071v1 (1995)
  31. 31.
    Demers, J.-G., Kiefer, C.: Decoherence of black holes by Hawking radiation. Phys. Rev. D 53, 7050–7061 (1996)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Louis-Martinez, D., Gegenberg, J., Kunstatter, G.: Exact Dirac quantization of all 2D dilaton gravity theories. Phys. Lett. B 321, 193–198 (1994)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Kiefer, C.: Hawking radiation from decoherence. Class. Quantum Grav. 18, L151–L154 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Kiefer, C.: Does time exist in quantum gravity? arXiv:0909.3767v1 [gr-qc] (2009)
  35. 35.
    Kiefer, C.: The Semiclassical Approximation to Quantum Gravity. In: Ehlers, J., Friedrich, H. (eds.) Canonical gravity: from classical to quantum, pp. 170–212. Springer, Berlin (1994)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Quantum DynamicsGriffith UniversityBrisbaneAustralia
  2. 2.Physikalisch-Technische BundesanstaltBraunschweigGermany

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