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Quantum Weak Measurements and Cosmology

  • P. C. W. DaviesEmail author
Conference paper

Abstract

The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre- and post-selection of states opens up a new, experimentally testable, sector of quantum mechanics, when combined with statistical averages of identical weak measurements. In this paper I apply the theory of weak quantum measurements combined with pre- and post-selection to cosmology. Here, pre-selection means specifying the wave function of the universe or, in a popular semi-classical approximation, the initial quantum state of a subset of quantum fields propagating in a classical background spacetime. The novel feature is post-selection: the additional specification of a condition on the quantum state in the far future. I discuss “natural” final conditions, and show how they may lead to potentially large and observable effects at the present cosmological epoch. I also discuss how pre- and post-selected quantum fields couple to gravity via the DeWitt-Schwinger effective action prescription, in contrast to the expectation value of the stress-energy-momentum tensor, resolving a vigorous debate from the 1970s. The paper thus provides a framework for computing large-scale cosmological effects arising from this new sector of quantum mechanics. A simple experimental test is proposed. [Editors note: for a video of the talk given by Prof. Davies at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-13.]

Keywords

Black Hole Weak Measurement Quantum Cosmology Bogoliubov Transformation Massless Scalar Field 
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.

Notes

Acknowledgements

I have greatly benefited from discussions with Alonso Botero, Jeff Tollaksen and Yakir Aharonov in preparing this paper. I would like to thank Katherine Lee and Saugata Chatterjee for their help reformatting and editing the paper.

References

  1. 1.
    Y. Aharonov, E. Gruss, Two-time interpretation of quantum mechanics (2005). arXiv:quant-ph/0507269
  2. 2.
    Y. Aharonov, D. Rohrlich, Quantum Paradoxes (Wiley-VCH, Weinheim, 2005) CrossRefGoogle Scholar
  3. 3.
    J. Hartle, S. Hawking, Wave function of the universe. Phys. Rev. D 28(12), 2960 (1983) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    N.D. Birrell, P.C.W. Davies, Curved Space. Quantum Fields (Cambridge University Press, Cambridge, 1982) CrossRefGoogle Scholar
  5. 5.
    P.C.W. Davies, C.H. Lineweaver, M. Ruse (eds.), Complexity and the Arrow of Time (Cambridge University Press, Cambridge, 2013) Google Scholar
  6. 6.
    F. Hoyle, J.V. Narlikar, Electrodynamics of direct interparticle action. I. The quantum mechanical response of the universe. Ann. Phys. 54, 207–239 (1969) MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    F.J. Tipler, Cosmological limits on computation. Int. J. Theor. Phys. 25(6), 617–661 (1986). doi: 10.1007/BF00670475 MathSciNetCrossRefGoogle Scholar
  8. 8.
    S.W. Hawking, R. Penrose, The Nature of Space and Time (Princeton University Press, Princeton, 1996) zbMATHGoogle Scholar
  9. 9.
    H. Price, Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time (Oxford University Press, New York, 1996) Google Scholar
  10. 10.
    M. Gell-Mann, J.B. Hartle, Complexity, entropy and the physics of information, in Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology, vol. VIII, ed. by W.H. Zurek (Addison-Wesley, Reading, 1990), p. 425 Google Scholar
  11. 11.
    D.N. Page, No time asymmetry from quantum mechanics. Phys. Rev. Lett. 70, 4034–4037 (1993) MathSciNetADSCrossRefzbMATHGoogle Scholar
  12. 12.
    C. Bernard, A. Duncan, Regularization and renormalization of quantum field theory in curved space-time. Ann. Phys. 107, 201–222 (1977) ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    Yu.V. Pavlov, Nonconformal scalar field in a homogeneous isotropic space and the method of Hamiltonian diagonalization (2000). gr-qc/0012082
  14. 14.
    T.S. Bunch, P.C.W. Davies, Quantum field theory in de Sitter space: renormalization by point-splitting. Proc. R. Soc. Lond. Ser. A 360, 117 (1978) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    B.S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965) zbMATHGoogle Scholar
  16. 16.
    D.G. Boulware, Quantum field theory in Schwarzschild and Rindler spaces. Phys. Rev. D 11, 1404–1424 (1975) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    J.B. Hartle, B.L. Hu, Quantum effects in the early universe. II. Effective action for scalar fields in homogeneous cosmologies with small anisotropy. Phys. Rev. D 20, 1772–1782 (1979) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    J.S. Dowker, R. Critchley, Effective Lagrangian and energy-momentum tensor in de Sitter space. Phys. Rev. D 13, 3224–3232 (1976) MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    B.S. DeWitt, Phys. Rep. 19C, 297 (1975) ADSGoogle Scholar
  20. 20.
    S.W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    R.B. Partridge, Absorber theory of radiation and the future of the universe. Nature 244, 263–265 (1973) ADSCrossRefGoogle Scholar
  22. 22.
    P.C.W. Davies, Is the universe transparent or opaque? J. Phys. A, Gen. Phys. 5, 1722–1737 (1972) ADSCrossRefGoogle Scholar
  23. 23.
    P.C.W. Davies, J. Twamley, Time-symmetric cosmology and the opacity of the future light cone. Class. Quantum Gravity 10, 931 (1993). doi: 10.1088/0264-9381/10/5/011 ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Arizona State UniversityTempeUSA

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