Can the Arrow of Time Be Understood from Quantum Cosmology?

Part of the Fundamental Theories of Physics book series (FTPH, volume 172)

Abstract

I address the question whether the origin of the observed arrow of time can be derived from quantum cosmology. After a general discussion of entropy in cosmology and some numerical estimates, I give a brief introduction into quantum geometrodynamics and argue that this may provide a sufficient framework for studying this question. I then show that a natural boundary condition of low initial entropy can be imposed on the universal wave function. The arrow of time is then correlated with the size of the Universe and emerges from an increasing amount of decoherence due to entanglement with unobserved degrees of freedom. Remarks are also made concerning the arrow of time in multiverse pictures and scenarios motivated by dark energy.

Keywords

Black Hole Dark Energy Quantum Gravity Event Horizon Gravitational Wave 
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 thank Max Dörner and Tobias Guggenmoser for a careful reading of this manuscript.

References

  1. 1.
    H.D. Zeh, The Physical Basis of the Direction of Time, 5th edn. (Springer, Berlin, 2007)Google Scholar
  2. 2.
    H.D. Zeh, Open questions regarding the arrow of time (2012). Contribution to this volumeGoogle Scholar
  3. 3.
    A. De Simone, A.H. Guth, A. Linde, M. Noorbala, M.P. Salem, A. Vilenkin, Boltzmann brains and the scale-factor cutoff measure of the multiverse Phys. Rev. D 82, 063520 (2010) [arXiv:0808.3778v1 [hep-th]]Google Scholar
  4. 4.
    C.A. Egan, C.H. Lineweaver, A larger estimate of the entropy of the universe Astrophys. J. 710, 1825–1834 (2010) [arXiv:0909.3983v1 [astro-ph.CO]]Google Scholar
  5. 5.
    A. Linde, V. Vanchurin, How many universes are in the multiverse? Phys. Rev. D 81, 083525 (2010) [arXiv:0910.1589v1 [hep-th]]Google Scholar
  6. 6.
    R. Penrose, Time-asymmetry and quantum gravity. In Quantum Gravity, vol. 2, ed. by C.J. Isham, R. Penrose, D.W. Sciama (Clarendon Press, Oxford, 1981), pp. 242–272Google Scholar
  7. 7.
    G.W. Gibbons, S.W. Hawking, Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 15, 2738–2751 (1977)Google Scholar
  8. 8.
    R. Penrose, Black holes, quantum theory and cosmology. J. Phys. Conf. Ser. 174, 012001 (2009)Google Scholar
  9. 9.
    C. Kiefer, Quantum Gravity, 2nd edn (Oxford University Press, Oxford, 2007)Google Scholar
  10. 10.
    M. Albers, C. Kiefer, M. Reginatto, Measurement analysis and quantum gravity. Phys. Rev. D 78, 064051 (2008)Google Scholar
  11. 11.
    C. Kiefer, Quantum geometrodynamics: whence, whither? Gen. Relativ. Gravit. 41, 877–901 (2009); C. Kiefer, Does time exist in quantum gravity? (2009) [arXiv:0909.3767v1 [gr-qc]]Google Scholar
  12. 12.
    B.S. DeWitt, Quantum theory of Gravity. I. The canonical theory. Phys. Rev. 160, 1113–1148 (1967)Google Scholar
  13. 13.
    C. Kiefer, J. Marto, and P.V. Moniz (2009): Indefinite oscillators and black-hole evaporation. Ann. Phys. (Berlin) 18, 722–735.Google Scholar
  14. 14.
    J.J. Halliwell, S.W. Hawking, Origin of structure in the universe. Phys. Rev. D 31, 1777–1791 (1985)Google Scholar
  15. 15.
    C. Kiefer, Continuous measurement of minisuperspace variables by higher multipoles. Class. Quantum Grav. 4, 1369–1382 (1987)Google Scholar
  16. 16.
    H.D. Zeh, Emergence of classical time from a universal wave function. Phys. Lett. A 116, 9–12 (1986)Google Scholar
  17. 17.
    E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edn (Springer, Berlin, 2003)Google Scholar
  18. 18.
    A.A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe. JETP Lett. 30, 682–685 (1979)Google Scholar
  19. 19.
    C. Kiefer, I. Lohmar, D. Polarski, A.A. Starobinsky, Pointer states for primordial fluctuations in inflationary cosmology. Class. Quantum Grav. 24, 1699–1718 (2007); C. Kiefer, D. Polarski, Why do cosmological perturbations look classical to us? Adv. Sci. Lett. 2, 164–173 (2009) [arXiv:0810.0087v2 [astro-ph]]Google Scholar
  20. 20.
    C. Kiefer, Entropy of gravitational waves and primordial fluctuations. In Cosmology and Particle Physics, ed. by J. Garcia-Bellido, R. Durrer, M. Shaposhnikov (American Institute of Physics, New York, 2001), pp. 499–504Google Scholar
  21. 21.
    R. Holman, L. Mersini-Houghton, Why the universe started from a low entropy state. Phys. Rev. D 74, 123510 (2006)Google Scholar
  22. 22.
    C. Kiefer, H.D. Zeh, Arrow of time in a recollapsing quantum universe. Phys. Rev. D 51, 4145–4153 (1995)Google Scholar
  23. 23.
    C. Kiefer, B. Sandhöfer, Quantum cosmology. In Beyond the Big Bang, ed. by R. Vaas (Springer, Berlin, 2012), [arXiv:0804.0672v2 [gr-qc]]Google Scholar
  24. 24.
    M. Novello, S.E.P. Bergliaffa, Bouncing cosmologies. Phys. Rep. 463, 127–213 (2008)Google Scholar
  25. 25.
    M. Bojowald, A momentous arrow of time (2012). Contribution to this volumeGoogle Scholar
  26. 26.
    G. Hinshaw et al., Five-year Wilkinson microwave anisotropy probe (WMAP) observations: Data processing, sky maps, and basic results. Astrophys. J. Suppl. 180, 225–245 (2009)Google Scholar
  27. 27.
    K.H. Geyer, Geometrie der Raum-Zeit der Maßbestimmung von Kottler, Weyl und Trefftz. Astron. Nachr. 301, 135–149 (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität zu KölnKölnGermany

Personalised recommendations