Arrow of time in a recollapsing quantum universe

Phys. Rev. D 51, 4145 – Published 15 April 1995
C. Kiefer and H. D. Zeh


We argue that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. To recover a classically recollapsing universe in terms of wave packets, we impose the usual boundary condition of excluding exponentially increasing wave functions for large scale factors. Consistency of these opposite arrows is then facilitated by quantum effects in the region of the classical turning point. We also discuss in this context the meaning of the time-asymmetric expression used in the definition of ‘‘consistent histories.’’ Since gravitational time dilation diverges at horizons, one has to conclude that collapsing matter must start reexpanding ‘‘anticausally’’ (controlled by the reversed arrow) in this scenario before horizons or singularities can form. There would then also be no mass inflation nor any information loss paradox.


  • Received 18 February 1994
  • Published in the issue dated 15 April 1995

© 1995 The American Physical Society

Authors & Affiliations

C. Kiefer

  • Fakultät für Physik, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany

H. D. Zeh

  • Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany

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