Foundations of Physics

, Volume 42, Issue 5, pp 656–673 | Cite as

Revisiting Consistency Conditions for Quantum States of Systems on Closed Timelike Curves: An Epistemic Perspective

  • Joel J. Wallman
  • Stephen D. BartlettEmail author


There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.


Closed timelike curves Epistemic interpretation 



We acknowledge helpful discussions with Eric Cavalcanti and Nick Menicucci. S.D.B. acknowledges the support of the ARC and the Perimeter Institute for Theoretical Physics.


  1. 1.
    Gödel, K.: Rev. Mod. Phys. 21, 447 (1949) ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Gott, J.R.: Phys. Rev. Lett. 66, 1126 (1991) MathSciNetADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Morris, M.S., Thorne, K.S., Yurtsever, U.: Phys. Rev. Lett. 61, 1446 (1988) ADSCrossRefGoogle Scholar
  4. 4.
    Ori, A.: Phys. Rev. D 76, 044002 (2007) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Tipler, F.J.: Phys. Rev. D 9, 2203 (1974) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Deutsch, D.: Phys. Rev. D 44, 3197 (1991) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Everett, H.: Rev. Mod. Phys. 29, 454 (1957) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Bacon, D.: Phys. Rev. A 70, 032309 (2004) ADSCrossRefGoogle Scholar
  9. 9.
    Aaronson, S., Watrous, J.: Proc. R. Soc. A 465, 631 (2009) MathSciNetADSCrossRefzbMATHGoogle Scholar
  10. 10.
    Brun, T., Harrington, J., Wilde, M.: Phys. Rev. Lett. 102, 210402 (2009) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    DeJonghe, R., Frey, K., Imbo, T.: Phys. Rev. D 81, 087501 (2010) ADSCrossRefGoogle Scholar
  12. 12.
    Durham, I.: arXiv:0803.3287v3 [quant-ph]
  13. 13.
    da Silva, R.D., Galvao, E.F., Kashefi, E.: Phys. Rev. A 83, 012316 (2011) ADSCrossRefGoogle Scholar
  14. 14.
    Lloyd, S., et al.: Phys. Rev. Lett. 106, 040403 (2011) ADSCrossRefGoogle Scholar
  15. 15.
    Svetlichny, G., et al.: arXiv:0902.4898v1 [quant-ph]
  16. 16.
    Bennett, C.H., Leung, D., Smith, G., Smolin, J.A.: Phys. Rev. Lett. 103, 170502 (2009) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Ralph, T.C.: Proc. SPIE 6305, 63050P (2006) ADSCrossRefGoogle Scholar
  18. 18.
    Fuchs, C.A.: J. Mod. Opt. 50, 987 (2003) ADSzbMATHGoogle Scholar
  19. 19.
    Cavalcanti, E.G., Menicucci, N.C.: arXiv:1004.1219v4 [quant-ph]
  20. 20.
    Harrigan, N., Spekkens, R.W.: Found. Phys. 40, 125 (2010) MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    Spekkens, R.W.: Phys. Rev. A 75, 032110 (2007) ADSCrossRefGoogle Scholar
  22. 22.
    Bartlett, S.D., Rudolph, T., Spekkens, R.W.: arXiv:1111.5057v1 [quant-ph]

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of PhysicsThe University of SydneySydneyAustralia

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