Foundations of Physics

, Volume 37, Issue 1, pp 159–168 | Cite as

Time-Symmetric Quantum Mechanics

Article

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P0 is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry.

Keywords

quantum mechanics time reversal symmetry time reversal operator 

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References

  1. Aharonov Y., Bergmann P., Lebovitz J. (1964) “Time symmetry in the quantum process of measurement”. Phys. Rev. 134: B1410CrossRefADSGoogle Scholar
  2. Griffiths R.B. (1984) “Consistent histories and the interpretation of quantum mechanics”. J. Stat. Phys. 36, 219MATHCrossRefGoogle Scholar
  3. W. G. Unruh, “Quantum measurement”, in New Techniques and Ideas in Quantum Measurement Theory, D. M. Greenberg, ed. (New York Academy of Science, New York, 1986) p. 242.Google Scholar
  4. M. Gell-Mann and J. B. Hartle, “Time symmetry and asymmetry in quantum mechanics and quantum cosmology”, in Proceedings of the NATO Workshop on the Physical Origins of Time Asymmetry, J. J. Halliwell, J. Perez-Mercader, and W. Zurek, eds. (Cambridge University Press, Cambridge, 1994).Google Scholar
  5. Schulman L.S. (1997) Time’s Arrows and Quantum Measurement. Cambridge University Press, CambridgeGoogle Scholar
  6. J. G. Cramer, “Generalized absorber theory and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. D 22, 362 (1980); “The transactional interpretation of quantum mechanics,” Rev. Mod. Phys. 58, 647 (1986).Google Scholar
  7. Aharonov Y., Vaidman L. (1991) “Complete description of a quantum system at a given time”. J. Phys. A 24: 2315CrossRefADSMathSciNetGoogle Scholar
  8. Y. Aharonov and L. Vaidman, “The two-state vector formalism of quantum mechanics”, in Time in Quantum Mechanics, J. G. Muga et al., eds. (Springer, Berlin, 2002), p. 369.Google Scholar
  9. E. P. Wigner, “On the time inversion operation in quantum mechanics”, Göttinger Nachr. 31, 546 (1932); E. P. Wigner, Group Theory (Academic, New York, 1959), Chap. 26.Google Scholar
  10. Bell J.S. (1996) “On the problem of hidden variables in quantum mechanics”. Rev. Mod. Phys. 38: 447CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsSan José State UniversitySan JoséUSA

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