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At What Time Does a Quantum Experiment Have a Result?

  • Thomas PashbyEmail author
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Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

Abstract

This paper provides a general method for defining a generalized quantum observable (or POVM) that supplies properly normalized conditional probabilities for the time of occurrence (i.e., of detection). This method treats the time of occurrence as a probabilistic variable whose value is to be determined by experiment and predicted by the Born rule. This avoids the problematic assumption that a question about the time at which an event occurs must be answered through instantaneous measurements of a projector by an observer, common to both Rovelli [22] and Oppenheim et al. [17]. I also address the interpretation of experiments purporting to demonstrate the quantum Zeno effect, used by Oppenheim et al. [17] to justify an inherent uncertainty for measurements of times.

Keywords

Positive Operator-valued Measure (POVM) Quantum Zeno Effect Rovelli Born Rule Instantaneous Measurements 
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.

References

  1. 1.
    L.E. Ballentine, Comment on “quantum Zeno effect”. Phys. Rev. A 43(9), 5165 (1991)Google Scholar
  2. 2.
    A. Beige, G.C Hegerfeldt, Projection postulate and atomic quantum Zeno effect. Phys. Rev. A 53(1), 53 (1996)Google Scholar
  3. 3.
    R. Brunetti, K. Fredenhagen, Time of occurrence observable in quantum mechanics. Phys. Rev. A 66(4), 044101 (2002)Google Scholar
  4. 4.
    P. Busch, Quantum states and generalized observables: a simple proof of Gleason’s theorem. Phys. Rev. Lett. 91(12), 120403 (2003)Google Scholar
  5. 5.
    P. Busch, M. Grabowski, P.J. Lahti, Time observables in quantum theory. Phys. Lett. A 191(5), 357–361 (1994)ADSCrossRefGoogle Scholar
  6. 6.
    P. Busch, M. Grabowski, P.J. Lahti, Operational Quantum Physics (Springer, Berlin, 1995)zbMATHGoogle Scholar
  7. 7.
    J. Conway, S. Kochen, The free will theorem. Found. Phys. 36(10), 1441–1473 (2006)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    P.A.M. Dirac, The Principles of Quantum Mechanics. (Clarendon Press, Oxford, 1930)Google Scholar
  9. 9.
    I. Egusquiza, J. Muga, A. Baute, “Standard” quantum–mechanical approach to times of arrival, in Time in Quantum Mechanics (Springer, New York, 2002), pp. 305–332zbMATHGoogle Scholar
  10. 10.
    M.O. Hoge, Relationale Zeit in der Quantenphysik. Master’s Thesis, University of Hamburg (2008)Google Scholar
  11. 11.
    W.M. Itano, D.J. Heinzen, J.J. Bollinger, D.J. Wineland, Quantum zeno effect. Phys. Rev. A 41(5), 2295 (1990)Google Scholar
  12. 12.
    K. Jacobs, D.A. Steck, A straightforward introduction to continuous quantum measurement. Contemp. Phys. 47(5), 279–303 (2006). http://dx.doi.org/10.1080/00107510601101934 ADSCrossRefGoogle Scholar
  13. 13.
    J. Kijowski, On the time operator in quantum mechanics and the Heisenberg uncertainty relation for energy and time. Rep. Math. Phys. 6(3), 361–386 (1974)ADSCrossRefMathSciNetGoogle Scholar
  14. 14.
    G.W. Mackey, The Mathematical Foundations of Quantum Theory (WA Benjamin, New York, 1963)zbMATHGoogle Scholar
  15. 15.
    B. Misra, E.C. George Sudarshan. The zeno’s paradox in quantum theory. J. Math. Phys. 18(4), 756–763 (1977)ADSCrossRefMathSciNetGoogle Scholar
  16. 16.
    W. Nagourney, J. Sandberg, H. Dehmelt, Shelved optical electron amplifier: observation of quantum jumps. Phys. Rev. Lett. 56(26), 2797 (1986)Google Scholar
  17. 17.
    J. Oppenheim, B. Reznik, W.G. Unruh, When does a measurement or event occur? Found. Phys. Lett. 13(2), 107–118 (2000)CrossRefMathSciNetGoogle Scholar
  18. 18.
    T. Pashby, Time and the foundations of quantum mechanics. Ph.D. Thesis, University of Pittsburgh (2014). http://philsci-archive.pitt.edu/10723/
  19. 19.
    T. Pashby. Time and quantum theory: a history and a prospectus. Stud. Hist. Phil. Sci. Part B: Stud. Hist. Phil. Mod. Phys. 52, 24–38 (2015)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Y.S. Patil, S. Chakram, M. Vengalattore, Measurement-induced localization of an ultracold lattice gas. Phys. Rev. Lett. 115(14), 140402 (2015)Google Scholar
  21. 21.
    A.N. Prior, Changes in Events and Changes in Things. (Department of Philosophy, University of Kansas, Lawrence, 1962)Google Scholar
  22. 22.
    C. Rovelli, “Incerto tempore, incertisque loci”: can we compute the exact time at which a quantum measurement happens? Found. Phys. 28(7) 1031–1043 (1998)CrossRefMathSciNetGoogle Scholar
  23. 23.
    A. Ruschhaupt, J. Gonzalo Muga, G.C. Hegerfeldt, Detector models for the quantum time of arrival, in Time in Quantum Mechanics-Vol. 2 (Springer, Berlin, 2009), pp. 65–96Google Scholar
  24. 24.
    M. Srinivas, R. Vijayalakshmi, The ‘time of occurrence’ in quantum mechanics. Pramana 16(3), 173–199 (1981)ADSCrossRefGoogle Scholar
  25. 25.
    A. Sudbery, Diese verdammte quantenspringerei. Stud. Hist. Phil. Sci. Part B: Stud. Hist. Phil. Mod. Phys. 33(3), 387–411 (2002)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    R. Werner, Screen observables in relativistic and nonrelativistic quantum mechanics. J. Math. Phys. 27, 793 (1986)ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    A.S. Wightman, On the localizability of quantum mechanical systems. Rev. Mod. Phys. 34, 845–872 (1962)ADSCrossRefGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of ChicagoChicagoUSA

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