Skip to main content

Quantum Measurement and Initial Conditions

Abstract

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schrödinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schrödinger equation.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

  1. Patching local solutions together to obtain global solution, and the obstructions preventing this, are studied in sheaf theory [43].

References

  1. von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press (1955)

  2. d’Espagnat, B.: Conceptual Foundations of Quantum Mechanics. W. A. Benjamin, Reading, Mass (1976)

  3. Joos, E., Zeh, H.: Z. Phys. B: Condens. Matter 59(2), 223 (1985)

    ADS  Article  Google Scholar 

  4. Zeh, H.: In: Ferrero, M., van der Merwe, A. (eds.) New Developments on Fundamental Problems in Quantum Physics, pp. 441–451. Springer (1997)

  5. Zurek, W.H.: Phil. Trans. Roy. Soc. London Ser. A A356, 1793 (1998)

    ADS  MathSciNet  Google Scholar 

  6. Everett, H.: Rev. Mod. Phys. 29(3), 454 (1957). doi:10.1103/RevModPhys.29.454

    ADS  MathSciNet  Article  Google Scholar 

  7. Everett, H.: The Many-Worlds Hypothesis of Quantum Mechanics. Press (1973)

  8. de Witt, B.S.: The Many-Universes Interpretation of Quantum Mechanics (1971)

  9. de Witt, B., Graham, N.: The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton series in physics, Princeton (1973)

  10. Griffiths, R.: J. Stat. Phys. 36(1), 219 (1984)

    ADS  MATH  Article  Google Scholar 

  11. Omnes, R.: J. Stat. Phys. 53(3–4), 893 (1988)

    ADS  MATH  MathSciNet  Article  Google Scholar 

  12. Gell-Mann, M., Hartle, J.: In: Proceedings of the 25th International Conference on High Energy Physics, Singapore (1990)

  13. Tegmark, M., Wheeler, J.A.: Sci. Am. 284(2), 68 (2001)

    Article  Google Scholar 

  14. Stoica, O.C.: PhilSci Archive (2008). http://philsci-archive.pitt.edu/archive/ 00004344/

  15. Stoica, O.C.: Noema. Romanian Committee for the History and Philosophy of Science and Technologies of the Romanian Academy XI, 431 (2012). http://www. noema.crifst.ro/doc/2012_5_01.pdf

    Google Scholar 

  16. ’t Hooft, G.: Arxiv preprint arXiv:1112.1811 (2011)

  17. ’t Hooft, G.: Arxiv preprint arXiv:1405.1548 (2014)

  18. Adler, S.: Philos, Stud. Hist. Mod. Phys. 34(1), 135 (2003)

    Article  Google Scholar 

  19. Schlosshauer, M.: Rev. Mod. Phys. 76(4), 1267 (2005)

    ADS  Article  Google Scholar 

  20. Schlosshauer, M.: Decoherence and the Quantum-To-Classical Transition. Springer (2007)

  21. Schlosshauer, M.: Elegance and Enigma: The Quantum Interviews. Springer (2011)

  22. Einstein, A., Podolsky, B., Rosen, N.: Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Phys. Rev. 47, 777–780 (1935)

    ADS  MATH  Article  Google Scholar 

  23. Bohm, D.: Quantum Th, 611–623 (1951)

  24. Bell, J.: Physics 1(3), 195 (1964)

    Google Scholar 

  25. Aharonov, Y., Cohen, E., Grossman, D., Elitzur, A.: Ann. Phys. 355, 258 (2015)

    ADS  Article  Google Scholar 

  26. Aharonov, Y., Bergmann, P., Lebowitz, J.: Physical Review 134, 1410 (1964)

    ADS  MathSciNet  Article  Google Scholar 

  27. Aharonov, Y., Vaidman, L.: Time in Quantum Mechanics (Springer) (2007)

  28. Wheeler, J.A., Marlow, A.R.: Mathematical Foundations of Quantum Theory (1978)

  29. de Beauregard, O.: C. R. Acad. Sci. 236, 1632–34 (1953)

    MATH  Google Scholar 

  30. Rietdijk, C.: Found. Phys. 8(7–8), 615 (1978)

    ADS  Article  Google Scholar 

  31. Aharonov, Y., Albert, D., Vaidman, L.: Phys. Rev. Lett. 60(14), 1351 (1988)

    ADS  MathSciNet  Article  Google Scholar 

  32. Aharonov, Y., Vaidman, L.: J. Phys. A 24, 2315 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  33. Aharonov, Y., Cohen, E., Gruss, E., Landsberger, T.: Quantum Studies: Mathematics and Foundations 1(1–2), 133 (2014)

    MATH  Article  Google Scholar 

  34. Elze, H.T.: Phys. Rev. A 89(1), 012111 (2014)

    ADS  Article  Google Scholar 

  35. Conway, J., Kochen, S.: Found. Phys. 36, 1441 (2006). arXiv:quant-ph/0604079

    ADS  MATH  MathSciNet  Article  Google Scholar 

  36. Stoica, O.C.: Foundational Questions Institute, http://fqxi.org/community/forum/topic/322 “The Nature of Time” essay contest (2008)

  37. Stoica, O.C.: In: Aguirre, A., Foster, B., Merali, Z. (eds.) It From Bit or Bit From It?: On Physics and Information, pp. 51–64. Springer (2015)

  38. Aaronson, S.: In: Cooper, S.B., Hodges, A. (eds.) To appear in “The Once and Future Turing: Computing the World,” a collection. arXiv:1306.0159 (2013)

  39. Stoica, O.C.: TM 2012 – The Time Machine Factory [unspeakable, speakable] on Time Travel in Turin, (EPJ Web of Conferences), vol. 58, p. 01017 (2013)

  40. Arnowitt, R., Deser, S., Misner, C.W.: Gen. Relativ. Gravitation 40(9), 1997 (2008)

    ADS  MATH  Article  Google Scholar 

  41. Schrödinger, E.: Phys. Rev. 28, 1049 (1926). doi:10.1103/PhysRev.28.1049

    ADS  MATH  Article  Google Scholar 

  42. de Broglie, L.: Ann. de Physique 3, 10 (1924). http://tel.archives-ouvertes.fr/ docs/00/04/70/78/PDF/tel-00006807.pdf

    Google Scholar 

  43. Bredon, G.: Sheaf Theory, vol. 170. Springer (1997)

Download references

Acknowledgments

The author cordially thanks Eliahu Cohen, Hans-Thomas Elze, Florin Moldoveanu, and the referees, for very helpful comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ovidiu Cristinel Stoica.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Stoica, O.C. Quantum Measurement and Initial Conditions. Int J Theor Phys 55, 1897–1911 (2016). https://doi.org/10.1007/s10773-015-2829-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2829-2

Keywords

  • Foundations of quantum mechanics
  • Measurement theory
  • Contextuality
  • Entanglement and quantum nonlocality
  • EPR paradox
  • Bell inequalities
  • Quantum mechanics