Skip to main content
SpringerLink
Log in
Book cover

Time in Quantum Mechanics pp 369–412Cite as

The Two-State Vector Formalism of Quantum Mechanics

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNPMGR,volume 72))

Abstract

We present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles. Several peculiar effects which naturally arise in this approach are considered. In particular, the concept of “weak measurements” (standard measurements with weakening of the interaction) is discussed in depth revealing a very unusual but consistent picture. Also, a design of a gedanken experiment which implements a kind of quantum “time machine” is described. The issue of time-symmetry in the context of the two-state vector formalism is clarified.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Aharonov, P.G. Bergmann, J.L. Lebowitz: Phys. Rev. B 134, 1410 (1964)

    ADS  MathSciNet  Google Scholar 

  2. Y. Aharonov, D. Albert, A. Casher, L. Vaidman: Phys. Lett. A 124, 199 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  3. Y. Aharonov, L. Vaidman: Phys. Rev. A 41, 11 (1990)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  5. L. Vaidman, Y. Aharonov, D. Albert: Phys. Rev. Lett. 58, 1385 (1987)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Y. Aharonov, J. Anandan, S. Popescu, L. Vaidman: Phys. Rev. Lett. 64, 2965 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Y. Aharonov, S. Popescu, D. Rohrlich, L. Vaidman: Phys. Rev. A 48, 4084 (1993)

    Article  ADS  Google Scholar 

  9. M.B. Berry: J. Phys. A 27, L391 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. S.M. Barnett, D.T. Pegg, J. Jeffers, O. Jedrkiewicz, R. Loudon: Phys. Rev. A 62, 022313 (2000)

    Article  ADS  Google Scholar 

  11. S.M. Barnett, D.T. Pegg, J. Jeffers, O. Jedrkiewicz: Jour. Phys. B 33, 3047 (2000)

    Article  ADS  Google Scholar 

  12. S.M. Barnett, D.T. Pegg, J. Jeffers: Jour. Mod. Opt. 47, 1779 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  13. B. Reznik, Y. Aharonov: Phys. Rev. A 52, 2538 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  14. J. von Neumann: Mathematical Foundations of Quantum Theory (Princeton, University Press, New Jersey 1983)

    Google Scholar 

  15. O. Cohen: Phys. Rev. A 51, 4373 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  16. L. Vaidman: Phys. Rev. A 57, 2251 (1998)

    Article  ADS  Google Scholar 

  17. D. Albert, Y. Aharonov, S. D’Amato: Phys. Rev. Lett. 54, 5 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  18. L. Vaidman: Phys. Rev. Lett. 70, 3369 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. L. Vaidman: “Elements of Reality” and the Failure of the Product Rule”. In Symposium on the Foundations of Modern Physics, ed. by P. J. Lahti, P. Bush, P. Mittelstaedt (World Scientific, Cologne 1993) pp. 406–417

    Google Scholar 

  20. Y. Aharonov, D. Albert, L. Vaidman: Phys. Rev. D 34, 1805 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  21. L. Hardy: Phys. Rev. Lett. 68, 2981 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Y. Aharonov, B.G. Englert: Zeit. Natur. 56a 16 (2001)

    Google Scholar 

  23. B.G. Englert, Y. Aharonov: Phys. Lett. A 284, 1 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  24. W. Unruh: Ann. NY Acad. Sci. 755, 560 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  25. Y. Aharonov, A. Botero, S. Popescu, B. Reznik, J. Tollaksen: quant-ph/0104062 (2001)

    Google Scholar 

  26. J.M. Knight, L. Vaidman: Phys. Lett. A 143, 357 (1990)

    Article  ADS  Google Scholar 

  27. M. Duck, P.M. Stevenson, E.C.G. Sudarshan: Phys. Rev. D 40, 2112 (1989)

    Article  ADS  Google Scholar 

  28. N.W.M. Ritchie, J.G. Story, R.G. Hulet: Phys. Rev. Lett. 66, 1107 (1991)

    Article  ADS  Google Scholar 

  29. A.D. Parks, D.W. Cullin, D.C. Stoudt: Proc. Roy. Soc. Lon. A 454, 2997 (1998)

    Article  MATH  ADS  Google Scholar 

  30. A.M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995)

    Article  ADS  Google Scholar 

  31. L. Vaidman: Found. Phys. 21, 947 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  32. D. Suter: Phys. Rev. A 51, 45 (1995)

    Article  ADS  Google Scholar 

  33. D. Suter, M. Ernst, R.R. Ernst: Molec. Phys. 78, 95 (1993)

    Article  ADS  Google Scholar 

  34. A. Shimony: Erken. 45, 337 (1997)

    MathSciNet  Google Scholar 

  35. L. Vaidman: Fortschr. Phys. 46, 729 (1998)

    Article  MathSciNet  Google Scholar 

  36. L. Vaidman: Found. Phys. 26, 895 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  37. W.D. Sharp, N. Shanks: Phil. Sci. 60, 488 (1993)

    Article  MathSciNet  Google Scholar 

  38. D.J. Miller: Phys. Lett. A 222, 31 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. L. Vaidman: Stud. Hist. Phil. Mod. Phys. 30, 373 (1999)

    Article  MathSciNet  Google Scholar 

  40. L. Vaidman: Found. Phys. 29, 755 (1999)

    Article  MathSciNet  Google Scholar 

  41. L. Vaidman: Found. Phys. 29, 865 (1999)

    Article  MathSciNet  Google Scholar 

  42. R.E. Kastner: Stud. Hist. Phil. Mod. Phys. 30, 237 (1999)

    Article  MathSciNet  Google Scholar 

  43. R.E. Kastner: Stud. Hist. Phil. Mod. Phys. 30, 399 (1999)

    Article  MathSciNet  Google Scholar 

  44. R.E. Kastner: Found. Phys. 29, 851 (1999)

    Article  MathSciNet  Google Scholar 

  45. R.E. Kastner: Am. J. Phys. to be published in August (2001)

    Google Scholar 

  46. U. Mohrhoff: Am. J. Phys. 68, 728 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  47. D. Lewis: Nous 13, 455 (1979); reprinted in Philosophical Papers Vol.II, (Oxford University Press, Oxford 1986) pp. 32

    Article  Google Scholar 

  48. Y. Aharonov, L. Vaidman: Phys. Lett. A 178, 38 (1993)

    Article  ADS  Google Scholar 

  49. Y. Aharonov, J. Anandan, L. Vaidman: Phys. Rev. A 47, 4616 (1993)

    Article  ADS  Google Scholar 

  50. Y. Aharonov, L. Vaidman: ‘Protective Measurements of Two-State Vectors’. In Potentiality, Entanglement and Passion-at-a-Distance, ed. by R.S. Cohen, et al. (Kluwer Academic Publishers, 1997) pp. 1–8

    Google Scholar 

  51. H. Everett: Rev. Mod. Phys. 29, 454 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  52. L. Vaidman: Int. Stud. Phil. Sci. 12, 245 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel-Aviv, 69978, Israel

    Yakir Aharonov & Lev Vaidman

  2. Physics Department, University of South Carolina, Columbia, SC, 29208, USA

    Yakir Aharonov

  3. Centre for Quantum Computation, Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, England

    Lev Vaidman

Authors
  1. Yakir Aharonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lev Vaidman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Química-Física Facultad de Ciencias, Universidad del País Vasco, Apdo. 644, Bilbao, Spain

    J. G. Muga

  2. Departamento de Física Fundamental II, Universidad de La Laguna, La Laguna (S/C de Tenerife), Spain

    R. Sala Mayato

  3. Fisika Teorikoaren Saila Zientzi Fakultatea, Euskal Herriko Unibertsitatea, 644 P.K., Bilbao, Spain

    I. L. Egusquiza

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Aharonov, Y., Vaidman, L. (2002). The Two-State Vector Formalism of Quantum Mechanics. In: Muga, J.G., Mayato, R.S., Egusquiza, I.L. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45846-8_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45846-8_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43294-4

  • Online ISBN: 978-3-540-45846-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation