Advertisement

Foundations of Physics

, Volume 35, Issue 2, pp 197–213 | Cite as

On Zurek’s Derivation of the Born Rule

  • Maximilian SchlosshauerEmail author
  • Arthur Fine
Article

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.

Keywords

Born rule quantum probabilities environment-assisted invariance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Born, “Zur Quantenmechanik der Stoßvorgänge”, Z. Phys. 37, 863 (1926). Reprinted and translated in Quantum Theory and Measurement, J. A. Wheeler and W. H. Zurek eds., (Princeton University Press, Princeton, NJ, 1963), p. 52.Google Scholar
  2. 2.
    N. D. Mermin, “What’s wrong with this pillow?”, Phys. Today 42(4), 9 (April 1989). Reprinted as Chapter 16 of his Boojums All the Way Through (Cambridge University Press, Cambridge, 1990); the phrase is on p. 199.Google Scholar
  3. 3.
    Fuchs, C. A., Peres, A. 2000“Quantum theory needs no ’interpretation”Phys. Today5370Google Scholar
  4. 4.
    Gleason, A. M. 1957“Measures on the closed subspaces of a Hilbert space”J. Math. Mech.6885Google Scholar
  5. 5.
    Everett, H. 1957“’Relative state’ formulation of quantum mechanics”Rev. Mod. Phys.29454462Google Scholar
  6. 6.
    Hartle, J. B. 1968“Quantum mechanics of individual systems”Am. J. Phys.36704Google Scholar
  7. 7.
    DeWitt, B. S. 1971“The many-universes interpretation of quantum mechanics”d’Espagnat, B. eds. Foundations of Quantum MechanicsAcademic PressNew York, NYGoogle Scholar
  8. 8.
    Graham, N. 1973“The measurement of relative frequency”DeWitt, B. S.Graham, N. eds. The Many-Worlds Interpretation of Quantum MechanicsPrinceton University PressPrinceton, NJGoogle Scholar
  9. 9.
    Geroch, R. 1984“The Everett interpretation”Noûs18617Google Scholar
  10. 10.
    Farhi, E., Goldstone, J. 1989“How probability arises in quantum mechanics”Ann Phys192368Google Scholar
  11. 11.
    Stein, H. 1984“The Everett interpretation of quantum mechanics Many worlds or none?”Nôus18635Google Scholar
  12. 12.
    Kent, A. 1990“Against many worlds interpretations”Int J Mod PhysA5 1745Google Scholar
  13. 13.
    Squires, E. J. 1990“On an alleged ’proof’ of the quantum probability law”Phys. Lett.A14567Google Scholar
  14. 14.
    Deutsch, D. 1999“Quantum theory of probability and decisions”Proc. Roy. Soc. LondonA4553129Google Scholar
  15. 15.
    Barnum, H., Caves, C. M., Finkelstein, J., Fuchs, C. A., Schack, R. 2000“Quantum probability from decision theory?”Proc. Roy. Soc. LondonA4561175Google Scholar
  16. 16.
    Wallace, D. 2003“Everettian rationality defending Deutsch’s approach to probability in the Everett interpretation”Stud. Hist. Phil. Mod. Phys34415Google Scholar
  17. 17.
    S. Saunders, “Derivation of the Born rule from operational assumptions”, eprint quant-ph/0211138 (2002).Google Scholar
  18. 18.
    Zurek, W. H. 2003“Environment-assisted invariance, entanglement, and probabilities in quantum physics”Phys. Rev. Lett.90120404Google Scholar
  19. 19.
    W. H. Zurek, “Quantum Darwinism and envariance”, eprint quant-ph/0308163 (2003).Google Scholar
  20. 20.
    Zurek, W. H. 2003“Decoherence, einselection, and the quantum origins of the classical”Rev. Mod. Phys.75715CrossRefGoogle Scholar
  21. 21.
    Schlosshauer, M. 2005“Decoherence, the measurement problem, and interpretations of quantum mechanics”Rev. Mod. Phys.771Google Scholar
  22. 22.
    Zurek, W. H. 1793“Decoherence, einselection, and the existential interpretation (The Rough Guide)”Phil. Trans. Roy. Soc. Lond.A3561793Google Scholar
  23. 23.
    H. D. Zeh, “What is achieved by decoherence?”, eprint quant-ph/9610014 (1996).Google Scholar
  24. 24.
    H. Barnum, “No-signalling-based version of Zurek’s derivation of quantum probabilities: A note on ’Environment-assisted invariance, entanglement, and probabilities in quantum physics”’, eprint quant-ph/0312150 (2003).Google Scholar
  25. 25.
    U. Mohrhoff, “Probabilities from envariance?”, eprint quant-ph/0401180 (2004).Google Scholar
  26. 26.
    W. H. Zurek, “Probabilities from envariance”, eprint quant-ph/0405161 (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WashingtonSeattleUSA
  2. 2.Department of PhilosophyUniversity of WashingtonSeattleWAUSA

Personalised recommendations