Skip to main content
SpringerLink
Log in

Many Worlds, the Born Rule, and Self-Locating Uncertainty

  • Conference paper
Quantum Theory: A Two-Time Success Story

Abstract

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule. [Editors note: for a video of the talk given by Prof. Carroll at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-14.]

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

Access this chapter

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Everett’s original paper is [1]. A comprehensive introduction to the theory in its modern version can be found in [2].

  2. 2.

    EQM is time-symmetric, but branching occurs toward the future, and not toward the past, because the low-entropy early universe was relatively free of entanglements between subsystems.

  3. 3.

    Page has recently argued that the prospect of classical self-locating uncertainty in large universes poses a crisis for quantum mechanics, as the Born Rule becomes insufficient for calculating the probability of measurement outcomes [8, 27–30]. Our approach provides a unified treatment of classical and quantum self-locating uncertainties, defusing the would-be crisis.

  4. 4.

    The ESP is implicit in Elga’s discussion of his TOSS & DUPLICATION thought experiment, where he notes that the outcome of an additional coin toss should not affect the credence we assign to being either an original or a duplicated person with identical experiences.

References

  1. H. Everett, “Relative state” formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation (Oxford University Press, London, 2012)

    Book  Google Scholar 

  3. C.T. Sebens, S.M. Carroll, Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics (2013)

    Google Scholar 

  4. L. Vaidman, Probability in the many-worlds interpretation of quantum mechanics, in The Probable and the Improbable: Understanding Probability in Physics, Essays in Memory of Itamar Pitowsky, ed. by Y. Ben-Menahem, M. Hemmo (Springer, Berlin, 2011)

    Google Scholar 

  5. W.H. Zurek, Probabilities from entanglement, Born’s Rule \(p_{k}=\left| \psi _{k}\right|^{2}\) from envariance. Phys. Rev. A 71(5), 052105 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  6. J.B. Hartle, Quantum mechanics of individual systems. Am. J. Phys. 36, 704–712 (1968)

    Article  ADS  Google Scholar 

  7. E. Farhi, J. Goldstone, S. Gutmann, How probability arises in quantum mechanics. Ann. Phys. 192, 368 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. A. Aguirre, M. Tegmark, Born in an infinite universe: a cosmological interpretation of quantum mechanics. Phys. Rev. D 84, 105002 (2011)

    Article  ADS  Google Scholar 

  9. D. Deutsch, Quantum theory of probability and decisions. Proc. R. Soc. Lond. Ser. A 458, 3129–3137 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  10. D. Wallace, Quantum probability and decision theory (2002). arXiv preprint. quant-ph/0211104

  11. H. Greaves, Understanding Deutsch’s probability in a deterministic multiverse. Stud. Hist. Philos. Sci. Part B, Stud. Hist. Philos. Mod. Phys. 35(3), 423–456 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Wallace, How to prove the Born Rule, in Many Worlds?: Everett, Quantum Theory, & Reality, ed. by S. Saunders, J. Barrett, A. Kent, D. Wallace (Oxford University Press, London, 2010), pp. 227–263

    Chapter  Google Scholar 

  13. A.M. Gleason, Measures on the closed subspaces of a Hilbert space. J. Appl. Math. Mech. 6, 885–894 (1957)

    MathSciNet  MATH  Google Scholar 

  14. D. Lewis, Attitudes de dicto and de se. Philos. Rev. 88(4), 513–543 (1979)

    Article  Google Scholar 

  15. T. Banks, Cosmological breaking of supersymmetry? or Little lambda goes back to the future 2 (2000)

    Google Scholar 

  16. S.M. Carroll, What If Time Really Exists? (2008)

    Google Scholar 

  17. W.H. Zurek, Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? Phys. Rev. D 24, 1516–1525 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  18. E. Joos, H.D. Zeh, The emergence of classical properties through interaction with the environment. Z. Phys. B, Condens. Matter 59, 223–243 (1985)

    Article  ADS  Google Scholar 

  19. D. Wallace, Decoherence and ontology, in Many Worlds?: Everett, Quantum Theory, & Reality, ed. by S. Saunders, J. Barrett, A. Kent, D. Wallace (Oxford University Press, London, 2010), pp. 53–72

    Chapter  Google Scholar 

  20. J.B. Hartle, M. Srednicki, Are we typical? Phys. Rev. D 75(12), 123523 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  21. D.N. Page, Typicality defended (2007). arXiv:0707.4169

  22. M. Srednicki, J. Hartle, Science in a very large universe. Phys. Rev. D 81(12), 123524 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  23. N. Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy (Routledge, London, 2002)

    Google Scholar 

  24. C.J.G. Meacham, Sleeping beauty and the dynamics of de se beliefs. Philos. Stud. 138(2), 245–269 (2008)

    Article  MathSciNet  Google Scholar 

  25. D. Manley, Self-Location, Existence, and Evidential Uniqueness (2013)

    Google Scholar 

  26. A. Elga, Defeating Dr. Evil with self-locating belief. Philos. Phenomenol. Res. 69(2), 383–396 (2004)

    Article  Google Scholar 

  27. D.N. Page, The Born Rule dies. J. Cosmol. Astropart. Phys. 0907, 008 (2009)

    Article  ADS  Google Scholar 

  28. D.N. Page, Born Again (2009)

    Google Scholar 

  29. D.N. Page, Born’s Rule Is Insufficient in a Large Universe (2010)

    Google Scholar 

  30. A. Albrecht, D. Phillips, Origin of Probabilities and Their Application to the Multiverse (2012)

    Google Scholar 

Download references

Acknowledgements

Sean Carroll feels that it has been an honor and a pleasure to take part in the celebration of Yakir Aharonov’s 80th birthday and would like to thank Jeff Tollaksen and the organizers of a very stimulating meeting. His work was supported in part by the U.S. Department of Energy, the National Science Foundation, and the Gordon and Betty Moore Foundation. Charles Sebens’s work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 0718128.

Author information

Authors and Affiliations

  1. Physics Department, California Institute of Technology, Pasadena, CA, USA

    Sean M. Carroll

  2. Philosophy Department, University of Michigan, Ann Arbor, MI, USA

    Charles T. Sebens

Authors
  1. Sean M. Carroll
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles T. Sebens
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sean M. Carroll .

Editor information

Editors and Affiliations

  1. Schmid College of Science and Technology, Chapman University, Orange, USA

    Daniele C. Struppa

  2. Schmid College of Science and Technology, Chapman University, Orange, USA

    Jeffrey M. Tollaksen

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Italia

About this paper

Cite this paper

Carroll, S.M., Sebens, C.T. (2014). Many Worlds, the Born Rule, and Self-Locating Uncertainty. In: Struppa, D., Tollaksen, J. (eds) Quantum Theory: A Two-Time Success Story. Springer, Milano. https://doi.org/10.1007/978-88-470-5217-8_10

Download citation

Publish with us

Policies and ethics

Search

Navigation