“It from Bit” and the Quantum Probability Rule

  • M. S. LeiferEmail author
Part of the The Frontiers Collection book series (FRONTCOLL)


I argue that, on the subjective Bayesian interpretation of probability, “it from bit” requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or “bit from it”. I then explain why this does not conflict with “it from bit”. This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.


Quantum Theory Boolean Algebra Wind Farm Fair Price Lottery Ticket 
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.


  1. 1.
    J.A. Wheeler, in Proceedings of the 3rd International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, ed. by S. Kobayashi, H. Ezawa, Y. Murayama, S. Nomura (Physical Society of Japan, Tokyo, 1990), pp. 354–368Google Scholar
  2. 2.
    J.A. Wheeler, in Problems in the Foundations of Physics: Proceedings of the International School of Physics “Enrico Fermi”, Course LXXII, ed. by G. Toraldo di Francia (North-Holland, Amsterdam, 1979), pp. 395–492Google Scholar
  3. 3.
    G. Birkhoff, J. von Neumann, Ann. Math. 37, 823 (1936)CrossRefGoogle Scholar
  4. 4.
    F.J. Murray, J. von Neumann, Ann. Math. 37, 116 (1936)CrossRefGoogle Scholar
  5. 5.
    M. Rédei, S.J. Summers, Stud. Hist. Philos. Mod. Phys. 38, 390 (2007)CrossRefzbMATHGoogle Scholar
  6. 6.
    M.S. Leifer, R.W. Spekkens, Phys. Rev. A 88, 052130 (2013). Eprint arXiv:1107.5849
  7. 7.
    D. Gillies, Philosophical Theories of Probability (Routledge, New York, 2000)Google Scholar
  8. 8.
    A. Eagle (ed.), Philosophy of Probability: Contemporary Readings (Routledge, 2011)Google Scholar
  9. 9.
    B. de Finetti, Fundamenta Mathematicae 17, 298 (1931)Google Scholar
  10. 10.
    F.P. Ramsey, The Foundations of Mathemaics and Other Logical Essays, ed. by R.B. Braithwaite (Routledge and Kegan Paul, 1931), pp. 156–198. Reprinted in [8]Google Scholar
  11. 11.
    R. Jeffrey, Subjective Probability: The Real Thing (Cambridge University Press, New York, 2004)CrossRefGoogle Scholar
  12. 12.
    C. Howson, P. Urbach, Scientific Reasoning: The Bayesian Approach, 3rd edn. (Open Court, 2005)Google Scholar
  13. 13.
    D. Lewis, Studies in Inductive Logic and Probability, ed. by R.C. Jeffrey (University of California Press, 1980). Reprinted with postscript in [8]Google Scholar
  14. 14.
    C.M. Caves, C.A. Fuchs, R. Schack, Phys. Rev. A 65, 022305 (2002)CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    C.A. Fuchs, J. Mod. Opt. 50, 987 (2003)CrossRefADSzbMATHGoogle Scholar
  16. 16.
    C.A. Fuchs, Phy. Can. 66, 77 (2010). Eprint arXiv:1003.5182
  17. 17.
    C.A. Fuchs, QBism, perimeter quantum Bayesianism (2010). Eprint arXiv:1003.5209
  18. 18.
    D. Deutsch, Proc. R. Soc. Lond. A 455, 3129 (1999). Eprint arXiv:quant-ph/9906015
  19. 19.
    D. Wallace, Stud. Hist. Philos. Mod. Phys. 38, 311 (2007). Eprint arXiv:quant-ph/0312157
  20. 20.
    D. Wallace, Many Worlds? Everett, Quantum Theory, and Reality, ed. by S. Saunders, J. Barrett, A. Kent, D. Wallace (Oxford University Press, 2010). Eprint arXiv:0906.2718
  21. 21.
    D. Wallace, The Emergent Multiverse, (Oxford University Press, 2012)Google Scholar
  22. 22.
    I. Pitowsky, Stud. Hist. Philos. Mod. Phys. 34, 395 (2003). Eprint arXiv:quant-ph/0208121
  23. 23.
    B. de Finetti, Philosophical Lectures on Probability. Synthese Library vol. 340 (Springer, 2008)Google Scholar
  24. 24.
    E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, 2003)Google Scholar
  25. 25.
    D. Kahneman, Thinking, Fast and Slow (Penguin, 2012)Google Scholar
  26. 26.
    C.A.B. Smith, J. R. Stat. Soc. B Met. 23, 1 (1961)ADSzbMATHGoogle Scholar
  27. 27.
    L.J. Savage, The Foundations of Statistics, 2nd edn. (Dover, 1972)Google Scholar
  28. 28.
    H. Greaves, W. Myrvold, Many Worlds?: Everett, Quantum Theory, and Reality, ed. by S. Saunders, J. Barrett, A. Kent, D. Wallace (Oxford University Press, 2010), chap. 9, pp. 264–306Google Scholar
  29. 29.
    J. Barrett, Phys. Rev. A 75, 032304 (2007). Eprint arXiv:quant-ph/0508211
  30. 30.
    S. Kochen, E.P. Specker, J. Math. Mech. 17, 59 (1967)zbMATHMathSciNetGoogle Scholar
  31. 31.
    W.H. Zurek, Phys. Rev. Lett. 90, 120404 (2003). Eprint arXiv:quant-ph/0211037
  32. 32.
    W.H. Zurek, Phys. Rev. A 71, 052105 (2005). Eprint arXiv:quant-ph/0405161
  33. 33.
    FQXi comment thread for this essay (2013).
  34. 34.
    A.M. Gleason, J. Math. Mech. 6, 885 (1957)zbMATHMathSciNetGoogle Scholar
  35. 35.
    J.S. Bell, Rev. Mod. Phys. 38, 447 (1966)CrossRefADSzbMATHGoogle Scholar
  36. 36.
    A. Chakravartty, The Stanford Encyclopedia of Philosophy, ed. by E.N. Zalta (2014), Spring 2014 edn. URL:
  37. 37.
    J. Ladyman, Understanding Philosophy of Science (Routledge, 2002)Google Scholar

Copyright information

© M.S. Leifer 2015

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsNorth WaterlooCanada

Personalised recommendations