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Foundations of Physics

, Volume 35, Issue 4, pp 627–668 | Cite as

Facts, Values and Quanta

  • D. M. ApplebyEmail author
Article

Abstract

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.

Keywords

quantum mechanics 

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References

  1. 1.
    Caves, C.M., Fuchs, C.A., Schack, R. 2002Quantum probabilities as Bayesian probabilitiesPhys. Rev. A65022305CrossRefGoogle Scholar
  2. 2.
    Caves, C.M., Fuchs, C.A., Schack, R. 2002Unknown quantum states: the quantum de Finetti representationJ.Math.Phys.434537Google Scholar
  3. 3.
    Caves, C.M., Fuchs, C.A., Schack, R. 2002Conditions for compatibility of quantum-state assignmentsPhys. Rev. A66062111CrossRefGoogle Scholar
  4. 4.
    C. A.Fuchs Notes on a Paulian Idea. e-print quant-ph/0105039.Google Scholar
  5. 5.
    Fuchs C.A., Quantum mechanics as quantum information (and only a little more). e-print quant-ph/0205039.Google Scholar
  6. 6.
    Cushing, J.T. 1994Quantum Mechanics: Historical Contingency and the Copenhagen HegemonyThe University of Chicago PressChicagoGoogle Scholar
  7. 7.
    Editorial Comment, Rev. Mod. Phys. 42: 357 (1970).Google Scholar
  8. 8.
    Ballentine, L.E. 1970The Statistical interpretation of quantum mechanicsRev. Mod. Phys.42358Google Scholar
  9. 9.
    Bell, J.S. 1987Speakable and Unspeakable in Quantum MechanicsCambridge University PressCambridgeGoogle Scholar
  10. 10.
    Hardy L., Quantum theory from five reasonable axioms. e-print quant-ph/0101012.Google Scholar
  11. 11.
    Hardy, L. 2002Why quantum theory?. Proceedings of the NATO Advanced Research Workshop on ModalityButterfield, J.Placek, T. eds. Probability and Bell’s TheoremIOS PressAmsterdame-print quant-ph/0111068.Google Scholar
  12. 12.
    Pitowsky, I. 2003Betting on the outcomes of measurements: a bayesian theory of quantum probabilityStud. Hist. Phil. Mod. Phys.34395Google Scholar
  13. 13.
    Perey F.G., Probabilities as measures of information. e-print quant-ph/0310073.Google Scholar
  14. 14.
    Valentini, A.,  et al. 2001Hidden variables, statistical mechanics and the early universe.Bricmont, J. eds. Chance in Physics: Foundations and PerspectivesSpringerBerlinGoogle Scholar
  15. 15.
    Valentini, A. 2002Signal-locality in hidden-variables theoriesPhys. Lett. A297273Google Scholar
  16. 16.
    Hacking, I. 1975The Emergence of ProbabilityCambridge University PressCambridgeGoogle Scholar
  17. 17.
    Daston, L. 1988Classical Probability in the EnlightenmentPrinceton University PressPrincetonGoogle Scholar
  18. 18.
    Poincar ’e, H. 1952Science and HypothesisDoverNew YorkEnglish translation, first published 1905.Google Scholar
  19. 19.
    Gillies, D. 2000Philosophical Theories of ProbabilityRoutledgeLondonGoogle Scholar
  20. 20.
    von Plato, J. 1994Creating Modern ProbabilityCambridge University PressCambridgeGoogle Scholar
  21. 21.
    Sklar, L. 1993Physics and ChanceCambridge University PressCambridgeGoogle Scholar
  22. 22.
    Sklar, L. eds. 2000Probability and ConfirmationGarland PublishingNew YorkGoogle Scholar
  23. 23.
    Guttman, Y.M. 1999The Concept of Probability in Statistical PhysicsCambridge UniversityCambridgeGoogle Scholar
  24. 24.
    Jeffreys, H. 1961Theory of Probability: 3rd edn.Clarendon PressOxfordGoogle Scholar
  25. 25.
    de Laplace, P. S. 1951A Philosophical Essay on ProbabilitiesDoverNewYork(trans. F. W.Truscott and F. L.Emory)French original published 1820.Google Scholar
  26. 26.
    Keynes, J.M. 1921A Treatise on ProbabilityMacmillanLondonGoogle Scholar
  27. 27.
    Jeffreys, H. 1973Scientific Inference: 3rd edn.Cambridge University PressCambridgeGoogle Scholar
  28. 28.
    Carnap, R. 1962Logical Foundations of ProbabilityUniversity of Chicago PressChicagoGoogle Scholar
  29. 29.
    Lewis, D. 1986Philosophical Papers: Vol.2Oxford University PressOxfordGoogle Scholar
  30. 30.
    Fin2 B.de Finetti, Probabilism. English Translation, Erkenntnis 31: 169 (1989). Italian original published 1931.Google Scholar
  31. 31.
    de Finetti, Fin1 B. 1975Theory of ProbabilityWileyNew York(trans. A.Mach ’i and A.Smith)Italian original published 1971.Google Scholar
  32. 32.
    Savage, L.J. 1972The Foundations of Statistics: 2nd edn.DoverNew YorkGoogle Scholar
  33. 33.
    Bernardo, J. M., Smith, A.F.M. 1994Bayesian TheoryJohn Wiley and SonsChichesterGoogle Scholar
  34. 34.
    E. T.Jaynes (ed. R. D.Rosenkrantz), Papers on Probability, Statistics and Statistical Physics (Reidel, Dordrecth, 1983).Google Scholar
  35. 35.
    Howson, C., Urbach, P. 1989Scientific Reasoning: The Bayesian ApproachOpen CourtLa SalleGoogle Scholar
  36. 36.
    Earman, J. 1992Bayes or Bust? A Critical Examination of Bayesian Confirmation TheoryMIT PressCambridge MassGoogle Scholar
  37. 37.
    Venn, J. 1962The Logic of Chance: 4th edn.ChelseaNew YorkReprint of 3rd edn., published 1888.Google Scholar
  38. 38.
    von Mises, R. 1981Probability, Statistics and TruthDoverNew YorkReprint of 2nd revised English edn., published 1957.Google Scholar
  39. 39.
    von Mises, R. 1964Mathematical Theory of Probability and StatisticsAcademic PressNew York(ed. H.Geiringer)Google Scholar
  40. 40.
    Reichenbach, H. 1971The Theory of ProbabilityUniversity of California PressBerkelelyGoogle Scholar
  41. 41.
    Popper, K.R. 1959The Logic of Scientific DiscoveryHutchinsonLondonGoogle Scholar
  42. 42.
    van Fraassen, B. C. 1980The Scientific ImageClarendon PressOxfordGoogle Scholar
  43. 43.
    Ramsey F.P., Truth and Probability” reprinted in Sklar. citeSklarB First published 1931.Google Scholar
  44. 44.
    Fisher, R. A. 1990Bennett, J. H. eds. Statistical Methods, Experimental Design, and Scientific InferenceOxford University PressOxfordGoogle Scholar
  45. 45.
    Neyman, J., Pearson, E.S. 1967Joint Statistical PapersCambridge University PressCambridgeGoogle Scholar
  46. 46.
    D.Hume (ed.L. A.Selby-Bigge, revised P. H.Nidditch), A Treatise of Human Nature: 2nd edn. (Clarendon Press, Oxford, 1978). Originally published 1739-40.Google Scholar
  47. 47.
    D.Hume (ed.L. A.Selby-Bigge, revised P. H.Nidditch), Enquiries Concerning Human Understanding and Concerning the Principles of Morals: 3rd edn. (Clarendon Press, Oxford, 1975). Originally published 1777.Google Scholar
  48. 48.
    Schilpp, P.A. 1982Albert Einstein: Philosopher Scientist: 3rd edn.Open CourtLa SalleGoogle Scholar
  49. 49.
    A. H, ’ajek 1997Redux’—Redux: fifteen arguments against finite frequentismErkenntnis45209227Google Scholar
  50. 50.
    Feller, W. 1950An Introduction to Probability Theory and its ApplicationsWileyNew YorkGoogle Scholar
  51. 51.
    Jeffrey, R.C. 1977Mises ReduxButts, E.Hintikka, J. eds. Basic Problems in Methodology and Linguistics: 5th International Congress of Logic, Methodology, and Philosophy of Science pt.,3R.ReidelDordrechtGoogle Scholar
  52. 52.
    Gillies, D.A. 1973An Objective Theory of ProbabilityMethuenLondonGoogle Scholar
  53. 53.
    Goodman, N. 1955Fact, Fiction and ForecastHarvard University PressCambridge MassGoogle Scholar
  54. 54.
    Popper, K.R. 1959The Propensity Interpretation of ProbabilityBrit. J. Phil. Sci.102542Google Scholar
  55. 55.
    Popper, K.R. 1983Realism and the Aim of ScienceHutchinsonLondonGoogle Scholar
  56. 56.
    Popper, K.R. 1990A World of PropensitiesThoemmesBristolGoogle Scholar
  57. 57.
    Wittgenstein, L. 1974Philosophical GrammarBasil BlackwellOxford(ed.Rhees R., trans.A.Kenny)Google Scholar
  58. 58.
    Wittgenstein, L. 1975Philosophical RemarksBasil BlackwellOxford(ed.Rhees R., trans.R.Hargreaves and R.White)Google Scholar
  59. 59.
    Wittgenstein, L. 1968Philosophical Investigations: 3rd edn.Basil BlackwellOxford(trans.G. E. M.Anscombe)Google Scholar
  60. 60.
    Fisher, Statistical Methods and Scientific Inference: 3rd edn. Page references to version reprinted in Fisher citeFisher.Google Scholar
  61. 61.
    Fisher R.A., The Design of Experiments: 8th edn. Page references to version reprinted in Fisher citeFisher.Google Scholar
  62. 62.
    Bohm, D., Hiley, B.J. 1993The Undivided UniverseRoutledgeLondonGoogle Scholar
  63. 63.
    Holland, P.R. 1993The Quantum Theory of MotionCambridge University PressCambridgeGoogle Scholar
  64. 64.
    Jaynes E.T., Confidence intervals vs. Bayesian intervals. in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science: W. L.Harper and Hooker C.A., eds. (Reidel, Dordrecht, 1976). Page references to version reprinted in Jaynes. citeJaynesGoogle Scholar
  65. 65.
    Born, M., Einstein, A. 1971The Born-Einstein LettersMacmillanLondon(trans.I.Born)Google Scholar
  66. 66.
    Newton, I. 1952Opticks: based on the 4th edn., 1730DoverNew YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of PhysicsQueen Mary University of LondonLondonUK

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