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Born Rule and its Interpretation

  • Nicolaas P. Landsman

The Born rule provides a link between the mathematical formalism of quantum theory and experiment, and as such is almost single-handedly responsible for practically all predictions of quantum physics. In the history of science, on a par with the ► Heisenberg uncertainty relations, the ► Born rule is often seen as a turning point where ► indeterminism entered fundamental physics. For these two reasons, its importance for the practice and philosophy of science cannot be overestimated.

Keywords

Copenhagen Interpretation Born Rule Modal Interpretation Consistent History Heisenberg Uncertainty Relation 
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.

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Primary Literature

  1. 1.
    M. Born: Quantenmechanik der Stoßvorgänge. Z. Phys. 38, 803–827 (1926).CrossRefADSGoogle Scholar
  2. 2.
    P. Dirac: The physical interpretation of the quantum dynamics. Proc. R. Soc. Lond. A113, 621–641 (1926).ADSGoogle Scholar
  3. 3.
    A. Einstein & M. Born: Briefwechsel 1916–1955 (Langen Müller, München 2005).Google Scholar
  4. 4.
    W. Heisenberg: Physics and Philosophy: The Revolution in Modern Science. (Allen & Unwin, London 1958).Google Scholar
  5. 5.
    P. Jordan: Über quantenmechanische Darstellung von Quantensprügen. Z. Phys. 40, 661–666 (1927).CrossRefADSGoogle Scholar
  6. 6.
    P. Jordan: Über eine neue Begründung der Quantenmechanik. Z. Phys. 40, 809–838 (1927).CrossRefADSGoogle Scholar
  7. 7.
    J. von Neumann: Mathematische Grundlagen der Quantenmechanik (Springer, Berlin 1932). English translation: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Berlin 1955).zbMATHGoogle Scholar
  8. 8.
    W. Pauli: Über Gasentartung und Paramagnetismus. Z. Phys. 41, 81–102 (1927).CrossRefADSGoogle Scholar

Secondary Literature

  1. 9.
    D.J. Baker: Measurement outcomes and probability in Everettian quantum mechanics. Stud. Hist. Philos. Mod. Phys. 38, 153–169 (2007).CrossRefGoogle Scholar
  2. 10.
    H. Barnum, C. M. Caves, J. Finkelstein, C. A. Fuchs, R. Schack: Quantum probability from decision theory? Proc. Roy. Soc. Lond. A456, 1175–1182 (2000).ADSMathSciNetGoogle Scholar
  3. 11.
    A. Cassinello & J.L. Sanchez-Gomez: On the probabilistic postulate of quantum mechanics. Found. Phys. 26, 1357–1374 (1996).CrossRefADSMathSciNetGoogle Scholar
  4. 12.
    C. Caves & R. Schack: Properties of the frequency operator do not imply the quantum probability postuate. Ann. Phys. (N.Y.) 315, 123–146 (2005).zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. 13.
    D. Deutsch: Quantum theory of probability and decisions. Proc. R. Soc. Lond. A455, 3129– 3137 (1999).ADSMathSciNetGoogle Scholar
  6. 14.
    E. Farhi, J. Goldstone & S. Gutmann: How probability arises in quantum mechanics. Ann. Phys. (N.Y.) 192, 368–382 (1989).zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. 15.
    T.L. Fine: Theories of Probability (Academic, New York, 1978).Google Scholar
  8. 16.
    D. Finkelstein: The logic of quantum physics. Trans. N. Y. Acad. Sci. 25, 621–637 (1965).MathSciNetGoogle Scholar
  9. 17.
    D. Gillies: Philosophical Theories of Probability (Cambridge University Press, Cambridge 2000).Google Scholar
  10. 18.
    A. Hajek: Interpretations of probability. In The Stanford Encyclopedia of Philosophy, ed. by Edward N. Zalta, http://www.science.uva.nl/seop/entries/probability-interpret/.
  11. 19.
    J.B. Hartle: Quantum mechanics of individual systems. Am. J. Phys. 36, 704–712 (1968).CrossRefADSGoogle Scholar
  12. 20.
    J. Mehra & H. Rechenberg: The Historical Development of Quantum Theory. Vol. 6: The Completion of Quantum Mechanics 1926–1941. Part 1: The Probabilistic Interpretation and the Empirical and Mathematical Foundation of Quantum Mechanics, 1926–1936 (Springer, New York 2000).Google Scholar
  13. 21.
    G.K. Pedersen: Analysis Now (Springer, New York 1989).zbMATHGoogle Scholar
  14. 22.
    J. von Plato: Creating Modern Probability (Cambridge University Press, Cambridge, 1994).CrossRefGoogle Scholar
  15. 23.
    S. Saunders: Derivation of the Born rule from operational assumptions. Proc. R. Soc. Lond. A460, 1771–1788 (2004).ADSMathSciNetGoogle Scholar
  16. 24.
    E. Scheibe: The Logical Analysis of Quantum Mechanics (Pergamon Press, Oxford 1973).Google Scholar
  17. 25.
    M. Schlosshauer & A. Fine: On Zureks derivation of the Born rule. Found. Phys. 35, 197–213 (2005).zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. 26.
    D. Wallace: Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation. Stud. Hist. Philos. Mod. Phys. 34 (2003), 415–438.CrossRefMathSciNetGoogle Scholar
  19. 27.
    W.H. Zurek: Probabilities from entanglement, Born's rule p k = |Ψk#x01C0;2 from envariance, Phys. Rev. A71, 052105 (2005).ADSMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2009

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  • Nicolaas P. Landsman

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