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Born Rule and its Interpretation

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Compendium of Quantum Physics

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.

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Primary Literature

  1. M. Born: Quantenmechanik der Stoßvorgänge. Z. Phys. 38, 803–827 (1926).

    Article  ADS  Google Scholar 

  2. P. Dirac: The physical interpretation of the quantum dynamics. Proc. R. Soc. Lond. A113, 621–641 (1926).

    ADS  MATH  Google Scholar 

  3. A. Einstein & M. Born: Briefwechsel 1916–1955 (Langen Müller, München 2005).

    MATH  Google Scholar 

  4. W. Heisenberg: Physics and Philosophy: The Revolution in Modern Science. (Allen & Unwin, London 1958).

    Google Scholar 

  5. P. Jordan: Über quantenmechanische Darstellung von Quantensprügen. Z. Phys. 40, 661–666 (1927).

    Article  ADS  Google Scholar 

  6. P. Jordan: Über eine neue Begründung der Quantenmechanik. Z. Phys. 40, 809–838 (1927).

    Article  ADS  Google Scholar 

  7. J. von Neumann: Mathematische Grundlagen der Quantenmechanik (Springer, Berlin 1932). English translation: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Berlin 1955).

    MATH  Google Scholar 

  8. W. Pauli: Über Gasentartung und Paramagnetismus. Z. Phys. 41, 81–102 (1927).

    Article  ADS  Google Scholar 

Secondary Literature

  1. D.J. Baker: Measurement outcomes and probability in Everettian quantum mechanics. Stud. Hist. Philos. Mod. Phys. 38, 153–169 (2007).

    Article  MathSciNet  Google Scholar 

  2. 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).

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Cassinello & J.L. Sanchez-Gomez: On the probabilistic postulate of quantum mechanics. Found. Phys. 26, 1357–1374 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  4. C. Caves & R. Schack: Properties of the frequency operator do not imply the quantum probability postuate. Ann. Phys. (N.Y.) 315, 123–146 (2005).

    Article  ADS  Google Scholar 

  5. D. Deutsch: Quantum theory of probability and decisions. Proc. R. Soc. Lond. A455, 3129– 3137 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  6. E. Farhi, J. Goldstone & S. Gutmann: How probability arises in quantum mechanics. Ann. Phys. (N.Y.) 192, 368–382 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  7. T.L. Fine: Theories of Probability (Academic, New York, 1978).

    Google Scholar 

  8. D. Finkelstein: The logic of quantum physics. Trans. N. Y. Acad. Sci. 25, 621–637 (1965).

    Article  MathSciNet  Google Scholar 

  9. D. Gillies: Philosophical Theories of Probability (Cambridge University Press, Cambridge 2000).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  12. 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).

    MATH  Google Scholar 

  13. G.K. Pedersen: Analysis Now (Springer, New York 1989).

    Book  Google Scholar 

  14. J. von Plato: Creating Modern Probability (Cambridge University Press, Cambridge, 1994).

    Book  Google Scholar 

  15. S. Saunders: Derivation of the Born rule from operational assumptions. Proc. R. Soc. Lond. A460, 1771–1788 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  16. E. Scheibe: The Logical Analysis of Quantum Mechanics (Pergamon Press, Oxford 1973).

    Google Scholar 

  17. M. Schlosshauer & A. Fine: On Zureks derivation of the Born rule. Found. Phys. 35, 197–213 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  18. D. Wallace: Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation. Stud. Hist. Philos. Mod. Phys. 34 (2003), 415–438.

    Article  MathSciNet  Google Scholar 

  19. W.H. Zurek: Probabilities from entanglement, Born's rule p k = |Ψk#x01C0;2 from envariance, Phys. Rev. A71, 052105 (2005).

    Article  ADS  Google Scholar 

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Landsman, N.P. (2009). Born Rule and its Interpretation. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_20

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  • DOI: https://doi.org/10.1007/978-3-540-70626-7_20

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