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International Journal of Theoretical Physics

, Volume 44, Issue 7, pp 999–1009 | Cite as

The Born Rule from a Consistency Requirement on Hidden Measurements in Complex Hilbert Space

  • Sven Aerts
Article

Abstract

We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming that the state space of a physical entity is a complex Hilbert space and introduce the principle of consistent interaction which effectively partitions the space of apparatus states. The normalized measure of the set of apparatus states that interact with a pure state giving rise to a fixed outcome is shown to be in accordance with the probability obtained using the Born rule.

Keywords

Born rule hidden measurements interactive probability model 

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References

  1. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics 27, 202–210.ADSMathSciNetCrossRefGoogle Scholar
  2. Aerts, S. (2002). Hidden measurements from contextual axiomatics. in Probing the Structure of Quantum Mechanics, D. Aerts, M. Czachor, and T. Durt, eds., World Scientific Publishers, Singapore, 149–164.Google Scholar
  3. Aerts, D., Coecke, B., and D'Hooghe, B. (1997a). A mechanistic macroscopical physical entity with a three dimensional Hilbert space quantum description. Helvetica Physica Acta 70, 793–802.MathSciNetGoogle Scholar
  4. Aerts, D., Coecke, B., Durt, T., and Valckenborgh, F. (1997b). Quantum, classical and intermediate I: a model on the poincaré sphere. Tatra Mountains Mathematical Publications 10, 225.MathSciNetGoogle Scholar
  5. Aerts, D., Coecke, B., Durt, T., and Valckenborgh, F. (1997c). Quantum, classical and intermediate II: the vanishing vector space structure. Tatra Mountains Mathematical Publications 10, 241.MathSciNetGoogle Scholar
  6. Aerts, D., Aerts, S., Durt, T., and Lévêque, O. (1999). Classical and quantum probability in the ∊-model. International Journal of Theoritical Physics 38, 407.Google Scholar
  7. Bohm, D. and Bub, J. (1966). A proposed solution of the measurement problem in quantum mechanics by a hidden variable model. Review of Modern Physics 38, 453–469.ADSMathSciNetGoogle Scholar
  8. Coecke, B. (1995). Generalization of the proof on the existence of hidden measurements to experiments with an infinite set of outcomes. Foundation of Physics Letters 8, 437–447.MathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.CLEA, Vrije Universiteit Brussel (VUB)BrusselsBelgium

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