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Foundations of Physics

, Volume 47, Issue 2, pp 294–315 | Cite as

On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

  • Benjamin H. Feintzeig
  • Samuel C. Fletcher
Article

Abstract

One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (Br J Philos Sci 66(4): 905–927, 2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.

Keywords

Quantum mechanics Hidden variables Non-Kolmogorovian probability 

Notes

Acknowledgements

SCF would like to thank audiences at Budapest, Tübingen, and Saig, Germany, especially Guido Bacciagalupi and Fay Dowker, for their comments. BHF would like to thank audiences at the Perimeter Institute and Chapman University. Both authors acknowledge the support of National Science Foundation Graduate Research Fellowships. In addition, the authors would like to thank an anonymous referee for helpful comments.

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Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of WashingtonSeattleUSA
  2. 2.Department of PhilosophyUniversity of MinnesotaMinneapolisUSA
  3. 3.Munich Center for Mathematical PhilosophyLudwig Maximilian UniversityMunichGermany

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