Abstract
We prove the existence of hidden variables, or, what we call generalized common causes, for finite sequences of pairwise correlated random variables that do not have a joint probability distribution. The hidden variables constructed have upper probability distributions that are nonmonotonic. The theorem applies directly to quantum mechanical correlations that do not satisfy the Bell inequalities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Walley,Statistical Reasoning with Imprecise Probabilities (Chapman, 1991).
P. Suppes and M. Zanotti,Synthese 36, 427 (1977).
P. Suppes and M. Zanotti,Erkenntnis 31, 323 (1989).
P. Suppes and M. Zanotti, inStudies in the Foundations of Quantum Mechanics, P. Suppes, ed. (1980), p. 173.
P. Suppes and M. Zanotti,Synthese 48, 191 (1981).
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969).
Author information
Authors and Affiliations
Additional information
It is a pleasure to dedicate this paper to Karl Popper in celebration of this 90th birthday. The first author has known Popper for more than three decades, and has profited much from their discussion of many different topics, among which have been the foundations of probability and the foundations of quantum mechanics, both central to the present paper.
Rights and permissions
About this article
Cite this article
Suppes, P., Zanotti, M. Existence of hidden variables having only upper probabilities. Found Phys 21, 1479–1499 (1991). https://doi.org/10.1007/BF01889653
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889653