Authors
Stephan Hartmann
Ludwig Maximilians Universität, München
Abstract
Quantum mechanical entangled configurations of particles that do not satisfy Bell’s inequalities, or equivalently, do not have a joint probability distribution, are familiar in the foundational literature of quantum mechanics. Nonexistence of a joint probability measure for the correlations predicted by quantum mechanics is itself equivalent to the nonexistence of local hidden variables that account for the correlations (for a proof of this equivalence, see Suppes and Zanotti, 1981). From a philosophical standpoint it is natural to ask what sort of concept can be used to provide a “joint” analysis of such quantum correlations. In other areas of application of probability, similar but different problems arise. A typical example is the introduction of upper and lower probabilities in the theory of belief. A person may feel uncomfortable assigning a precise probability to the occurrence of rain tomorrow, but feel comfortable saying the probability should be greater than ½ and less than ⅞. Rather extensive statistical developments have occurred for this framework. A thorough treatment can be found in Walley (1991) and an earlier measurement-oriented development in Suppes (1974). It is important to note that this focus on beliefs, or related Bayesian ideas, is not concerned, as we are here, with the nonexistence of joint probability distributions. Yet earlier work with no relation to quantum mechanics, but focused on conditions for existence has been published by many people. For some of our own work on this topic, see Suppes and Zanotti (1989). Still, this earlier work naturally suggested the question of whether or not upper and lower measures could be used in quantum mechanics, as a generalization of..
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References found in this work BETA

Toward a Quantum Theory of Observation.H. D. Zeh - 1973 - Foundations of Physics 3 (1):109-116.
Probability Concepts in Quantum Mechanics.Patrick Suppes - 1961 - Philosophy of Science 28 (4):378-389.

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Citations of this work BETA

Imprecise Probabilities.Seamus Bradley - 2019 - Stanford Encyclopedia of Philosophy.
Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 115-142.
Yes, More Decoherence: A Reply to Critics.Elise M. Crull - 2017 - Foundations of Physics 47 (11):1428-1463.

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