Conditionals, Probability and Bell’s Theorem

Abstract

A new version of Bell’s theorem is proved which shows the inconsistency of locality, realism and quantum theory. By using Mermin s technique of randomising over the settings on the measurement apparatus, the proof avoids Stapp’s assumption that probabiIities can be equated with relative frequencies. It also avoids the assumption, which Bell and Signer make, that there is a phase-space distribution for which the probabi1ities of quantum theory are marginals. Instead it derives the latter assumption from realism, quantum theory, and standard probability theory. Care is taken throughout to make clear which conditionals are being used and to relate them to the relevant probabi1ities.