Abstract

It is argued that while classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering rst the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebu of the Copenhagen interpretation is shown to be adequate to this challenge. In the EPR experiment of Aspect, and the violation of the Bell inequalities, the matter is more delicate: it is not directly the last axiom, but rather the relevance of Kolmogorovian independence that is at issue. It is explained how two events with space-like separation cannot be independent in Kolmogorov's sense, even in the presence of hidden variables. The escape route of supposing these variables to be nonlocal, with a heavy metaphysical ballast of holism, which however is cosmically censored to prevent superluminal information transfer, has all the trappings of an ad hoc makeshift. The adoption of quantum mechanical probability, which does not obey the rules of Kolmogorov, but does survive empirical testing in terms of relative frequencies of events, is more economical. The solution is simple: correlations obey the rules of quantum mechanics and probability is a theory-laden concept that is tested by, but not de ned in terms of, the relative frequency of selected classes of events.