Abstract

Bell's theorem shows that it is not possible to give a local contextual hidden variables interpretation of quantum theory. This conclusion is based on the conflict between Bell's inequality and the predictions of quantum mechanics. A version of Bell's inequality can be derived from a mathematical condition called factorizability. The violation of Bell's inequality implies the violation of factorizability. Factorizability asserts the independence, relative to hidden variables, lambda, of probabilities of outcomes of spin measurements on correlated particle pairs in separated systems experiments. Factorizability was initially interpreted as a locality condition on the basis of the space-like separation of the particles at the time of measurement. ;Jarrett showed that factorizability is logically equivalent to the conjunction of two mathematical conditions called parameter independence and outcome independence . PI has been interpreted as a locality condition. OI has been interpreted as involving assumptions about completeness, separability, and causality, yielding interpretations of the violation of Bell's inequality involving incompleteness, nonseparability, and the rejection of causality. ;It is shown here that all these interpretations rely on a basic set of underlying assumptions concerning the nature and behavior of quantum systems: quantum systems are physical bodies with localized spatial extension; quantum systems have properties independent of observation or measurement; quantum systems exist in space-time and propagate in a spatio-temporally continuous manner through space-time; genuine statistical correlations have causal implications which entail some kind of causal connection between the physical circumstances of systems and outcomes of measurement. ;Eachinterpretation of OI arrives at its conclusion about the implications of Bell's theorem by rejecting one of these basic assumptions, while retaining the remaining assumptions. The conjunction of these assumptions amounts to the attempt to fit the behavior of quantum systems into the mathematical structure of events in the four-dimensional space-time manifold. It appears that this mathematical structure is incompatible with the mathematical structure of quantum mechanics, and this incompatibility may be responsible for the conceptual difficulties that arise in interpreting Bell's theorem