In this paper, I want to present a family of results that may seem to add up to a new proof of the impossibility of hidden variables. In fact, I very much doubt that that’s really what really emerges, but I think the results are nonetheless interesting because they help to sharpen the discussion of Jon Jarrett’s very useful decompostion theorem, in particular, of the condition he calls locality. Jarrett (1984) and Ballentine and Jarrett (1987) have suggested that the so-called (...) condition of locality is the one that provides the conceptual link between hidden variable theories and relativity: if locality is violated, so is relativity. On the other hand, a theory may violate the condition Jarrett calls completeness without running afoul of relativity. Now I agree with Jarrett and Ballentine about completeness, but I strongly suspect that we have quite a way to go before we really understand what would be involved in a violation of locality. (shrink)

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when factorisability (...) is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed. (shrink)

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; (...) we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics. (shrink)