The Bell-Kochen-Specker Theorem

Abstract

Meyer, Kent and Clifton (MKC) claim to have nullified the Bell-Kochen-Specker (Bell-KS) theorem. It is true that they invalidate KS's account of the theorem's physical implications. However, they do not invalidate Bell's point, that quantum mechanics is inconsistent with the classical assumption, that a measurement tells us about a property previously possessed by the system. This failure of classical ideas about measurement is, perhaps, the single most important implication of quantum mechanics. In a conventional colouring there are some remaining patches of white. MKC fill in these patches, but only at the price of introducing patches where the colouring becomes ''pathologically'' discontinuous. The discontinuities mean that the colours in these patches are empirically unknowable. We prove a general theorem which shows that their extent is at least as great as the patches of white in a conventional approach. The theorem applies, not only to the MKC colourings, but also to any other such attempt to circumvent the Bell-KS theorem (Pitowsky's colourings, for example). We go on to discuss the implications. MKC do not nullify the Bell-KS theorem. They do, however, show that we did not, hitherto, properly understand the theorem. For that reason their results (and Pitowsky's earlier results) are of major importance.