In the contemporary discussion of hidden variable interpretations of quantum mechanics, much attention has been paid to the “no hidden variable” proof contained in an important paper of Kochen and Specker. It is a little noticed fact that Bell published a proof of the same result the preceding year, in his well-known 1966 article, where it is modestly described as a corollary to Gleason's theorem. We want to bring out the great simplicity of Bell's formulation of this result and to (...) show how it can be extended in certain respects. (shrink)

The work of Gleason and of Kochen and Specker has been thought to refute a naïve realist approach to quantum mechanics. The argument of this paper substantially bears out this conclusion. The assumptions required by their work are not arbitrary, but have sound theoretical justification. Moreover, if they are false, there seems no reason why their falsity should not be demonstrable in some sufficiently ingenious experiment. Suitably interpreted, the work of Bell and Wigner may be seen to yield independent arguments (...) for the falsity of naïve realistic approach to quantum mechanics. Quantum mechanics is no more like classical statistical mechanics than its creators thought it was. (shrink)

The debate between Glymour and Fine hinges in part on a comparison of the width of the incoming wave packet in momentum space with the angles intercepted by the detectors in the Cross-Ramsey experiment. As Fine argues, it follows from the quantum formalism that the initial dispersion will be conserved in Compton scattering, and he allows that the Sum Rule is constrained by the statistical results of quantum mechanics. The Sum Rule may fail, but it will not fail in any (...) way that violates quantum mechanics. Thus most of the time the individual momentum value does not change more than the width of the initial wave packet: usually the value of Qγe at t must equal the value of Qγ at t′ plus the value of Qe at t′ ± Δp/2, where Δp represents the dispersion in momentum for the initial gamma ray. Thus in order to refute Fine's thesis, the detectors must discriminate finely enough to pick out changeovers of individual values within Δp. (shrink)

Simon Kochen and Ernst Specker's well-known argument against hidden variable theories for quantum mechanics is also an argument against the possibility of quantum systems having, simultaneously, precise values for all of the dynamical quantities associated with such systems. Devices for defeating the argument were in the literature even before its publication, but recently Arthur Fine has raised a new difficulty. Fine points out that Kochen and Specker's argument requires the following principles:Sum Rule: At all times, in all states, the value (...) of the quantity with operator A + B is the sum of the values of the quantity with operator A and the quantity with operator B, provided A, B commute.Product Rule: At all times, in all states, the value of the quantity with operator AB is the product of the values of the quantities with operators A and B, provided A, B commute. (shrink)