A combination of methodological considerations and propositions about the causal structure of spacetime provides a reply to Fine's criticisms of the "factorizability requirement" used in several versions of Bell's theorem. His proposal of "action in harmony" is criticized. Experimental tests are proposed for both the "synchronization models" and the "prism models", which Fine has invented as loopholes to Bell's theorem. A theorem of Suppes and Zanotti which purports to show the impossibility of hidden variables is criticized. One of their crucial (...) premisses seems to be justifiable only if one accepts a Parmenidean metaphysics. (shrink)

A general algorithm is given for determining whether or not a given set of pair distributions allows for the construction of all the members of a specified set of higher-order distributions which return the given pair distributions as marginals. This mathematical question underlies studies of quantum correlation experiments such as those of Bell or of Clauser and Horne, or their higher-spin generalizations. The algorithm permits the analysis of rather intricate versions of such problems, in a form readily adaptable to the (...) computer. The general procedure is illustrated by simple derivations of the results of Mermin and Schwarz for the symmetric spin-1 and spin-3/2 Einstein-Podolsky-Rosen problems. It is also used to extend those results to the spin-2 and spin-5/2 cases, providing further evidence that the range of strange quantum theoretic correlations does not diminish with increasing s. The algorithm is also illustrated by giving an alternative derivation of some recent results on the necessity and sufficiency of the Clauser-Horne conditions. The mathematical formulation of the algorithm is given in general terms without specific reference to the quantum theoretic applications. (shrink)

A method is given to determine whether or not the distribution functions describing the two spin measurements in the spin-s Einstein-Podolsky-Rosen experiment are compatible with the existence of distributions describing three spin measurements (not all of which can actually be performed). When applied to the spin-1/2 case the method gives the results of Wigner, or of Clauser, Holt, Horne, and Shimony, depending on whether or not the two-spin distributions are assumed to have the forms given by the quantum theory. Generalizations (...) of the conditions of Wigner or of Clauser et al. to the spin-1 case are explicitly calculated. The spin-3/2 case is examined in some simple geometries to show that an apparently monotonic trend toward local realism as s increases from1/2 to1 is, in fact, violated when s increases from1 to3/2. The analysis is based on a novel representation of the modulus squared of a rotation matrix element. The structure of that matrix element responsible for the restoration of local realism in the classical (large s) limit is identified, but a rigorous treatment of the classical limit is not attempted. The higher-spin results are significantly stronger than those given by Mermin's spin-s Bell inequality. (shrink)