Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin-1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; (...) through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables are found, all the problems of quantum field theory and of quantum gravity might melt away. (shrink)

Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the (...) observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's newtransactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theoremreinforces arguments in favor of hidden variables. (shrink)

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A i 〉, 〈B〉, 〈A i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation (...) 〈A 1 A 2〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality. (shrink)

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.