  Bell's theorem is a statement by which averages obtained from specific types
of statistical distributions must conform to a family of inequalities. These
models, in accordance with the EPR argument, provide for the simultaneous
existence of quantum mechanically incompatible quantities. We first recall
several contradictions arising between the assumption of a joint distribution
for incompatible observables and the probability structure of
quantum-mechanics, and conclude that Bell's theorem is not expected to be
relevant to quantum phenomena described by non-commuting observables,
irrespective of the issue of locality. Then, we try to disentangle the locality
issue from the existence of joint distributions by introducing two models
accounting for the EPR correlations but denying the existence of joint
distributions. We will see that these models do not need to resort explicitly
to non-locality: the first model relies on conservation laws for ensembles, and
the second model on an equivalence class by which different configurations lead
to the same physical predictions.
