Bell's theorem based on a generalized EPR criterion of reality

Franck Laloë

The Bell theorem [103] can be seen in several different ways, as the EPR argument. Initially, Bell invented it as a direct logical continuation of the EPR theorem: the idea is to take the existence of the EPR elements of reality seriously, and to push it further by introducing them explicitly into the mathematics with the notation λ; one then proceeds to study all possible kinds of correlations that can be obtained from the fluctuations of one or several variables λ, making the condition of locality explicit in the mathematics (locality was already useful in the EPR theorem, but not used in equations). The reasoning develops within determinism (considered as proved by the EPR reasoning) and classical probabilities; it studies in a completely general way all kinds of correlations that can be predicted from the fluctuations of some classical common cause in the past – if one prefers, from some random choice concerning the initial state of the system. This leads to the famous inequalities. But subsequent studies have shown that the scope of the Bell theorem is not limited to determinism; for instance, the λ variables may determine the probabilities of the results of future experiments, instead of the results themselves (see Appendix B), without canceling the theorem. We postpone the discussion of the various possible generalizations to §4.2.3. For the moment, we just emphasize that the essential condition for the validity of the Bell theorem is locality: all kinds of fluctuations can be assumed, but their effect must affect physics only locally.

Henry Pierce Stapp

Dipankar Home, F. Selleri

B. Schulz

This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior to measurement. The article describes the relation between Bell's theorem and the Strong Free Will theorem of Conway and Kochen. Then, the original articles of Bell are analyzed in detail. Following an article of Faris, it is explained that Bell's work on the hidden variable question in fact describes two separate theorems. Bell's first theorem says that there can be no model for the singlet state where an outcome does not depend locally on the settings of the detector where the outcome was measured. Bell's second theorem shows that Bell's inequalities can be violated by a theory that is either not deterministic, or violates causality in the sense of relativity or the free will assumption of the experimenters. It is shown in detail where Bell implicitly makes the various locality assumptions that Nelson has shown to be necessary for deriving Bell's inequality. The article closes by relating the various assumptions needed to derive Bell's theorem with the reality criterion of EPR

Daniel Baker

The Einstein–Podolsky–Rosen (EPR) argument was originally posed as a challenge to the completeness of quantum mechanics, rather than its empirical adequacy. While subsequent developments—most notably Bell’s theorem and experimental tests of nonlocal correlations— have constrained classes of hidden-variable theories, they have not resolved the underlying on- tological question raised by EPR: whether the quantum state exhausts physical reality. In this paper, we revisit the EPR criterion of completeness from the perspective of a temporally grounded physical framework, the Temporal Inertia Framework (TIF). We argue that the orig- inal EPR dilemma rests on an implicit assumption that physical reality must be specified on spacelike hypersurfaces, an assumption shared by both EPR and Bohr. By relaxing this assump- tion and allowing physical correlations to arise from shared temporal structure rather than local spatial variables or superluminal influence, one may satisfy the EPR realism criterion without violating relativistic causality or Bell-type constraints. Quantum mechanics is thus interpreted as operationally complete but ontologically incomplete, with quantum indeterminacy emerging from dynamical interactions with a proposed underlying temporal structure.