Bell's theorem in an indeterministic universe

A logical analysis of Stapp's non-locality theorem

“…The object of the analysis performed in the present work is the final result of an investigation pursued by Stapp during many years [12]- [18] with the aim of proving inconsistency between Quantum Mechanics and locality without the need of attributing values to unmeasured observables. The earlier proposals [19]- [21] were explicitly based on counterfactual reasonings; they received severe criticisms [22], [23] which questioned the validity of the proof just on the ground of counterfactuals theory [24]. Stapp disputed [21], [25] these criticisms, but also expressed dissatisfaction with proofs based on counterfactual concepts: "[...] these theories, though useful in other ways, do not provide a completely adequate foundation for the study of the deep physical question of locality: basic physical conclusions should not rest on arbitrary conventions [which infiltrate counterfactuals theory]" [25].…”

“…The earlier proposals [19]- [21] were explicitly based on counterfactual reasonings; they received severe criticisms [22], [23] which questioned the validity of the proof just on the ground of counterfactuals theory [24]. Stapp disputed [21], [25] these criticisms, but also expressed dissatisfaction with proofs based on counterfactual concepts: "[...] these theories, though useful in other ways, do not provide a completely adequate foundation for the study of the deep physical question of locality: basic physical conclusions should not rest on arbitrary conventions [which infiltrate counterfactuals theory]" [25]. Then he presented improvements of the proof, with the aim of making the argument valid without the need of rules of counterfactuals theory [26], [27], [16], [17], until the final version [6] about which he states: "my 2004 proof, although retaining some of the trappings and language of counterfactual argumentation, is based on a substantially different foundation.…”

Time-Symmetrized Quantum Theory

“…There are many discussions of counterfactuals in quantum theory, mostly in the context of EPR-Bell type experiments. Some of the examples are Skyrms (1982), Peres (1993), Mermin (1989) (which, however, does not use the word counterfactual), and Bedford and Stapp (1995) who even present an analysis of a Bell-type argument in the formal language of the Lewis theory of counterfactuals. The common situation is that a composite system is described at a certain time by some entangled state and then an array of incompatible measurements on this system at a later time is considered.…”

Counterfactuals and Non-locality of Quantum Mechanics: The Bedford–Stapp Version of the GHZ Theorem

“…3 And there is a third version of Stapp's theorem, dealing with the socalled GHZ example. This argument was originally formulated in Stapp (1991) and then refined and formalized in Bedford and Stapp (1995) with explicit reference to the Lewis calculus of counterfactuals.…”

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In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals.

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