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Counterfactuality, Definiteness, and Bell's Theorem

Jonte R. Hance

Published Sep 14, 2019• 0 citations
OpenAlex

Abstract

Counterfactual definiteness is shown from analysis of Bell's Theorem to be the factor separating classical from quantum theories. From this, it is shown that, by replacing it with 'counterfactual semi-definiteness', the definiteness of possible options available after a measurement event, some apt analysis of possible states can be kept. While not as solid as that forbidden by the EPR paradox and Bell's Theorem, it allows us to start investigating the physical implementation of possible states in a way that has rarely been done. Working from this, the idea of counterfactuality, and interaction between counterfactual possibilities, is developed further.

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•Dec 26, 2025•1 citation
Counterfactual definiteness is shown from analysis of Bell's Theorem to be the factor separating classical from quantum theories. From this, it is shown that, by replacing it with 'counterfactual semi-definiteness', the definiteness of possible options available after a measurement event, some apt analysis of possible states can be kept. While not as solid as that forbidden by the EPR paradox and Bell's Theorem, it allows us to start investigating the physical implementation of possible states in a way that has rarely been done. Working from this, the idea of counterfactuality, and interaction between counterfactual possibilities, is developed further.
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
Abstract We show that the ability to consider counterfactual situations is a necessary assumption of Bell’s theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices be counterfactually restricted, rather than the full removal of counterfactual definiteness. We illustrate how the counterfactual definiteness assumption formally arises from the statistical independence assumption. Counterfactual restriction therefore provides a way to interpret statistical independence violation different to what is typically assumed (i.e. that statistical independence violation means either retrocausality or superdeterminism). We tie counterfactual restriction to contextuality, and show the similarities to that approach.
Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that not only is commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness. However, his particular choice of variables reduces the generality of his theory, as well as the physics of all Bell-type theories, so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.
Blaylock argues that the derivation of Bell’s inequality requires a hidden assumption, counterfactual definiteness, of which Bell was unaware. A careful analysis of Bell’s argument shows that Bell presupposes only locality and the predictions of standard quantum mechanics. Counterfactual definiteness, insofar as it is required, is derived in the course of the argument rather than presumed. Bell’s theorem has no direct bearing on the many worlds interpretation not because that interpretation denies counterfactual definiteness but because it does not recover the predictions of standard quantum mechanics.
Bell's theorem states that no description of a Bell experiment can be simultaneously local, realistic in the sense of counterfactual definiteness, and free of conspiracy between settings and hidden state. The recent generation of experiments has confirmed the predicted violation of the CHSH inequality, so one of the assumptions must be abandoned. Which one, and how one reconstructs a coherent worldview after doing so, is a question on which many authors disagree. This paper is written by three such authors. All three reject both counterfactual definiteness and conspiratorial violation of statistical independence of setting choices and state. After a joint exposition of the classical half of Bell's theorem in the language of Pearl-style causal graphs, a joint summary of the loophole-free experiments, and a joint survey of the recent literature, each author states where they have presently arrived. Gill accepts irreducible and non-local quantum randomness and finds the choice between locality and realism a false dichotomy. In his later works, Bell derives counterfactual definiteness from classical local causality, and that is what has to go. The metaphysical concepts "realism", "locality", "causality" need to be reconsidered. Helland reconstructs the Hilbert-space formalism from a theory of accessible variables, and from this theory he concludes that every observer must be limited in a specific sense. Jongejan proposes a geometric hidden-variable construction in which the degree of violation of the CHSH inequality depends on the number of dimensions of space, Tsirelson's bound corresponding to three dimensions. The authors conclude with a discussion.
This essay proposes a philosophical reading of Bell’s theorem as an ontological constraint rather than as a technical curiosity of quantum physics. Starting from the EPR argument (Einstein, Podolsky and Rosen), the demand for “completeness” is interpreted as the defence of an inventory ontology: a conception of the real as a set of pre-inscribed properties, locally attributable and defined for measurement counterfactuals. It then shows how Bell formalises this ontology, and how the CHSH inequality (Clauser–Horne–Shimony–Holt) functions as a symbol-operator: a quantitative device that renders testable the compatibility between that ontological grammar and empirically inscribable patterns of correlation. The analysis of experimental practices shifts the focus from “confirmation” to the production of public, repeatable and auditable marks, whose material status makes it possible to exclude entire classes of descriptions of the real. Against the dominant reading in terms of “non-locality” as a mechanism, it is argued that the central consequence is the failure of classical separability and the consequent need for an ontology of material non-separability. The essay concludes with a reformulation of the status of scientific truth after Bell—as material correspondence under constraint—and with a minimal map of interpretations according to their ontological costs.