Bell's Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality. Invariant set theory is a finite theory of quantum physics which violates the Bell inequality exactly as does quantum theory: in it neither Free Choice nor Local Causality hold, consistent with Bell's Theorem. However, within the proposed theory, the mathematical expressions of both Free Choice and Local Causality involve states which, for number-theoretic reasons, cannot be ontic (cannot lie on the theory's fractal-like invariant set $I_U$ in state space). Weaker versions of Free Choice and Local Causality are proposed involving only the theory's ontic states. Conventional hidden-variable theories satisfying only these weaker definitions still obey the Bell inequality. However, invariant set theory, which violates the Bell inequality, satisfies these weaker definitions. It is argued that the weaker definitions are consistent with the physical meaning behind free choice and local causality as defined in space-time, and hence that Free Choice and Local Causality are physically too strong. It is concluded that the experimental violation of the Bell inequality may have less to do with free choice or local causality \emph{per se}, and more to do with the presence of a holistic but causal state-space geometry onto which quantum ontic states are constrained.Bell's Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality. Invariant set theory is a finite theory of quantum physics which violates the Bell inequality exactly as does quantum theory: in it neither Free Choice nor Local Causality hold, consistent with Bell's Theorem. However, within the proposed theory, the mathematical expressions of both Free Choice and Local Causality involve states which, for number-theoretic reasons, cannot be ontic (cannot lie on the theory's fractal-like invariant set $I_U$ in state space). Weaker versions of Free Choice and Local Causality are proposed involving only the theory's ontic states. Conventional hidden-variable theories satisfying only these weaker definitions still obey the Bell inequality. However, invariant set theory, which violates the Bell inequality, satisfies these weaker definitions. It is argued that the weaker definitions are consistent with the physical meaning behind free choice and local causality as defined in space-time, and hence that Free Choice and Local Causality are physically too strong. It is concluded that the experimental violation of the Bell inequality may have less to do with free choice or local causality \emph{per se}, and more to do with the presence of a holistic but causal state-space geometry onto which quantum ontic states are constrained.

arXiv:1903.10537Mar 25, 20192 citations

Local Causality: A Historical Introduction

Gábor Hofer‐Szabó, Péter Vecsernyés

SpringerBriefs in philosophyJan 1, 20180 citations

Re-thinking local causality

Simon Friederich

SyntheseOct 6, 20142 citations

Context-independent mapping and free choice are equivalent

Ehtibar N. Dzhafarov

Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in an HVM means that the results of a measurement do not depend on settings for other measurements. If the measurements are spacelike separated, this assumption is known as local causality. Both free choice and CI mapping assumptions are considered necessary for derivation of the Bell-type criteria of contextuality/nonlocality. It is known, however, for a variety of special cases, that the two assumptions are not logically independent. We show here, in complete generality, for any system of random variables with or without disturbance/signaling, that an HVM that postulates CI mapping is equivalent to an HVM that postulates free choice. If one denies the possibility that a given empirical scenario can be described by an HVM in which measurements depend on other measurements' settings, free choice violations should be denied too, and vice versa. KEYWORDS: Contextuality; context-independent mapping; free choice; local causality; nonlocality.Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in an HVM means that the results of a measurement do not depend on settings for other measurements. If the measurements are spacelike separated, this assumption is known as local causality. Both free choice and CI mapping assumptions are considered necessary for derivation of the Bell-type criteria of contextuality/nonlocality. It is known, however, for a variety of special cases, that the two assumptions are not logically independent. We show here, in complete generality, for any system of random variables with or without disturbance/signaling, that an HVM that postulates CI mapping is equivalent to an HVM that postulates free choice. If one denies the possibility that a given empirical scenario can be described by an HVM in which measurements depend on other measurements' settings, free choice violations should be denied too, and vice versa. KEYWORDS: Contextuality; context-independent mapping; free choice; local causality; nonlocality.

arXiv:2110.15910Oct 29, 20211 citation

I_U

in state space). Weaker versions of Free Choice and Local Causality are proposed involving only the theory's ontic states. Conventional hidden-variable theories satisfying only these weaker definitions still obey the Bell inequality. However, invariant set theory, which violates the Bell inequality, satisfies these weaker definitions. It is argued that the weaker definitions are consistent with the physical meaning behind free choice and local causality as defined in space-time, and hence that Free Choice and Local Causality are physically too strong. It is concluded that the experimental violation of the Bell inequality may have less to do with free choice or local causality \emph{per se}, and more to do with the presence of a holistic but causal state-space geometry onto which quantum ontic states are constrained.