Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)

TL;DR

This paper explores the implications of Bell's theorem, showing that violations of Bell inequalities imply fundamental unpredictability in quantum events, grounded in signal locality and relativity, regardless of determinism or indeterminism.

Contribution

It clarifies that Bell inequality violations imply unpredictability based on signal locality, independent of assumptions about locality or determinism, offering new insights into quantum foundations and historical debates.

Findings

Bell violations imply fundamental unpredictability

Signal locality is empirically testable and consistent with relativity

Deterministic models can violate locality, indeterministic models can satisfy locality

Abstract

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally \emph{unpredictable}, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr.