Time series and the meaning of quantum non-locality

TL;DR

This paper clarifies the meaning of quantum non-locality through a time series approach, showing how Bell's inequalities relate to factual and counter-factual data, and explaining why faster-than-light signaling remains impossible.

Contribution

It introduces a novel time series framework that defines quantum non-locality without relying on traditional notions of Locality and Realism, providing a clearer interpretation.

Findings

Bell's inequalities derived from time series properties.

Violation of Bell's inequalities indicates differences in outcome series when settings change.

Factual and counter-factual data can always be embedded in a classical framework.

Abstract

Quantum non-locality has become a popular term. Yet, its precise meaning, and even its mere existence, is the subject of controversies. The main cause of the controversies is the never ending discussion on the appropriate definitions of Locality and Realism in the derivation of Bell's inequalities. On the other hand, Louis Sica derived Bell's inequalities from the hypothesis that time series of outcomes observed in one station do not change if the setting in the other (distant) station is changed. The derivation is based on arithmetical properties of time series only; it does not involve the definitions of Locality, Realism and probabilities, and is valid for series of any length. An important consequence is that violation of Bell's inequalities implies the series recorded (at the same time) in one station to be different if the setting in the other station is changed. This result gives precise meaning to the idea of quantum non-locality, and also makes evident why using it for faster than light signaling is impossible (because the difference is between factual and counter-factual series). Finally, it is demonstrated that series of outcomes, even if they violate Bell's inequalities, can be always embedded in a set of factual and counter-factual data that does hold to Bell's inequalities. Loosely speaking, the factual world may be quantum or not, but the union of factual and counter-factual worlds is always classical.