Random Variables Recorded under Mutually Exclusive Conditions: Contextuality-by-Default

TL;DR

This paper develops a general framework for analyzing how random variables depend on deterministic conditions, especially when recorded under mutually exclusive inputs, with applications in quantum physics and other sciences.

Contribution

It introduces principles for analyzing stochastically unrelated variables under different contexts, expanding the understanding of dependence in systems with mutually exclusive conditions.

Findings

Framework applies to quantum entanglement experiments.

Provides a method to characterize dependence constraints via couplings.

Applicable across physical, biological, and behavioral sciences.

Abstract

We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered stochastically unrelated, possessing no joint distribution. An input that does not directly influence an output creates a context for the latter. Any constraint imposed on the dependence of random outputs on inputs can be characterized by considering all possible couplings (joint distributions) imposed on stochastically unrelated outputs. The target application of these principles is a quantum mechanical system of entangled particles, with directions of spin measurements chosen for each particle being inputs and the spins recorded outputs. The sphere of applicability, however, spans systems across physical, biological, and behavioral sciences.