# Hidden variables, free choice, context-independence and all that

## TL;DR

This paper explores hidden variable models and their implications for understanding randomness and context in physical systems.

## Contribution

The paper introduces a new perspective on hidden variable models by showing their equivalence and unfalsifiability.

## Key findings

- Two types of hidden variable models are equivalent and unfalsifiable.
- Freedom of choice and context-independent mapping are not meaningful assumptions.
- A falsifiable model is defined by the conjunction of freedom of choice and context-independent mapping.

## Abstract

This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but generally context-dependent mapping of the hidden variables into observable ones, or by a model with context-independent mapping but generally compromised free choice. These two types of HVMs are equivalent, one can always be translated into another. They are also unfalsifiable, applicable to all possible systems. These facts, the equivalence and unfalsifiability, imply that freedom of choice and context-independent mapping are no assumptions at all, and they tell us nothing about freedom of choice or physical influences exerted by contexts as these notions would be understood in science and philosophy. The conjunction of these two notions, however, defines a falsifiable HVM that describes non-contextuality when applied to systems with no disturbance or to consistifications of arbitrary systems. This HVM is most adequately captured by the term ‘context-irrelevance’, meaning that no distribution in the model changes with context.

This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.