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

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 equivalently 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 HVMs are unfalsifiable, applicable to all possible systems. This implies 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 noncontextuality 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.Comment: 17 pp; version 2 is a minor revisio

Embedding Quantum into Classical: Contextualization vs Conditionalization

We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions, because any set of such distributions is compatible with any distribution assigned to the conditions.Comment: PLoS One 9(3): e92818 (2014