Random Variables Recorded under Mutually Exclusive Conditions: Contextuality-by-Default
This provides a foundational framework for analyzing contextuality in systems like quantum mechanics, but it is incremental as it builds on existing principles of stochastic unrelatedness and couplings.
The paper tackles the problem of analyzing how random variables depend on deterministic conditions by treating outputs recorded under mutually exclusive inputs as stochastically unrelated, with no joint distribution, and characterizes constraints using couplings. The result is a general framework applicable to quantum entangled particles and broader systems in physical, biological, and behavioral sciences.
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.