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Summary

Hidden variable models (HVMs) for random variables with exclusive contexts are equivalent and unfalsifiable. This implies freedom of choice and context-independent mapping are not assumptions, revealing insights into non-contextuality and

Keywords:
context-independent mappingcontext-irrelevancecontextualitycouplingfree choicehidden-variable

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Area of Science:

  • Quantum mechanics
  • Foundations of probability
  • Information theory

Background:

  • Hidden variable models (HVMs) are used to describe systems of random variables.
  • These models often involve concepts like free choice and context-dependent mappings.
  • Understanding contextuality is crucial in quantum mechanics and philosophy.

Purpose of the Study:

  • To provide a systematic account of hidden variable models (HVMs) for systems with mutually exclusive contexts.
  • To analyze the implications of equivalence and unfalsifiability of certain HVMs.
  • To define a falsifiable HVM capturing non-contextuality.

Main Methods:

  • Systematic analysis of two types of HVMs: free choice with context-dependent mapping, and context-independent mapping with compromised free choice.
  • Demonstration of the equivalence and unfalsifiability of these HVMs.
  • Definition of a falsifiable HVM based on the conjunction of freedom of choice and context-independent mapping.

Main Results:

  • All systems with mutually exclusive contexts can be described by equivalent, unfalsifiable HVMs.
  • Equivalence and unfalsifiability show that freedom of choice and context-independent mapping are not restrictive assumptions.
  • A falsifiable HVM, termed 'context-irrelevance', is defined for non-contextual systems.

Conclusions:

  • The study clarifies the nature of freedom of choice and context-dependent influences in HVMs.
  • It establishes that certain HVMs are unfalsifiable, providing no empirical constraints.
  • The concept of 'context-irrelevance' offers a falsifiable framework for non-contextuality.