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Hidden variables, free choice, context-independence and all that.
1Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA.
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
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.
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