Hidden variables in quantum mechanics: Generic models, set-theoretic forcing, and the appearance of probability

2005/06/07 by Robert A. Van Wesep
Mathematics · Physics and Astronomy · #Equivalence (formal languages) #Hidden variable theory #Mathematical and Theoretical Analysis #Observable #Quantum #Quantum Mechanics and Applications #Quantum probability #Quantum process #Quantum system #Set (abstract data type) #Statistical Mechanics and Entropy #math.LO #quant-ph

paper · pdf · doi:10.1016/j.aop.2006.02.003

published as Annals of Physics 321 (2006) 2453-2490 · 67 pages. Corrected formulas for conditional and joint probabilities per comment of J. Malley

arxiv created 2005/06/07 · openalex publication_date 2006/07/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in light of the theory of generic filters and boolean-valued models in set theory (the method of forcing). The apparent stochastic nature of quantum observation is derived for these hidden-variables models.

Citations

• A Model of Set-Theory in Which Every Set of Reals is Lebesgue Measurable
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• Hidden Variables and the Two Theorems of John Bell
• On the Einstein Podolsky Rosen paradox
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS, II
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

Cited by

• Many worlds and the appearance of probability in quantum mechanics