Approximate and exact consistency of histories

1995/06/30 by Jim McElwaine, J. N. McElwaine · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computability, Logic, AI Algorithms #Consistency (knowledge bases) #Discrete mathematics #Formalism (music) #Logic, programming, and type systems #Mathematics #Pure mathematics #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.53.2021

32 pages, revtex, no figures. Explanations improved, one proof extended. To appear Phys. Rev A 1st March 96

arxiv created 1996/01/19 · openalex publication_date 1996/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The consistent histories formalism is discussed using path-projected states. These are used to analyze various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several bounds on the violation of probability sum rules. The quantum Zeno effect is also analyzed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed. \textcopyright 1996 The American Physical Society.

Citations

• Quantum logic and the histories approach to quantum theory
• Quantum-mechanical histories and the uncertainty principle. II. Fluctuations about classical predictability
• Sphere Packings, Lattices and Groups

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