2005/09/23 by Thomas Marlow
Arts and Humanities · Mathematics · Physics and Astronomy · #Artificial intelligence #Axiom #Bayes' theorem #Bayesian probability #CLARITY #Class (philosophy) #Computer science #Consistent histories #Epistemology #Interpretation (philosophy) #Mathematical economics #Mathematics #Philosophy #Philosophy and History of Science #Physics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Quantum operation #Series (stratigraphy) #Statistical Mechanics and Entropy #Theoretical physics #quant-ph
paper · pdf · doi:10.1016/j.aop.2005.09.006
published as Annals of Physics 321 (2006) 1103--1125 · 24 pages, accepted for publication in Annals of Physics, minor correction
arxiv created 2005/09/23 · openalex publication_date 2005/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive `probabilities'. The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistent with Bayes' rule. We show that certain class of histories are given a natural Bayesian interpretation, namely the linearly positive histories originally introduced by Goldstein and Page. Thus we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox's axioms of probability theory.