Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions containing $R$ . However, subspace implications are generally violated by versions of quantum theory that assign probabilities to histories, such as the consistent histories approach. I define here a new criterion, ordered consistency, which refines the criterion of consistency and has the property that inferences made by ordered consistent sets do not violate subspace relations. This raises the question: do the operators defining our observations form an ordered consistent history? If so, ordered consistency defines a version of quantum theory with greater predictive power than the consistent histories formalism. If not, and our observations are defined by a non-ordered consistent quantum history, then subspace implications are not generally valid.Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions containing $R$. However, subspace implications are generally violated by versions of quantum theory that assign probabilities to histories, such as the consistent histories approach. I define here a new criterion, ordered consistency, which refines the criterion of consistency and has the property that inferences made by ordered consistent sets do not violate subspace relations. This raises the question: do the operators defining our observations form an ordered consistent history? If so, ordered consistency defines a version of quantum theory with greater predictive power than the consistent histories formalism. If not, and our observations are defined by a non-ordered consistent quantum history, then subspace implications are not generally valid.

arXiv:gr-qc/9607073Jul 30, 19969 citations

Quantum histories and measurements

D. Sokolovski, Y. Liu

Physics Letters AMar 1, 20016 citations

A complementary perspective on quantum history

Alan Chodos

Physics TodayAug 1, 20250 citations

History, Causation, and the Many-Worlds Interpretation of Quantum Mechanics

Bruce S. Bennett, Moletlanyi Tshipa

Abstract The Many-Worlds Interpretation (MWI) is a theory in physics which proposes that, rather than quantum-level events being resolved randomly as according to the Copenhagen Interpretation, the universe constantly divides into different versions or worlds. All physically possible worlds occur, though some outcomes are more likely than others, and therefore all possible histories exist. This paper explores some implications of this for history, especially concerning causation. Unlike counterfactuals, which concern different starting conditions, MWI concerns different outcomes of the same starting conditions. It is argued that analysis of causation needs to take into account the divergence of outcomes and the possibility that we inhabit a less probable world. Another implication of MWI is convergent history: for any given world there will be similar worlds which are the result of different pasts which are, however, more or less probable. MWI can assist in thinking about historical causation and indicates the importance of probabilistic causation.Abstract The Many-Worlds Interpretation (MWI) is a theory in physics which proposes that, rather than quantum-level events being resolved randomly as according to the Copenhagen Interpretation, the universe constantly divides into different versions or worlds. All physically possible worlds occur, though some outcomes are more likely than others, and therefore all possible histories exist. This paper explores some implications of this for history, especially concerning causation. Unlike counterfactuals, which concern different starting conditions, MWI concerns different outcomes of the same starting conditions. It is argued that analysis of causation needs to take into account the divergence of outcomes and the possibility that we inhabit a less probable world. Another implication of MWI is convergent history: for any given world there will be similar worlds which are the result of different pasts which are, however, more or less probable. MWI can assist in thinking about historical causation and indicates the importance of probabilistic causation.

Journal of the Philosophy of HistorySep 16, 20190 citations

Quantum Histories, Mysteries, and Measurements

N. G. van Kampen, Bryce Seligman DeWitt, Sheldon Goldstein +3 more

Physics TodayMay 1, 20003 citations

Entropy of classical histories

Todd A. Brun, James B. Hartle

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and we prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and we prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.

arXiv:quant-ph/9808024Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 199914 citations

Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region

R

of space, then in these theories we can deduce that it is confined in regions containing

R

. However, subspace implications are generally violated by versions of quantum theory that assign probabilities to histories, such as the consistent histories approach. I define here a new criterion, ordered consistency, which refines the criterion of consistency and has the property that inferences made by ordered consistent sets do not violate subspace relations. This raises the question: do the operators defining our observations form an ordered consistent history? If so, ordered consistency defines a version of quantum theory with greater predictive power than the consistent histories formalism. If not, and our observations are defined by a non-ordered consistent quantum history, then subspace implications are not generally valid.