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The Consistent Histories Interpretation of Quantum Mechanics

Edward M. MacKinnon

Published Apr 1, 2009• 5 citations
OpenAlex

Abstract

The consistent histories reformulation of quantum mechanics was developed by Robert Griffiths, given a formal logical systematization by Roland Omn\`{e}s, and under the label `decoherent histories', was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of philosophy and physics. We will briefly consider the original formulation of CH and some basic objections. The reply to these objections, like the objections themselves, involves a mixture of physics and philosophy. These replies support an evaluation of the CH formulation as a replacement for the measurement, or orthodox, interpretation.

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A Brief Historical Perspective on the Consistent Histories Interpretation of Quantum Mechanics

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It will be presented in this chapter a historical account of the consistent histories interpretation of quantum mechanics based on primary and secondary literature. Firstly, the formalism of the consistent histories approach will be outlined. Secondly, the works by Robert Griffiths and Roland Omnès will be discussed. Griffiths' seminal 1984 paper, the first physicist to have proposed a consistent-histories interpretation of quantum mechanics, followed by Omnès' 1990 paper, were instrumental to the consistent-histories model based on Boolean logic. Thirdly, Murray Gell-Mann and James Hartle's steps to their own version of consistent-histories approach, motivated by a cosmological perspective, will then be described and evaluated. Gell-Mann and Hartle understood that spontaneous decoherence could path the way to a concrete physical model to Griffiths' consistent histories. Moreover, the collective biography of these figures will be put in the context of the role played by the Santa Fe Institute, co-founded by Gell-Mann in 1984 in Santa Fe, New Mexico, where Hartle is also a member of the external faculty.

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Towards the consistent histories approach to quantum mechanics

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We introduce and review the consistent (decoherent) histories approach to quantum mechanics due to Griffiths, to Gell-Mann and Hartle, and to Omnes. We will not attempt an in depth look at this approach as it would be impossible to treat it in such a short review. The emphasis is on understanding the broader meaning of the consistency and decoherence. The consistent history approach to quantum mechanics provides a precise conceptual framework for describing how a closed quantum system develops in time. The approach also provides a framework from which we may observe the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscopic subsystems. We will study the formalism of decoherence and look at several approaches to decoherence. In examining a system of quantum Brownian motion and using the methods of Feynman and Vernon, we derive an equation of motion for the density matrix, the master equation of the system. This leads us to a brief overview of decoherence. PACS Nos.: 03.65.Ta, 03.65.–w, 03.65.Yz, 04.60.–m, 05.30.–d

Canadian Journal of Physics•Jan 1, 2004•6 citations

A Review of the Decoherent Histories Approach to Quantum Mechanicsa

J. J. Halliwell

I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may predict the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is closed related to the quantum state diffusion approach of Gisin and Percival.

arXiv:gr-qc/9407040•Annals of the New York Academy of Sciences•Apr 1, 1995•109 citations

Aspects of the Decoherent Histories Approach to Quantum Mechanics

J. J. Halliwell

I give an informal overview of the decoherent histories approach to quantum mechanics, due to Griffiths, to Omnès, and to Gell-Mann and Hartle is given. Results on the connections between decoherence, records, correlation and entropy are described. The emphasis of the presentation is on understanding the broader meaning of the conditions of consistency and decoherence, and in particular, the extent to which they permit one to assign definite properties to the system. The quantum Brownian motion model is briefly discussed. (To appear in proceedings of the workshop, "Stochastic Evolution of Quantum States in Open Systems and Measurement Processes", Budapest, March, 1993, edited by L.Diosi).

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Review of R. Omnes, THE INTERPRETATION OF QUANTUM MECHANICS

Robert B. Griffiths

Omnes' interpretation of quantum mechanics is summarized, and compared with other consistent-history approaches by Gell-Mann and Hartle, and by Griffiths.

arXiv:quant-ph/9505008•May 16, 1995•2 citations

Consistent Histories

Jonathan Allday

The consistent histories approach was initially proposed by Robert Griffiths in 1984. Roland Omnes then developed a more mathematically rigorous version based on the rules of classical probability and logic. In the consistent histories terminology, each projective decomposition defines a framework, which is, in essence, a context for discussing the system. As Griffith describes it: In quantum mechanics, each Boolean event algebra constitutes what is in effect a “language” out of which one can construct a quantum description of some physical system. A crucial and distinctive feature of the consistent histories approach is the single framework rule , which provides guidance for quantum reasoning. From the perspective of consistent histories, the emergence of classical physics from the quantum level is linked to the suppression of interference, so that the normal rules of probability apply.

CRC Press eBooks•Sep 21, 2022•0 citations
The consistent histories reformulation of quantum mechanics was developed by Robert Griffiths, given a formal logical systematization by Roland Omn`{e}s, and under the label `decoherent histories', was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of philosophy and physics. We will briefly consider the original formulation of CH and some basic objections. The reply to these objections, like the objections themselves, involves a mixture of physics and philosophy. These replies support an evaluation of the CH formulation as a replacement for the measurement, or orthodox, interpretation.
It will be presented in this chapter a historical account of the consistent histories interpretation of quantum mechanics based on primary and secondary literature. Firstly, the formalism of the consistent histories approach will be outlined. Secondly, the works by Robert Griffiths and Roland Omnès will be discussed. Griffiths' seminal 1984 paper, the first physicist to have proposed a consistent-histories interpretation of quantum mechanics, followed by Omnès' 1990 paper, were instrumental to the consistent-histories model based on Boolean logic. Thirdly, Murray Gell-Mann and James Hartle's steps to their own version of consistent-histories approach, motivated by a cosmological perspective, will then be described and evaluated. Gell-Mann and Hartle understood that spontaneous decoherence could path the way to a concrete physical model to Griffiths' consistent histories. Moreover, the collective biography of these figures will be put in the context of the role played by the Santa Fe Institute, co-founded by Gell-Mann in 1984 in Santa Fe, New Mexico, where Hartle is also a member of the external faculty.
We introduce and review the consistent (decoherent) histories approach to quantum mechanics due to Griffiths, to Gell-Mann and Hartle, and to Omnes. We will not attempt an in depth look at this approach as it would be impossible to treat it in such a short review. The emphasis is on understanding the broader meaning of the consistency and decoherence. The consistent history approach to quantum mechanics provides a precise conceptual framework for describing how a closed quantum system develops in time. The approach also provides a framework from which we may observe the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscopic subsystems. We will study the formalism of decoherence and look at several approaches to decoherence. In examining a system of quantum Brownian motion and using the methods of Feynman and Vernon, we derive an equation of motion for the density matrix, the master equation of the system. This leads us to a brief overview of decoherence. PACS Nos.: 03.65.Ta, 03.65.–w, 03.65.Yz, 04.60.–m, 05.30.–d
I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may predict the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is closed related to the quantum state diffusion approach of Gisin and Percival.
I give an informal overview of the decoherent histories approach to quantum mechanics, due to Griffiths, to Omnès, and to Gell-Mann and Hartle is given. Results on the connections between decoherence, records, correlation and entropy are described. The emphasis of the presentation is on understanding the broader meaning of the conditions of consistency and decoherence, and in particular, the extent to which they permit one to assign definite properties to the system. The quantum Brownian motion model is briefly discussed. (To appear in proceedings of the workshop, "Stochastic Evolution of Quantum States in Open Systems and Measurement Processes", Budapest, March, 1993, edited by L.Diosi).
The consistent histories approach was initially proposed by Robert Griffiths in 1984. Roland Omnes then developed a more mathematically rigorous version based on the rules of classical probability and logic. In the consistent histories terminology, each projective decomposition defines a framework, which is, in essence, a context for discussing the system. As Griffith describes it: In quantum mechanics, each Boolean event algebra constitutes what is in effect a “language” out of which one can construct a quantum description of some physical system. A crucial and distinctive feature of the consistent histories approach is the single framework rule , which provides guidance for quantum reasoning. From the perspective of consistent histories, the emergence of classical physics from the quantum level is linked to the suppression of interference, so that the normal rules of probability apply.