Consistent interpretations of quantum mechanics

Omnès, Roland

doi:10.1103/revmodphys.64.339

Cited by 585 publications

(361 citation statements)

References 98 publications

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“…Because the probabilities can be measured experimentally, they should be unambiguously predicted -at least to within experimental precision. [16,[19][20][21][22][23][24], and Gell-Mann and Hartle [3,18,25] make the same point.…”

Section: Approximate Consistencymentioning

confidence: 67%

Approximate and exact consistency of histories

McElwaine

1996

Phys. Rev. A

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The consistent histories formalism is discussed using path-projected states.These are used to analyse various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed 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.

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Section: Approximate Consistencymentioning

confidence: 67%

Approximate and exact consistency of histories

McElwaine

1996

Phys. Rev. A

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“…As well known, Everett assumed that every quantum possibility is actualized in some branch of a multi-valued universe [11]. An opposite viewpoint stressed that every theory -even a classical one-can only deal with potentialities and never with actuality, so that the problem of reduction might well be outside the reach of theoretical physics [12]. Many people nevertheless consider that the problem of reduction belongs properly to physics and should even be considered among the most significant ones in understanding the foundations of science.…”

Section: Introductionmentioning

confidence: 99%

“…The projection operators P j and the densities are time-dependent (think for instance of a moving part of an apparatus). Very often, they are microlocal (semi-classical) projection operators, whose definition has been given elsewhere [12,25,26]. The quantity T r(P j ρ S P j ) is a constant, equal to the standard probability p j for observing at any time t after decoherence the property j with projection operator P j (t).…”

Section: Introductionmentioning

confidence: 99%

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Model of quantum reduction with decoherence

Omnès

2005

Phys. Rev. D

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The problem of reduction (wave packet reduction) is reexamined under two simple conditions: Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame of quantum field theory and the standard model.These conditions lead to an essentially unique model for reduction. Consistency with renormalization and time-reversal violation suggest however a primary action in the vicinity of Planck's length. The inclusion of quantum gravity and the uniqueness of space-time point moreover to generalized quantum theory, first proposed by Gell-Mann and Hartle, as a convenient framework for developing this model into a more complete theory.

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“…Griffiths and Omnes [2][3][4][5][6] have proposed an interpretive scheme for traditional quantum mechanics in which the Hilbert space based mathematical formalism is retained, the reduction postulate is discarded and Eq. (2) is interpreted as the probability for the history (1) for a closed system S (no external observers).…”

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confidence: 99%

Symmetries and Conservation Laws in Histories-Based Theories

Dass¹,

Joglekar²

2001

Annals of Physics

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Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of 'temporal sequences' of 'events' using partial semigroups) and logic structure for 'single-time histories'. Symmetries are classified into orthochronous (those preserving the 'temporal order' of 'events') and nonorthochronous. A straightforward criterion for physical equivalence of histories is formulated in terms of orthochronous symmetries; this criterion covers various notions of physical equivalence of histories considered by Gell-Mann and Hartle as special cases. In familiar situations, a reciprocal relationship between traditional symmetries (Wigner symmetries in quantum mechanics and Borel-measurable transformations of phase space in classical mechanics) and symmetries defined in this work is established. In a restricted class of theories, a definition of conservation law is given in the history language which agrees with the standard ones in familiar situations; in a smaller subclass of theories, a Noether type theorem (implying a connection between continuous symmetries of dynamics and conservation laws) is proved. The

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Consistent interpretations of quantum mechanics

Cited by 585 publications

References 98 publications

Approximate and exact consistency of histories

Approximate and exact consistency of histories

Model of quantum reduction with decoherence

Symmetries and Conservation Laws in Histories-Based Theories

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