Probabilities for histories in nonrelativistic quantum mechanics

Yamada, Norifumi L.

doi:10.1103/physreva.54.182

Cited by 37 publications

(13 citation statements)

References 31 publications

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“…There are a number of approaches to this problem [2]. In this paper, an unexpected close relationship is found between a real time Feynman path integral approach [3,4,5] and the quantum shutter approach [6,7], which are, at first sight, unlikely to be related.…”

Section: Introductionmentioning

confidence: 83%

“…The definability of the probability distribution depends on whether or not the amplitude distribution has the property of orthogonality, i.e., whether or not the classes of Feynman paths taking time τ 1 and τ 2 (τ 1 = τ 2 ) to traverse the region interfere. For rectangular barriers, one of the authors studied the interference quantitatively to conclude that (i) a probability distribution is not definable [3,4] but (ii) the range of the values of tunneling time is definable [4]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [4] concerns the resident time, while Refs. [3,5] and this paper concern the passage time. We shall attach, if necessary, subscript r to the quantities for the resident time (e.g., G r (τ )) and subscript p for the passage time (e.g., G p (τ )).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the “passage time” in tunneling

2003

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Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

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Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the “passage time” in tunneling

2003

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“…The literature on propositions in quantum mechanics that refer to more than one time is long [22][23][24][25][26][27][28]. To deal with this, people have tried to define time in quantum mechanics as an operator [29][30][31], or using physical internal clocks [19,20] or using path integral approaches [21,[32][33][34][35][36][37][38]. In this paper we will use the decoherent histories approach as in [39].…”

Section: Arrival Time Problemmentioning

confidence: 99%

Spacetime Coarse Grainings and the Problem of Time in the Decoherent Histories Approach to Quantum Theory

Wallden

2007

Int J Theor Phys

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We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem, as a warm up, to deal with the problem of time in reparametrization invariant theories (as for example in canonical quantum gravity) which subsequently we examine. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related to our results, is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem and the problem of time in general.

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“…Although the results of such papers are not necessarily wrong, they often do not have sensible classical limits and in measurement-based models, they may, unknowingly, only be valid in the regime of strong measurement. These problems with the Zeno effect in path integral constructions can be seen in a number of early attempts to define probabilities for spacetime regions in the context of the decoherent histories approach [23,24,25,26,27,28,32] and in some papers on the decoherent histories approach to quantum cosmology [10,11,12,13,14]. A possible resolution was given in Refs.…”

Section: Introductionmentioning

confidence: 99%

Amplitudes for spacetime regions and the quantum Zeno effect: pitfalls of standard path integral constructions

Halliwell

Yearsley

2013

J. Phys.: Conf. Ser.

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Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect -the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequentlyoccurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale ǫ, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as ǫ ≫ 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to measurement-based models.

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Probabilities for histories in nonrelativistic quantum mechanics

Cited by 37 publications

References 31 publications

Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the “passage time” in tunneling

Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the “passage time” in tunneling

Spacetime Coarse Grainings and the Problem of Time in the Decoherent Histories Approach to Quantum Theory

Amplitudes for spacetime regions and the quantum Zeno effect: pitfalls of standard path integral constructions

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