Aharonov-Bohm effect versus causality?

Troudet, T.

doi:10.1016/0375-9601(85)90625-5

Cited by 7 publications

(15 citation statements)

References 4 publications

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Section: Physical Discussionmentioning

confidence: 99%

“…This conclusion originates from the path-integral approach (that is almost always followed), but, nevertheless, our present work shows that fields do contribute nonlocally. A more general discussion on this issue is given in the final Section, after discussion of the van Kampen thought-experiment, and also in connection to related path-integral approaches [16].…”

Section: Comments On the General Behavior Of The (X T)-solutionsmentioning

confidence: 99%

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Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Moulopoulos

2011

JMP

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Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schrödinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. For particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certain time-dependent semiclassical arguments are consistent with static results in purely quantal Aharonov-Bohm configurations. These nonlocalities also provide a remedy for misleading results propagating in the literature (concerning an uncritical use of Dirac phase factors, that persists since the time of Feynman's work on path integrals).They are shown to conspire in such a way as to exactly cancel the instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thoughtexperiment), and to also complete Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner. The present formulation offers a direct way to address time-dependent singlevs double-slit experiments and the associated causal issues -issues that have recently attracted attention, with respect to the inability of current theories to address them.∂A 2 (r,t) ∂t = −∇φ 1 (r, t) − 1 c ∂A 1 (r,t) ∂t = E 1 (r, t) for the electric fields, is obviously consistent with all equations (2) (as is easy to see if we take

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Section: Physical Discussionmentioning

confidence: 99%

Section: Comments On the General Behavior Of The (X T)-solutionsmentioning

confidence: 99%

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Moulopoulos

2011

JMP

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“…Troudet [12] clearly (and correctly) states that his treatment is good for not highly-delocalized states in space, and that in case of delocalization the proper treatment "would be much more complicated, and would require a much more complete analysis". We believe we have provided one in this paper.…”

Section: Discussionmentioning

confidence: 99%

“…This view originates from the path-integral treatments widely used (where the Lagrangian determines directly the phases of Propagators), but, nevertheless, our canonical formulation treatment shows that fields do contribute nonlocally, and they are actually crucial in recovering Relativistic Causality. Moreover, path-integral discussions [12] of the van Kampen case use wave (retarded)-solutions for the vector potentials A (hence they are treated in Lorenz gauge, which is not sufficiently general: even if A has not yet reached the screen, we can always add a constant A (a pure gauge) over all space, and there are no more retarded wave-solutions for the potentials, the path-integral resolution of the paradox being, therefore, at least incomplete). Our results are gauge-invariant and take advantage of only the retardation of fields E and B (true in any gauge), and not of potentials.…”

Section: Discussionmentioning

confidence: 99%

“…This conclusion originates from the path-integral approach (that is almost always followed), but, nevertheless, our present work shows that fields do contribute nonlocally. A more general discussion on this issue is given in the final Section, after discussion of the van Kampen thought-experiment, and also in relation to the path-integral work of Troudet [12].…”

Section: (Up To the Same Constant C) In Order Tomentioning

confidence: 99%

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Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

Moulopoulos¹

2010

J. Phys. A: Math. Theor.

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We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schrödinger equation: the phases of wavefunctions in the Schrödinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric).

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The Aharonov-Bohm Effect from the Point of View of Local Realism

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Selleri

1992

Wave-Particle Duality

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Aharonov-Bohm effect versus causality?

Cited by 7 publications

References 4 publications

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

The Aharonov-Bohm Effect from the Point of View of Local Realism

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Aharonov-Bohm effect versus causality?

Cited by 7 publications

References 4 publications

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schr&#246;dinger Picture

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schr&#246;dinger Picture

Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

The Aharonov-Bohm Effect from the Point of View of Local Realism

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Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture