A Critical Reexamination of the Electrostatic Aharonov-Bohm Effect

Walstad, Allan

doi:10.1007/s10773-010-0485-0

Cited by 11 publications

(8 citation statements)

References 8 publications

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“…However, the non-zero vector potential can have a local effect that results in a phase shift. Notwithstanding the general acceptance of these ideas, this issue remains a topic of debate on non-locality 7–10 , the interpretation 11–14 , and existence of the effect 15,16 .…”

Section: Introductionmentioning

confidence: 99%

Asymmetry and non-dispersivity in the Aharonov-Bohm effect

et al. 2019

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Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger’s theorem describes this absence of classical force in quantum terms as the “dispersionless” nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum “force” for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov’s prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov’s prediction and Zeilinger’s theorem. The experiment consists of the Aharonov-Bohm physical system; free electrons pass a magnetized nanorod and far-field electron diffraction is observed. The diffraction pattern is asymmetric confirming one of Shelankov’s predictions and giving indirect experimental evidence for the presence of a quantum “force”. Our theoretical analysis shows that Zeilinger’s theorem and Shelankov’s result are both special cases of one theorem.

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Section: Introductionmentioning

confidence: 99%

Asymmetry and non-dispersivity in the Aharonov-Bohm effect

et al. 2019

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“…The potentials depend on the choice of gauge, which cannot affect the motion of particles, but there are gauge invariant properties of the potentials (apart from the fields) that specify the motion of particles. The validity and the meaning of the AB effect has been extensively discussed [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. I argue that there is an alternative to commonly accepted mechanism which leads to the effect, and that we might change our understanding of the nature of physical interactions back to that of the time before the AB effect was discovered.…”

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confidence: 97%

Role of potentials in the Aharonov-Bohm effect

2012

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There is a consensus today that the the main lesson of the Aharonov-Bohm effect is that a picture of electromagnetism based on the local action of the field strengths is not possible in quantum mechanics. Contrary to this statement it is argued here that when the source of the electromagnetic potential is treated in the framework of quantum theory, the Aharonov-Bohm effect can be explained without the notion of potentials. It is explained by local action of the field of the electron on the source of the potential. The core of the Aharonov-Bohm effect is the same as the core of quantum entanglement: the quantum wave function describes all systems together.PACS numbers: 03.65.Vf, 03.65.Ta, 03.65.Ud Before the Aharonov-Bohm effect [1] (AB) was discovered, the general consensus was that particles can change their motion only due to fields at their locations, fields which were created by other particles. The main revolutionary aspect of the AB effect was that this is not generally true, and that in certain setups two particles, prepared in identical states, move in the same fields but end up in different final states. In particular, the electromagnetic field can vanish at every place where the electron has been, yet the electron motion is affected by the electromagnetic interaction. The AB effect states that the motion of an electron is completely defined by the potentials in the region of its motion and not just by the fields. The potentials depend on the choice of gauge, which cannot affect the motion of particles, but there are gauge invariant properties of the potentials (apart from the fields) that specify the motion of particles. The validity and the meaning of the AB effect has been extensively discussed [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. I argue that there is an alternative to commonly accepted mechanism which leads to the effect, and that we might change our understanding of the nature of physical interactions back to that of the time before the AB effect was discovered. The quantum wave function changes due to local actions of fields.The discussion will be on the level of gedanken experiments, without questioning the feasibility of such experiments in today's laboratory. Consider a Mach-Zehnder interferometer for electrons tuned in such a way that the electron always ends up in detector B, see Fig. 1. We can change the electric potential in one arm of the interferometer such that there will be no electromagnetic field at the location of the wave packets of the electron but, nevertheless, the electron will change its behavior and sometimes (or it can be arranged that always) will end up in detector A. This is the electric AB effect. Alternatively, in the magnetic AB effect, the interference picture can be changed due to a solenoid inside the interferometer which produces no electromagnetic field at the arms of the interferometer.Let us start our analysis with the electric AB effect. In the original proposal, the potential was created using conductors, capacitors etc. While those are closer...

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“…As has recently been pointed out [3], however, interference takes place in the configuration space of the entire system, including the source of potentials acting on the particle. The relevant phase is not only the phase generated by the energy and momentum of the particle; if the phase associated with the rest of the system is sufficiently affected by its interaction with the particle, then it cannot be ignored.…”

Section: Introductionmentioning

confidence: 99%

“…The relevant phase is not only the phase generated by the energy and momentum of the particle; if the phase associated with the rest of the system is sufficiently affected by its interaction with the particle, then it cannot be ignored. (In a 1961 paper [4], Aharonov and Bohm sought to demonstrate that their results would not be affected by considering the wavefunction of the entire system; the error in their treatment has been identified [3].) Vaidman [5], Wang [6], and McGregor et.…”

Section: Introductionmentioning

confidence: 99%

Further Considerations Regarding the Aharonov-Bohm Effect and the Wavefunction of the Entire System

Walstad

2016

Int J Theor Phys

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In an earlier paper it was demonstrated that the hypothesized electrostatic version of the Aharonov-Bohm ("AB") effect does not exist. The conclusion follows straightforwardly once one recognizes that interference takes place in the configuration space of the entire system, including the experimental apparatus, and the wavefunction of the apparatus cannot be ignored. Two additional results are presented here. 1. Observations of interference that had been attributed to an analogue of the electrostatic AB effect (or "scalar effect") are actually due to a magnetic AB effect. 2. In the original magnetic AB effect itself, there is no phase shift if it is possible effectively to shield the solenoid from the influence of the passing electron. This result is not in conflict with the landmark experiments of Tonomura and colleagues if Wang's recent claim is correct, that superconductive shielding could not have isolated the toroidal magnet from the magnetic pulse of the passing electron.

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A Critical Reexamination of the Electrostatic Aharonov-Bohm Effect

Cited by 11 publications

References 8 publications

Asymmetry and non-dispersivity in the Aharonov-Bohm effect

Asymmetry and non-dispersivity in the Aharonov-Bohm effect

Role of potentials in the Aharonov-Bohm effect

Further Considerations Regarding the Aharonov-Bohm Effect and the Wavefunction of the Entire System

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