Role of potentials in the Aharonov-Bohm effect

  title={Role of potentials in the Aharonov-Bohm effect},
  author={Lev Vaidman},
  journal={Physical Review A},
  • L. Vaidman
  • Published 25 October 2011
  • Physics
  • Physical Review A
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… 

Figures from this paper

On the Interpretation of the Aharonov-Bohm Effect
The Aharonov-Bohm (A-B) effect showed that the phase of electron wave pattern could be changed by the excluded electromagnetic field, the region where electromagnetic field is zero. This apparent
Observation of Quantum Forces in the Aharonov-Bohm effect
Decades ago, the idea that electrons can be affected by electromagnetic potentials without experiencing force-fields changed our thinking with the advent of the Aharonov-Bohm effect. Zeilingers
The Aharonov Bohm effect as a material phenomenon
An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on
New Perspectives on the Aharonov-Bohm Effect
The Aharonov-Bohm effect is a quantum mechanical effect, that is, has no classical counterpart. The effect was predicted in 1959 in a seminal paper of Y. Aharonov and D. Bohm [AB59] in which they
Paradoxes of the Aharonov-Bohm and the Aharonov-Casher Effects
For a believer in locality of Nature, the Aharonov-Bohm effect and the Aharonov-Casher effect are paradoxes. I discuss these and other Aharonov’s paradoxes and propose a local explanation of these
A study of Aharonov-Bohm effect: from quantum electrodynamics to one particle quantum mechanics
In this article, we start with the discussions on the Aharonov-Bohm effect then raise a plausible interpretation within the quantum electrodynamics (QED) framework. We provide a quantum treatment of
Classical nonlocality and the Aharonov-Bohm effect
The Aharonov-Bohm effect is a quantum mechanical phenomenon in which it is widely accepted that the observed Aharonov-Bohm phase can be explained by assuming that the magnetic field can produce
Demystifying the nonlocality problem in Aharonov–Bohm effect
In this paper, we present a novel semi-classical theory of the electrostatic and magnetostatic fields and explain the nonlocality problem in the context of the Aharonov–Bohm effect [1]. Specifically,
Nonlocality of the Aharonov-Bohm Effect
Although the Aharonov-Bohm and related effects are familiar in solid-state and high-energy physics, the nonlocality of these effects has been questioned. Here we show that the Aharonov-Bohm effect
On the paper 'Role of potentials in the Aharonov-Bohm effect'
When the magnetic vector potential is expressed in terms of the magnetic field it, is found to be explicitly non-local in space. This gives support to the conclusions of Aharonov et al. in a recent


Significance of the Aharonov-Bohm effect
SummaryIt is shown that in an Aharonov-Bohm experiment: i) Due to superposition of the electron’s magnetic field and the solenoid’s interior magnetic field there exists an interaction energyUmwhose
A Critical Reexamination of the Electrostatic Aharonov-Bohm Effect
This paper undertakes a critical reexamination of the electrostatic version of the Aharonov-Bohm (“AB”) effect. The conclusions are as follows: 1. Aharonov and Bohm’s 1959 exposition is invalid
Further Considerations on Electromagnetic Potentials in the Quantum Theory
In this article, we discuss in further detail the significance of potentials in the quantum theory, and in so doing, we answer a number of arguments that have been raised against the conclusions of
Significance of Electromagnetic Potentials in the Quantum Theory
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist
Dynamical features of interference phenomena in the presence of entanglement
A strongly interacting, and entangling, heavy nonrecoiling external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized
Condition for Nonexistence of Aharonov-Bohm Effect
It is shown that electromagnetic effects of a vector potential on a charged particle confined to a region R (multiply or simply connected) are completely determined by field strengths in R, if the
Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields
Through an examination of the Bohm-Aharonov experiment an intrinsic and complete description of electromagnetism in a space-time region is formulated in terms of a nonintegrable phase factor. This
Nonexistence of the Aharonov-Bohm effect
SummaryIn this paper the Aharonov-Bohm effect is investigated and it is shown that it has a purely mathematical origin. All the physical consequences of quantum mechanics turn out to be dependent on