I defend the interpretation of the Aharonov-Bohm effect originally advanced by Aharonov and Bohm, i.e., that it is caused by an interaction between the electron and the vector potential. The defense depends on taking the fiber bundle formulation of electrodynamics literally, or almost literally.

The main experiments concerning the Aharonov–Bohm phase shifts, seen in an electron interference pattern, and their Boyer semiclassical explanations are reviewed. A new experiment is also presented which emphasizes the subtleties involved in the interpretations of the magnetic Aharonov–Bohm phase shift as a result of a non-dispersive or dispersive effect.

I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of (...) electrodynamics ; I sketch a possible such account. (shrink)

The objective of this paper is to show that, instead of quantum probabilities, wave packets are physically real. First, Cartwright's recent argument for the reality of quantum probabilities is criticized. Then, the notion of ‘physically real’ is precisely defined and the difference between wave functions and quantum probabilities clarified. Being thus prepared, some strong reasons are discussed for considering the wave packet to be physically real. Finding the reasons inconclusive, I explain how the Aharonov—Bohm effect delivers the final (...) punch. I conclude that wave packets are the quantum objects that underlie the indeterministic quantum processes and have the propensity of displaying probabilistic (or indeterministic) behavior. (shrink)

I address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real. I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into ‘gauge-underdetermination’: different gauge choices represent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature, neither by proponents nor (...) by opponents of the potentials view. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory—an even narrower gauge equivalence relation—as the ontology of electrodynamics. (shrink)

Richard Healey argues that the Aharonov-Bohm effect demands the recognition of either nonlocal or nonseparable physics in much the way that violations of Bell's inequality do. A careful examination of the effect and the arguments, though, shows that Healey's interpretation of the Aharonov-Bohm effect depends critically on his interpretation of gauge theories, and that the analogy with violations of Bell's inequalities fails.

The analysis of a previous paper, in which it was shown that the energy for the Aharonov-Bohm effect could be traced to the interaction energy between the magnetic field of the electron and the background magnetic field, is extended to cover the case in which the magnetic field of the electron is shielded from the background magnetic field by a superconducting material. The paradox that arises from the fact that such a shielding would apparently preclude the possibility of (...) an interaction energy is resolved and, within the limits of the ideal situation considered, the observed experimental result is derived. (shrink)

At first sight the Aharonov- Bohm effect appears nonlocal, though not in the way EPR/Bell correlations are generally acknowledged to be nonlocal. This paper applies an analysis of nonlocality to the Aharonov- Bohm effect to show that its peculiarities may be blamed either on a failure of a principle of local action or on a failure of a principle of separability. Different interpretations of quantum mechanics disagree on how blame should be allocated. The parallel between the (...) Aharonov- Bohm effect and violations of Bell inequalities turns out to be so close that a balanced assessment of the nature and significance of quantum nonlocality requires a detailed study of both effects. (shrink)

Richard Healey argues that the Aharonov- Bohm effect demands the recognition of either nonlocal or nonseparable physics in much the way that violations of Bell's inequality do. A careful examination of the effect and the arguments, though, shows that Healey's interpretation of the Aharonov- Bohm effect depends critically on his interpretation of gauge theories, and that the analogy with violations of Bell's inequalities fails.

In the seminal works from Santos and Gozalo and Marletto and Vedral, it is shown how the Aharonov–Bohm effect can be described as the result of an exchange of virtual photons between the solenoid and the quantum charged particle along its propagation through the interferometer, where both the particle and the solenoid interact locally with the quantum electromagnetic field. This interaction results in a local and gauge-independent phase generation for the particle propagation in each path of the interferometer. (...) Here we improve the cited treatments by using the quantum electrodynamics formalism in the Lorentz gauge, with a manifestly gauge-independent Hamiltonian for the interaction and the presence of virtual longitudinal photons. Only with this more complete and gauge-independent treatment it is possible to justify the acquired phases for interferometers with arbitrary geometries. We also extend the results to the electric version of the Aharonov–Bohm effect. Finally, we propose an experiment that could test the locality of the Aharonov–Bohm phase generation. (shrink)

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations (...) of the involved particles is discussed for low energies. (shrink)

We draw a distinction between the Aharonov–Bohm phase shift and the Aharonov–Bohm effect. Although the Aharonov–Bohm phase shift occurring when an electron beam passes around a magnetic solenoid is well-verified experimentally, it is not clear whether this phase shift occurs because of classical forces or because of a topological effect occurring in the absence of classical forces as claimed by Aharonov and Bohm. The mathematics of the Schroedinger equation itself does not reveal (...) the physical basis for the effect. However, the experimentally observed Aharonov–Bohm phase shift is of the same form as the shift observed due to electrostatic forces for which the consensus view accepts the role of the classical forces. The Aharonov–Bohm phase shift may well arise from classical electromagnetic forces which are simply more subtle in the magnetic case since they involve relativistic effects of the order v 2 /c 2 . Here we first review the experimentally observable differences between phenomena arising from classical forces and phenomena arising from the quantum topological effect suggested by Aharonov and Bohm. Second we point out that most discussions of the classical electromagnetic forces involved when a charged particle passes a solenoid are inaccurate because they omit the Faraday induction terms. The subtleties of the relativisitic v 2 /c 2 classical electromagnetic forces between a point charge and a solenoid have been explored by Coleman and Van Vleck in their analysis of the Shockley–James paradox; indeed, we point out that an analysis exactly parallel to that of Coleman and Van Vleck suggests that the Aharonov–Bohm phase shift is actually due to classical electromagnetic forces. Finally we note that electromagnetic velocity fields penetrate even excellent conductors in a form which is unfamiliar to many physicists. An ohmic conductor surrounding a solenoid does not screen out the magnetic field of the passing charge, but rather the time-integral of the magnetic field is an invariant; this time integral is precisely what is involved in the classical explanation of the Aharonov–Bohm phase shift. Thus the persistence of the Aharonov–Bohm phase shift when the solenoid is surrounded by a conductor does not exclude a classical force-based explanation for the phase shift. At present there is no experimental evidence for the Aharonov–Bohm effect. (shrink)

By appealing to resources found in the scientific understanding literature, I identify in what senses idealisations afford understanding in the context of the (magnetic) Aharonov-Bohm effect. Three types of concepts of understanding are discussed: understanding-what, which has to do with understanding a phenomenon; understanding-with, which has to do with understanding a scientific theory; and understanding-why, which has to do with the reason some phenomenon occurs. Consequently, I outline an account of understanding-with that is suggested by the historical controversy (...) surrounding the Aharonov-Bohm effect. (shrink)

In the Aharonov- Bohm effect, electromagnetic potentials alter the two-slit interference pattern formed by an electron beam. We discuss here a curious feature of this effect, namely that, even though the interference pattern changes, none of its moments are shifted.

This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a quantum particle, its law of coupling to electromagnetic fields is obtained. It is suggested to understand the Aharonov-Bohm effect in light of these principles, and the implications for some related foundational controversies are discussed.

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that (...) a treatment exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift. (shrink)

The transference theory reduces causation to the transmission of physical conserved quantities, like energy or momenta. Although this theory aims at applying to all felds of physics, we claim that it fails to account for a quantum electrodynamic effect, viz. the Aharonov-Bohm effect. After having argued that the Aharonov-Bohm effect is a genuine counter-example for the transference theory, we offer a new physicalist approach of causation, ontic and modal, in which this effect is embedded.

It is shown, in a large variety of manifestations, that the Aharonov—Bohm effect has classical counterparts in aspects concerning energy and momentum balance. No counterexamples are found in the cases considered, although whenever image charges shield the magnetic field region from the electric field of the passing electron the classical momentum effects, while present, would not be observable. Similarly, if the magnetic flux is maintained by superconductors, magnetic shielding will also render the classical energy effect unobservable. Partial shieldings (...) of either type will reduce but not totally eliminate the corresponding observable classical manifestations of these effects. (shrink)

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual (...) world. The point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (shrink)

Aharonov and Bohm showed that, far from being merely a mathematical tool, the vector potential \ can have a microphysical effect even when irrotational, in which case the magnetic field is null. Still, at first sight there is something weird about this situation. Do we have to admit a new force? I argue that there is no paradox in the potentials-formulation of electrodynamics, for it shows that, while “\” represents a vanishing magnetic field, it alters the motion of (...) charged matter dragged by the electric field. (shrink)

Recent experiments undertaken by Caprez, Barwick, and Batelaan should clarify the connections between classical and quantum theories in connection with the Aharonov–Bohm phase shift. It is pointed out that resistive aspects for the solenoid current carriers play a role in the classical but not the quantum analysis for the phase shift. The observed absence of a classical lag effect for a macroscopic solenoid does not yet rule out the possibility of a lag explanation of the observed phase shift (...) for a microscopic solenoid. (shrink)

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual (...) world. The point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (shrink)

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the (...) so-called holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function. (shrink)

Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable “real” forces, but also the equivalence of potentials of such inertial forces and the potentials of (...) suitable real forces. The two types of cancellation are physically independent of each other, because of the Aharonov-Bohm effect. Finally, we show that the latter effect itself can be understood “geometrically” as a kinematic effect arising upon the transformation between the two reference frames. (shrink)

Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the (...) effect. First, Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory (...) role of said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

A thought experiment is reviewed which shows two things. First, in a region of a rotating frame that is not simply connected, the inertial forces can be canceled without completely canceling the inertial vector potential (whose curl determines the Coriolis force); second, the presence of this uncanceled potential can be detected in a quantum interference experiment. It is then argued that the thought experiment was realized in an earlier experiment involving a rotating superconductor, and that the experimental results confirm the (...) theoretical prediction. In this way, the first experimental verification of a physical effect due to a nonelectromagnetic potential in a force-free region is established. An analogous experiment for the gravitational vector potential is also discussed. Finally, it is pointed out that the close connection between electromagnetic and inertial vector potentials provides an intuitive way to make predictions about rotating superconductors. (shrink)

The ideal scalar Aharonov–Bohm (SAB) and Aharonov–Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the (...) dipole is affected by a nonvanishing torque that causes pure precession around the directions defined by the ideal set ups. It is shown that the precession angles are in the quantal case linearly related to the ideal phase differences, and that the nonideal phase differences are nonlinearly related to the ideal phase differences. It is argued that the latter nonlinearity is due to the appearance of a geometric phase associated with the nontrivial spin path. It is further demonstrated that the spatial force vanishes in all cases except in the classical treatment of the nonideal AC set up, where the occurring force has to be compensated by the experimental arrangement. Finally, for a closed space-time loop the local precession effects can be inferred from the interference pattern characterized by the nonideal phase differences and the visibilities. It is argued that this makes it natural to regard SAB and AC as essentially local and nontopological effects. (shrink)

An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.

In this article, we demonstrate a sense in which the one-particle quantum mechanics and the classical electromagnetic four-potential arise from the quantum field theory. In addition, the classical Maxwell equations are derived from the QFT scattering process, while both classical electromagnetic fields and potentials serve as mathematical tools to approximate the interactions among elementary particles described by QFT physics. Furthermore, a plausible interpretation of the Aharonov–Bohm effect is raised within the QFT framework. We provide a quantum treatment of (...) the source of electromagnetic potentials and argue that the underlying mechanism in the AB effect can be understood via interactions among electrons described by QFT theory where the interactions are mediated by virtual photons. (shrink)

The vacuum structure for the massive charged scalar field in the region of two parallel, infinitely long and thin solenoids confining the fluxesn 1 andn 2 is studied. By using the Green function method, it is found that the vacuum expectation value of the system's energy has a finite mutual interaction term depending on the distance a between the solenoids, which implies an attractive force per unit length given by F n1n2 =−(ℏc/π2)(n 1 n 2)2/a 3.

We propose a simple situation in which the magnetic Aharonov–Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whether the particle interacts with the solenoid or not. Even with the particle excluded from the magnetic field, the number of self-adjoint extensions of the initial Hamiltonian depends on the magnetic flux. This is a new point of view of the Aharonov–Bohm effect.

We point out that the Aharonov-Bohm effect is a 4-dimensional nonlocal geometric phenomenon. We give two examples which in 3 dimensions appear rather mysterious, but which are easily understood in 4 dimensions. We also discuss why it is integrated effects over fields (potentials) rather than the fields themselves that are important.

Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due (...) to its topological nature. We propose a third alternative interpretation based on the loop space of holonomies which serves to solve some of the problems and we trace back the topological nonlocality and thereby the Aharonov-Bohm effect to their quantum mechanical origin. All three discussed interpretations are, of course, empirically equivalent. In fact, they present us with an instructive case study for the thesis of theory underdetermination by empirical data. (shrink)

Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due (...) to its topological nature. We propose a third alternative interpretation based on the loop space of holonomies which serves to solve some of the problems and we trace back the topological nonlocality and thereby the Aharonov-Bohm effect to their quantum mechanical origin. All three discussed interpretations are, of course, empirically equivalent. In fact, they present us with an instructive case study for the thesis of theory underdetermination by empirical data. (shrink)

I study in detail a proposal made by T. H. Boyer in an attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In (...) this paper I make explicit calculations which show that Boyer's conjecture fails. Indeed I find that the perturbation produced on the solenoid, and then its effect on the external charge, is independent of the solenoid current and consequently cannot account for the AB effect, which is current dependent. (shrink)

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a (...) connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c 2 , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems. (shrink)

David Bohm, Emeritus Professor of Theoretical Physics at Birkbeck College of the University of London and Fellow of the Royal Society, died of a heart attack on October 29, 1992 at the age of 74. Professor Bohm had been one of the world’s leading authorities on quantum theory and its interpretation for more than four decades. His contributions have been critical to all aspects of the field. He also made seminal contributions to plasma physics. His name appears prominently (...) in the modern physics literature, through the Aharonov- Bohm effect , the Bohm-EPR experiment , the Bohm-Pines collective description of particle interactions (random phase approximation), Bohm diffusion and the Bohm causal interpretation of quantum mechanics, also sometimes called the de Broglie-Bohm pilot wave theory. David Bohm was born in Wilkes-Barre, Pennsylvania on December 20, 1917. A student of J. Robert Oppenheimer, Bohm received his Ph.D. from the University of California at Berkeley in 1943. In 1950 he completed the first of his six books, Quantum Theory, which became the definitive exposition of the orthodox (Copenhagen) interpretation of quantum mechanics. Here Bohm presented his reformulation of the paradox of Einstein, Podolsky, and Rosen. It is this Bohm version of EPR which has provided the basis for the enormous expansion of research on the foundations of quantum theory, focusing on nonlocality and the possible incompleteness of the quantum description (the question of “hidden variables”), which has occurred during the past several decades. (shrink)

Classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric dipoles or a line of magnetic dipoles (a solenoid) is placed between the electron beams forming the interference pattern.

We prove that the general scheme for physical theories that we have called semantic realism(SR) in some previous papers copes successfully with a number of EPR-like paradoxes when applied to quantum physics (QP). In particular, we consider the old arguments by Furry and Bohm- Aharonov and show that they are not valid within a SR framework. Moreover, we consider the Bell-Kochen-Specker und the Bell theorems that should prove that QP is inherently contextual and nonlocal, respectively, and show that (...) they can be invalidated in the SR approach. This removes the seeming contradiction between the basic assumptions of SR and QP, and proves that some problematic features that are usually attributed to QP, us contextuality and nonlocality, occur because of the adoption of a verificationist position, from one side, and from an insufficient adherence to the operational principles that have inspired QP itself, from the other side. (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is (...) outlined and endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication' - as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity - to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm (...) the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles. (shrink)

An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of $\mathcal{C}$ - and $\mathfrak{D}$ -differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as a special case, quantisation in arbitrary curvilinear coordinates when space is (...) flat.) The influence of curvature is emphasised throughout, with an illustration provided by the Aharonov-Bohm effect. (shrink)

A generic non-conservative force, applied to an interferometer particle for a period in the past and then turned off, leaves stationary phase and fringe shifts in the now force-free interferometer. Both Aharonov-Bohm and Aharonov-Casher topological phase and fringe shifts can be created in this way. The specific sources of the non-conservative forces behind Aharonov-Bohm and Aharonov-Casher stationary fringe shifts are, respectively, Faraday induction fields and Maxwell displacement currents, now off.

Electromagnetic gauge as an integration condition was my wording in previous publications. I argue here, on the examples of the Möllenstaedt-Bayh and Tonomura tests of the Ahraronov–Bohm (AB) effect, that not only the trapped flux Φ but also, under the integration condition A ≡ 0 if Φ = 0, the local value of the vector potential is measured.