## 1. Introduction

[2] In classical electromagnetic theory the electromagnetic potentials (**A**, Φ) are introduced mainly as useful mathematical constructs to compute the true force fields (**E**, **B**). Only the fields are thought to be physically real. In contrast, in quantum physics the potentials can play, under certain circumstances, even a more fundamental role than the corresponding fields. In fact, it is known that an electron can be influenced in a physically measurable way, e.g., in the form of a quantum-mechanical wavefunction phase shift, in regions of vanishing electromagnetic fields (**E** = 0, **B** = 0) but nonvanishing electromagnetic potentials (**A** ≠ 0, Φ ≠ 0). For example, quantum mechanics tells us that if an electron in an electromagnetic field region is split into two alternative trajectories, say, **x**_{1}(*t*) and **x**_{2}(*t*), then an (**A**, Φ)-dependent relative phase shift [*Lee et al.*, 1992]

appears between the Schrödinger wavefunctions Ψ_{1}(**r**, *t*) = Ψ_{1}^{(0)}(**r**, *t*)*e*^{i}ϕ_{1}(*t*) and Ψ_{2}(**r**, *t*) = Ψ_{2}^{(0)}(**r**, *t*)*e*^{i}ϕ_{2}(*t*) associated with each path; Ψ_{1}^{(0)}(**r**, *t*) and Ψ_{2}^{(0)}(**r**, *t*) are reference electron wavefunctions associated with the first and second trajectories, respectively, in the absence of electromagnetic potentials (**A** = 0, Φ = 0); *e* is the electron charge, *h* is Planck's constant and *c* is the speed of light. The phase shift in Equation (1) is physically measurable, e.g., it can be observed by carrying out electron interference experiments [*Peshkin and Tonomura*, 1989]. More importantly, this form of phase shift can occur even in the extreme situation where the electron traveling paths **x**_{1}(*t*) and **x**_{2}(*t*) are entirely inside regions of vanishing electromagnetic fields and nonvanishing electromagnetic potentials. This situation is known to occur, e.g., in the exterior of certain static toroidal solenoids having vanishing external magnetostatic fields but nonvanishing external magnetostatic potentials [*Carron*, 1995]. Under such circumstances that were first postulated by *Aharonov and Bohm* [1959] (see Figure 1a) and later verified experimentally in electron interference experiments [*Peshkin and Tonomura*, 1989], it appears that the potentials (as opposed to the fields) are the physically relevant electromagnetic entities. This effect is known as the Aharonov-Bohm (A-B) effect and applies in different forms to other fields, e.g., the gravitational field [*Harris*, 1996].

[3] The A-B effect has been the subject of more than 1400 papers to date, and in recent years has been proposed as the basis of novel devices that claim to measure the electromagnetic vector potential **A** directly [*Lee et al.*, 1992; *Gelinas*, 1984]. *Lee et al.* [1992] proposes the measurement of the potentials associated with a light beam by letting the light beam suffer total internal reflection from a crystal surface; the resulting evanescent electromagnetic potentials that emanate from the crystal are deduced via Equation (1) with electron interference experiments. *Gelinas* [1984] proposes the use of a superconducting Josephson junction, the tunneling current of which can be shown to depend (again, via Equation (1)) on the value of the vector potential around the junction.

[4] Although a few papers have addressed the A-B phase shift under time-varying, electrodynamic conditions [see, e.g., *Lee et al.*, 1992], most have dealt with static versions of the effect [see, e.g., *Aharonov and Bohm*, 1959]. The main focus has been on showing that, even in the extreme case of vanishing electromagnetic fields, one can measure quantum-mechanical effects of nonvanishing electromagnetic potentials such as those produced in the exterior of magnetostatic toroidal solenoids, infinite solenoids, and similar field-confining structures. Thus, the emphasis has been on showing how in certain static situations, the electromagnetic interaction can be mediated locally only by means of the potentials, and not by the corresponding zero fields. It is the enforcing of locality in the electron-electromagnetic field interactions that automatically forces one to attach a special physical significance to the potentials whenever the A-B conditions (**E** = 0, **B** = 0, **A** ≠ 0, Φ ≠ 0) are met.

[5] However, the ideas for measuring the electromagnetic potentials contained in works by *Lee et al.* [1992] and *Gelinas* [1984] suggest the possibility of carrying out such measurements by means of the A-B effect also under time-varying conditions. From an engineering standpoint, this immediately leads to a number of fundamental and practical questions. For example, from the points of view of communications and remote sensing, one naturally wonders whether anything fundamentally new can be obtained by using devices that measure the potentials, e.g., by means of the A-B effect, as opposed to more conventional devices (antennas) that sense the electric and magnetic field vectors. The central goal of this paper is thus to elucidate the role of time-dependent potentials in more general electrodynamic versions of the A-B effect. The question raised in the electrodynamic case is schematically illustrated in Figure 1b. Ultimately we wish to clarify whether the potentials and the A-B effect can (or cannot) yield anything fundamentally new in communications and remote sensing applications with time-varying, information-carrying electromagnetic fields. Methodologically, we use a new nonradiating (NR) source [*Devaney and Wolf*, 1973] presentation from the point of view of electromagnetic potentials to examine the realizability of the postulated A-B conditions.