In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.

One of the classical tests of general relativity is the precision measurements by Pound and Rebka of red-shift/blue-shift of photons in a gravitational field. In this essay, we lay out a temporal version of the Pound-Rebka experiment. The emission and absorption of photons occurs at different times, rather than at different spatial locations as in the original Pound-Rebka experiment. This temporal Pound-Rebka experiment is equivalent to a gravitational Aharonov-Bohm Effect and is testable via current or near future satellite experiments.

We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time-it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the AharonovBohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.

A novel version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time varying, spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the 2-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric AB effect and the AC Stark effect.

In this paper we investigate the scalar Aharonov-Bohm (AB) effect in two of its forms, i.e., its electric form and its gravitational form. The standard form of the electric AB effect involves having particles (such as electrons) move in regions with zero electric field but different electric potentials. When a particle is recombined with itself, it will have a different phase, which can show up as a change in the way the single particle interferes with itself when it is recombined with itself. In the case where one has quasi-static fields and potentials, the particle will invariably encounter fringing fields, which makes the theoretical and experimental status of the electric AB effect much less clear than that of the magnetic (or vector) AB effect. Here we propose using time varying fields outside of a spherical shell, and potentials inside a spherical shell to experimentally test the scalar AB effect. In our proposal a quantum system will always be in a field-free region but subjected to a non-zero time-varying potentials. Furthermore, our system will not be spatially split and brought back together as in the magnetic AB experiment. Therefore there is no spatial interference and hence no shift in a spatial interference pattern to observe. Rather, there arises purely temporal interference phenomena. As in the magnetic AB experiments, these effects are non-classical. We present two versions of this idea: (i) a Josephson temporal interferometry experiment inside a superconducting spherical shell with a time-varying surface charge; (ii) a two-level atom experiment in which the atomic spectrum acquires FM sidebands when it is placed inside a spherical shell whose exterior mass is sinusoidally varying with time. The former leads to a time-varying internal magnetic field, and the latter leads to a time-varying gravitational redshift.