  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.
