Freely falling point-like objects converge towards the center of the Earth.
Hence the gravitational field of the Earth is inhomogeneous, and possesses a
tidal component. The free fall of an extended quantum object such as a hydrogen
atom prepared in a high principal-quantum-number stretch state, i.e., a
circular Rydberg atom, is predicted to fall more slowly that a classical
point-like object, when both objects are dropped from the same height from
above the Earth. This indicates that, apart from "quantum jumps," the atom
exhibits a kind of "quantum incompressibility" during free fall in
inhomogeneous, tidal gravitational fields like those of the Earth. A
superconducting ring-like system with a persistent current circulating around
it behaves like the circular Rydberg atom during free fall. Like the electronic
wavefunction of the freely falling atom, the Cooper-pair wavefunction is
"quantum incompressible." The ions of the ionic lattice of the superconductor,
however, are not "quantum incompressible," since they do not possess a globally
coherent quantum phase. The resulting difference during free fall in the
response of the nonlocalizable Cooper pairs of electrons and the localizable
ions to inhomogeneous gravitational fields is predicted to lead to a charge
separation effect, which in turn leads to a large repulsive Coulomb force that
opposes the convergence caused by the tidal, attractive gravitational force on
the superconducting system. A "Cavendish-like" experiment is proposed for
observing the charge separation effect induced by inhomogeneous gravitational
fields in a superconducting circuit. This experiment would demonstrate the
existence of a novel coupling between gravity and electricity via
macroscopically coherent quantum matter.Comment: `2nd Vienna Symposium for the Foundations of Modern Physics'
Festschrift MS for Foundations of Physic