  In [M. Zych et al., Nat. Commun. 2, 505 (2011)], the authors predicted that
the interferometric visibility is affected by a gravitational field in way that
cannot be explained without the general relativistic notion of proper time. In
this work, we take a different route and start deriving the same effect using
the unitary representation of the local Lorentz transformation in the Newtonian
Limit. In addition, we show that the effect on the interferometric visibility
due to gravity persists in different spacetime geometries. However, the
influence is not necessarily due to the notion of proper time. For instance, by
constructing a `astronomical' Mach-Zehnder interferometer in the Schwarzschild
spacetime, the influence on the interferometric visibility can be due to
another general relativistic effect, the geodetic precession. Besides, by using
the unitary representation of the local Lorentz transformation, we show that
this behavior of the interferometric visibility is general for an arbitrary
spacetime, provided that we restrict the motion of the quanton to a
two-dimensional spacial plane.
