  We study relativistic effects on polarised photons that travel in a curved
spacetime. As a concrete application, we consider photons in the gravitational
field of the Earth, on a closed path that starts at a terrestial laboratory, is
reflected at one or more satellites, and finally returns to the laboratory. We
find that the photons acquire a non-trivial Wigner phase already when the
gravitational field is static, such as the Schwarzschild spacetime, where
previous studies have found a trivial Wigner phase for closed photon paths. A
gauge-invariant description of this nontrivial Wigner phase remains an open
question, to be resolved before the formalism can provide predictions for
experiments.
