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We study relativistic effects on polarised photons that travel in a curvedspacetime. As a concrete application, we consider photons in the gravitationalfield of the Earth, on a closed path that starts at a terrestial laboratory, isreflected at one or more satellites, and finally returns to the laboratory. Wefind that the photons acquire a non-trivial Wigner phase already when thegravitational field is static, such as the Schwarzschild spacetime, whereprevious studies have found a trivial Wigner phase for closed photon paths. Agauge-invariant description of this nontrivial Wigner phase remains an openquestion, to be resolved before the formalism can provide predictions forexperiments.

Wigner phase of photonic helicity states in the spacetime of the Earth