  A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has
triggered interest in the question of how to include relativistic corrections
in the quantum dynamics governing many-particle systems in a gravitational
field. Here we show how the center-of-mass motion of a quantum system subject
to gravity can be derived more rigorously, addressing the ambiguous definition
of relativistic center-of-mass coordinates. We further demonstrate that,
contrary to the prediction by Pikovski et al., external forces play a crucial
role in the relativistic coupling of internal and external degrees of freedom,
resulting in a complete cancellation of the alleged coupling in Earth-bound
laboratories for systems supported against gravity by an external force. We
conclude that the proposed decoherence effect is an effect of relative
acceleration between quantum system and measurement device, rather than a
universal effect in gravitational fields.
