Signatures of a gravitational quantum vacuum on massive particles

We study the interaction of massive particles with a quantized gravitational field in its vacuum state. We study two specific scenarios: free particles and two particles coupled through a linear spring. We find that the dynamics of the particles depend on the choice of coordinate or geodesic separation. In the case of the free particles, the dynamics of the frame-dependent coordinate depend only on the momentum of the system. This contrasts with the dynamics of the geodesic separation which also depends on position. For the spring system the signatures of the vacuum, such as a frequency shift, depend strongly on the high-frequency cut-off of the gravitational field. These findings highlight the crucial role of different position observables at the interface of quantum mechanics and gravity. It should clarify discrepancies among existing models of gravitational decoherence, potentially advancing our understanding of quantum gravitational effects in massive systems.