Quantum gravity proposals at the leading perturbative order, such as the quantisation of linearized gravity, or the low-energy effective action like in string theory, provide the dynamics for the gravitons.
However, the kinematic picture is often not mentioned, or at least how they are consistent with the classical descriptions. In GR, kinematics is expressed in terms of events, curves, etc on the manifold. In a quantum superposition of two different graviton excitations in a weak regime, is the kinematic description simply an effective superposition of two geometries sourced by the gravitons?
In particular, how does the geodesic principle change? Can one depict a test particle's trajectory as superpositions of two geodesics on different backgrounds corresponding to different graviton excitations?
Does string theory or any other QG proposals give answers to how the kinematics scheme change and consistent with GR in some classical limit?
Any relevant literature is welcome.