Clocks and dynamics in quantum models of gravity

Abstract

We investigate how the quantum dynamics of gravitational models depends on the internal clock employed in quantisation. Our previous result on the quantum Friedmann-Lemaitre model demonstrates that almost all physical predictions from the quantum cosmological dynamics, e.g. the scale of the quantum bounce or the number of bounces, depend on the choice of internal clock. In the present paper we show that there exists an important prediction concerning the quantum dynamics which holds in all internal clocks. Namely, we prove that any quantum state asymptotically, i.e. away from a quantum interaction regime, admits a unique classical limit described by unique classical solutions irrespectively of the internal clock used for dynamical description of the given state. We demonstrate this property explicitly for the semiclassical Bianchi Type I model, which includes the semiclassical Friedmann-Lemaitre model as a special case. Our methods include the theory of pseudo-canonical transformations and the phase space portraits based on coherent states. As a by-product of the pursuit of our main goal, we elaborate the semiclassical description of anisotropic singularity resolution.