Time dependent perturbation theory from Wheeler De Witt solutions

TL;DR

This paper develops a framework in quantum cosmology to derive time and space intervals from Wheeler-DeWitt solutions, incorporating matter interactions and radiative processes to unify the emergence of spacetime concepts.

Contribution

It generalizes previous models by including matter interactions in Wheeler-DeWitt solutions and introduces a formalism for deriving space and time from quantum radiative processes.

Findings

Transition amplitudes derived from entangled gravity-matter systems.

Time parameter defined dynamically from matter transitions.

Spatial displacements emerge from radiative processes.

Abstract

We describe radiative processes in Quantum Cosmology, from the solutions of the Wheeler De Witt equation. By virtue of this constraint equation, the quantum propagation of gravity is modified by the matter interaction hamiltonian at the level of amplitudes. In this we generalize previous works where gravity was coupled only to expectation values of matter operators. By a ``reduction formula'' we show how to obtain transition amplitudes from the entangled gravity+matter system. Then we show how ``each'' transition among matter constituents of the universe determines dynamically ``its'' background from which a time parameter is defined. Finally, we leave the mini-superspace context by introducing an extended formalism in which the momenta of the exchanged quanta no longer vanish. Then, the concept of spatial displacement emerges from radiative processes like the time parametrization did, thereby unifying the way by which space and time intervals are recovered in quantum cosmology.