Emergence of Time from Quantum Interaction with the Environment

The nature of time as emergent for a system by separating it from its environment has been put forward by Page and Wootters [Phys. Rev. D 27, 2885 (1983)PRVDAQ0556-282110.1103/PhysRevD.27.2885] in a quantum mechanical setting neglecting interaction between system and environment. Here, we add strong support to the relational concept of time by deriving the time-dependent Schrödinger equation for a system from an energy eigenstate of the global Hamiltonian consisting of system, environment, and their interaction. Our results are consistent with concepts for the emergence of time where interaction has been taken into account at the expense of a semiclassical treatment of the environment. Including the coupling between system and environment without approximation adds a missing link to the relational time approach opening it to dynamical phenomena of interacting systems and entangled quantum states.