A Quantum Informational Approach to the Problem of Time

TL;DR

This paper uses quantum information theory to argue that the Hamiltonian constraint cannot define time in quantum gravity, but spontaneous symmetry breaking via quantum cosmological time crystals may enable the emergence of time.

Contribution

It introduces a quantum informational perspective to the problem of time and proposes that quantum cosmological time crystals can resolve existing issues.

Findings

Hamiltonian constraint cannot probe change in quantum gravity

Quantum Fisher information is absent for time-reparametrization invariant systems

Spontaneous symmetry breaking via quantum time crystals can enable time emergence

Abstract

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to obtain a meaningful notion of time. This is due to the absence of quantum Fisher information with respect to the quantum Hamiltonian of a time-reparametization invariant system. We also observe that the inability of this Hamiltonian to probe change can be related to its inability to discriminate between states of such a system. However, if the time-reparametization symmetry is spontaneously broken due to the formation of quantum cosmological time crystals, these problems can be resolved, and it is possible for time to emerge in quantum gravity.