  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.

General Relativity and Quantum Cosmology;Quantum Physics