A lightbulb-and-mirror protocol defines diffeomorphism-invariant elapsed proper time, and its leading quantum gravity correction makes the time a noncommuting quantum operator.
Observables in Quantum Gravity: from Theory to Experiment
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Observer Time from Causality in Perturbative Quantum Gravity
A lightbulb-and-mirror protocol defines diffeomorphism-invariant elapsed proper time, and its leading quantum gravity correction makes the time a noncommuting quantum operator.