Quantum rods and clock in a gravitational universe

Local operators are the basic observables in quantum field theory which encode the physics observed by a local experimentalist. However, when gravity is dynamical, diffeomorphism symmetries are gauged which apparently obstruct a sensible definition of local operators, as different locations in spacetime are connected by these gauged symmetries. This consideration brings in the puzzle of reconciling our empirical world with quantum gravity. Intuitively, this puzzle can be avoided using relatively defined observables when there exists a natural reference system such as a distribution of galaxies in our Universe. Nevertheless, this intuition is classical as the rods and clock defined in this way may also have quantum fluctuations, so it is not clear if it can be realized in the quantum regime. In this paper, we provide an affirmative answer to this question. Interestingly, we notice that the quantum fluctuations of the reference system are in fact essential for the realization of the above intuition in the quantum regime.