Quantum astrometric observables II: time delay in linearized quantum gravity

Understand

A clock synchronization thought experiment is modeled by a diffeomorphism invariant "time delay" observable.

• In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime.
• Thus, upon quantization, it is sensitive to the long expected smearing of the light cone by vacuum fluctuations in quantum gravity.
• After perturbative linearization, its mean and variance are computed in the Minkowski Fock vacuum of linearized gravity.