  A class of diffeomorphism invariant, physical observables, so-called
astrometric observables, is introduced. A particularly simple example, the time
delay, which expresses the difference between two initially synchronized proper
time clocks in relative inertial motion, is analyzed in detail. It is found to
satisfy some interesting inequalities related to the causal structure of
classical Lorentzian spacetimes. Thus it can serve as a probe of causal
structure and in particular of violations of causality. A quantum model of this
observable as well as the calculation of its variance due to vacuum
fluctuations in quantum linearized gravity are sketched. The question of
whether the causal inequalities are still satisfied by quantized gravity, which
is pertinent to the nature of causality in quantum gravity, is raised, but it
is shown that perturbative calculations cannot provide a definite answer. Some
potential applications of astrometric observables in quantum gravity are
discussed.
