Quantum astrometric observables I: time delay in classical and quantum gravity

TL;DR

This paper introduces and analyzes astrometric observables, focusing on time delay, as tools to probe causal structure in classical and quantum gravity, including quantum fluctuations and implications for causality in quantum gravity.

Contribution

It defines diffeomorphism invariant astrometric observables, analyzes the classical time delay, and sketches a quantum model with vacuum fluctuation effects, exploring causality in quantum gravity.

Findings

Time delay satisfies inequalities related to causal structure.

Quantum fluctuations affect the variance of the observable.

Perturbative calculations cannot definitively determine causality violations.

Abstract

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.