Quantum astrometric observables: Time delay in classical and quantum gravity

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.

Observables for general relativity related to geometry

“…Notice, however, that as geometric as it is, GPS needs at least n observers to identify points of an n-dimensional spacetime. It is worth noting, that there are modifications of the idea of GPS which use only two observers to define a sensible observable [4,5].…”

Gauge-invariant quantum gravitational corrections to correlation functions

“…Therefore, in a sense the field-dependent coordinatesX µ determine a coordinate system which is "as straight as possible" in the perturbed geometry. While usually one would think of constructing such a coordinate system using (perturbed) geodesics, using geodesics in the construction of invariant correlation functions leads to highly singular results [26,42,43], and does not seem very viable. Note that in contrast to other approaches to construct invariant observables at higher order, in particular in the context of cosmology [44][45][46][47][48][49][50], our construction is systematic to all orders and independent of the actual gravitational theory.…”

Local and gauge invariant observables in gravity

“…That is, given a particular observable of this kind, it may not be immediately clear what kind of experimental protocol would be modeled by it (this issue is discussed clearly in [22]). On the other hand, there is some existing literature that has considered relational observables in linearized and perturbative gravity with more clear phenomenological interpretations, but ran into UV divergences in explicit computations [14,39,5,35,38,36,27,22,4]. Perhaps replacing the overly singular proposed observables in these references with regularized versions written as local and gauge invariant observables would yield a double benefit: provide certain local observables with phenomenological interpretations, diffuse UV singularities in explicit computations.…”