GPS observables in general relativity

TL;DR

This paper introduces gauge-invariant observables in general relativity, defined via GPS-like measurements, providing a realistic physical interpretation and local evolution equations for the metric components.

Contribution

It presents a complete set of gauge-invariant observables in general relativity using a minimal matter setup, linking them to practical GPS measurements.

Findings

Gauge-invariant metric components defined by GPS readings

Physical reference system established by GPS signals

Local evolution equations for metric components

Abstract

I present a complete set of gauge invariant observables, in the context of general relativity coupled with a minimal amount of realistic matter (four particles). These observables have a straightforward and realistic physical interpretation. In fact, the technology to measure them is realized by the Global Positioning System: they are defined by the physical reference system determined by GPS readings. The components of the metric tensor in this physical reference system are gauge invariant quantities and, remarkably, their evolution equations are local.