Discrete Relativistic Positioning Systems

TL;DR

This paper proposes a discrete, self-sufficient relativistic positioning system capable of operating without calibration or ground control, adaptable to various spacetime geometries and capable of testing gravitational theories.

Contribution

It introduces a novel relativistic positioning system that self-operates without calibration, applicable in multiple spacetime models, and can be used to test gravitational theories near horizons.

Findings

System works without calibration or clock synchronization.

Can determine gravitational mass in Schwarzschild spacetime.

Operates near horizons without weak field assumptions.

Abstract

We discuss the design for a discrete, immediate, simple relativistic positioning system (rPS) which is potentially able of self-positioning (up to isometries) and operating without calibration or ground control assistance. The design is discussed in dimension two on spacetime (i.e. one spatial dimension plus one time dimension), in Minkowski and Schwarzschild solutions, as well as in dimension three (i.e. two spatial dimensions plus one time dimension) in Minkowski. The system works without calibration, clock synchronizations, or a priori knowledge about the motion of clocks, it is able to self-diagnose hypotheses break down (for example, if one clock temporarily becomes not-freely falling, or the gravitational field changes) and it is automatically back and operational when the assumed conditions are restored. In the Schwarzschild case, we show that the system can also best fit the gravitational mass of the source of the gravitational field and stress that no weak field assumptions are made anywhere. In particular, the rPS we propose can work in a region close to the horizon since it does not use approximations or PPN expansions. More generally, the rPS can be adapted as detectors for the gravitational field and we shall briefly discuss their role in testing different theoretical settings for gravity. In fact, rPS is a natural candidate for a canonical method to extract observables out of a gravitational theory, an activity also known as designing experiments to test gravity.