Relativistic versus Newtonian frames: emission coordinates

TL;DR

This paper discusses the unique causal class of null emission coordinates in relativistic spacetime, which enable gravity-free, immediate positioning systems based on four emitters broadcasting proper times, applicable universally to any observer.

Contribution

It identifies the privileged causal class of null emission coordinates that do not exist in Newtonian spacetime, establishing a foundation for relativistic positioning systems.

Findings

Null emission coordinates form a unique causal class in Lorentzian spacetime.

These coordinates are covariant and frame-independent.

Any observer can determine their position from four emitters broadcasting proper times.

Abstract

Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian spacetime, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his(her) null emission coordinates from the emitters which provide him his(her) trajectory.