Frames of Reference and Some of its Applications

TL;DR

This paper introduces a novel framework combining meta-rigid motions and chorodesic synchronization to analyze a 3D geometry with constant curvature, with implications for physical applications.

Contribution

It defines a new concept of frames of reference integrating geometric and physical elements, extending previous notions like Born motion.

Findings

Uncovered a 3D geometry with constant curvature.

Linked geometric structures to physical applications.

Provided a unified view of reference frames and synchronization.

Abstract

We define a Frame of reference as a two ingredients concept: A meta-rigid motion, which is a generalization of a Born motion, and a chorodesic synchronization, which is an adapted foliation. At the end of the line we uncover a low-level 3-dimensional geometry with constant curvature and a corresponding coordinated proper-time scale. We discuss all these aspects both from the geometrical point of view as from the point of view of some of the physical applications derived from them.