On the physical meaning of Fermi coordinates

TL;DR

This paper investigates the limitations of Fermi coordinates in curved spacetime, proposes modifications, and explores their implications for physical systems like atomic interferometry.

Contribution

It introduces a modified construction of Fermi coordinates applicable in curved spacetime and analyzes its effects on physical predictions, such as phase shifts in atomic interferometry.

Findings

Modified Fermi coordinates can be constructed with different principles.

The modifications lead to different predictions for physical systems.

In particular, phase shifts in atomic interferometry are affected.

Abstract

(Some Latex problems should be removed in this version) Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space and even not in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. One proposal for a modification is made and applied to the observer with constant acceleration in the two and four dimensional Minkowski space. The two dimensional case has some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification leads also to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.