On Reference Frames and Coordinate Transformations

TL;DR

This paper clarifies the distinctions between frame and coordinate transformations in relativity, emphasizing the role of tetrad fields and analyzing electromagnetic energy-momentum in various frames.

Contribution

It provides a detailed comparison of frame and coordinate transformations, highlighting the importance of tetrad fields and their impact on electromagnetic theory.

Findings

Maxwell's equations are invariant under coordinate transformations.

Maxwell's equations are covariant under frame transformations.

Electromagnetic energy-momentum varies with different frames.

Abstract

This article explores the differences between frame and coordinate transformations in relativistic theories. We highlight the key role of tetrad fields in connecting spacetime and frame indices. Using Maxwell's electrodynamics as an example, we show that Maxwell's equations are invariant under coordinate transformations but exhibit covariant behavior under frame transformations. We also analyze the energy-momentum of an electromagnetic field in different frames, providing deeper insights into the implications of different frames of reference and coordinate systems.