Physical Components, Coordinate Components, and the Speed of Light

TL;DR

This paper explains how to convert coordinate components to physical components in generalized coordinate systems, clarifies their importance in experiments, and discusses the implications for the speed of light in non-inertial frames.

Contribution

It provides a comprehensive derivation of the method to obtain physical components from coordinate components, a topic rarely covered in relativity education.

Findings

Method for converting coordinate to physical components explained

Clarification on whether the speed of light equals c in non-inertial frames

Bridging the gap between applied mechanics and relativity calculations

Abstract

For generalized coordinate systems, the numerical values of vector and tensor components do not generally equal the physical values, i.e., the values one would measure with standard physical instruments. Hence, calculating physical components from coordinate components is important for comparing experiment with theory. Surprisingly, however, this calculational method is not widely known among physicists, and is rarely taught in relativity courses, though it is commonly employed in at least one other field (applied mechanics.) Different derivations of this method, ranging from elementary to advanced level, are presented. The result is then applied to clarify the oftentimes confusing issue of whether or not the speed of light in non-inertial frames is equal to c.