The role of the two postulates of special relativity

TL;DR

This paper clarifies the distinct roles of the two postulates of special relativity using geometric methods, enhancing understanding of how they lead to covariance and analyzing standard derivations for clarity.

Contribution

It provides a clear geometric elucidation of the roles of the postulates and analyzes textbook derivations to clarify their physical basis.

Findings

Separation of the roles of the postulates improves conceptual understanding.

Geometric methods effectively illustrate the derivation of covariance.

Analysis of textbook derivations highlights their physical assumptions.

Abstract

Students are often mystified by the reasoning that leads from the postulates of special relativity to the requirement of covariance. This is partly due to the lack of transparency resulting from the failure to clearly separate the roles the postulates of the constancy of the speed of light and of relativity play. Their roles are elucidated here by mainly geometric means. Finally some standard derivations found in textbooks are analyzed in order to sort out the basic physical ingredients.