Subtleties of Invariance, Covariance and Observer Independence

TL;DR

This paper clarifies the distinctions between invariance, covariance, and observer dependence in physics, emphasizing the importance of explicit observer roles in relativistic and classical contexts.

Contribution

It provides a clear analysis of how observer roles influence physical quantities, addressing common misconceptions in relativity and electrodynamics.

Findings

Highlights the importance of explicit observer roles in physical equations

Clarifies the difference between invariance and observer dependence

Provides examples in relativistic kinematics and electrodynamics

Abstract

The role of the observers is frequently obscured in the literature, either by writing equations in a coordinate system implicitly pertaining to some specific observer or by entangling the invariance and the observer dependence of physical quantities. Using examples in relativistic kinematics and classical electrodynamics we clarify the confusion underlying these misconceptions.