Are Maxwell's equations Lorentz-covariant?

TL;DR

This paper examines whether Maxwell's equations are inherently Lorentz-covariant or if they require specific transformation properties to exhibit covariance, clarifying the distinction between potentiality and actual covariance.

Contribution

It clarifies that Maxwell's equations are capable of being Lorentz-covariant when appropriate transformation properties are postulated, distinguishing potentiality from actual covariance.

Findings

Maxwell's equations are compatible with Lorentz covariance

Covariance depends on postulated transformation properties

The covariance is a potentiality, not an inherent feature

Abstract

The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are perfectly fit to be Lorentz-covariant; they become Lorentz-covariant if we construct to be so, by postulating certain transformation properties of field functions. In Aristotelian terms, the covariance is a plain potentiality, but not necessarily entelechy.