Electric and magnetic fields: Do they need Lorentz covariance?

Abstract

Electric and magnetic fields are relative. They depend not only on a choice of electromagnetic sources via Maxwell equations, but also on a choice of observer, a choice of material reference-system. In 1908 Minkowski defined electric and magnetic fields on a four-dimensional spacetime, as tensorial concomitants of observer. Minkowski defined Lorentz-group-covariance of concomitant tensor field as group-action that commute with contractions. Present-day textbooks interpret Lorentz-group-covariance of concomitant tensor differently than Minkowski in 1908. In 2003-2005 Tomislav Ivezíc re-invented Minkowski's group-covariance. Different interpretations of group-covariance, lead to different relativity transformations of electric and magnetic fields. An objective of present article is to explore third possibility, implicit in [Minkowski 1908, 11.6], where a set of all relativity transformations of all material observers forms a groupoid category, which is not a group. © Published under licence by IOP Publishing Ltd.