Electric and Magnetic Fields: Do They Need Lorentz Covariance?
|Title||Electric and Magnetic Fields: Do They Need Lorentz Covariance?|
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|No. of pages||29|
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7th Biennial Conf. on Classical and Quantum Relativistic Dynamics of Particles and Fields. Electric and magnetic �elds 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 defi�ned electric and magnetic �fields on a four-dimensional spacetime, as tensorial concomitants of observer. Minkowski de�ned Lorentzgroup-covariance of concomitant tensor �eld as group-action that commute with contractions. Present-day textbooks interpret Lorentz-group-covariance of concomitant tensor di�erently than Minkowski in 1908. In 2003-2005 Tomislav Ivez��ic re-invented Minkowski's group-covariance. Diff�erent interpretations of group-covariance, lead to di�fferent relativity transformations of electric and magnetic �fields.
An objective of present article is to explore third possibility, implicit in [Minkowski 1908, x11.6], where a set of all relativity transformations of all material observers forms a groupoid category, which is not a group.