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 defined electric and magnetic fields on a four-dimensional spacetime, as tensorial concomitants of observer. Minkowski dened Lorentzgroup-covariance of concomitant tensor eld as group-action that commute with contractions. Present-day textbooks interpret Lorentz-group-covariance of concomitant tensor dierently than Minkowski in 1908. In 2003-2005 Tomislav Ivezic 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, x11.6], where a set of all relativity transformations of all material observers forms a groupoid category, which is not a group.