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Invariance of Maxwell’s equations to Lorentz transformations: conceptual bridges through derivation as an alternative to tensorial calculus

In the tradition of the disciplinary field of Physics, and in the underlying textbooks, the invariance of Maxwell’s equations by Lorentz transformations is usually presented via tensor calculus, which results in its teaching being postponed until (supposedly) the target students master this formalism. This can result, in the most deformed curriculum disputes, that many do not even have instructional access to this topic, with relevant implications for the advanced knowledge of Modern and Contemporary Physics. From this diagnosis, we developed an alternative to proceed with that presentation using only basic derivation operations, such as the chain rule. In the direction of associable teaching and learning processes, we rely on the theoretical contribution of conceptual bridges, developed by us from Gérard Vergnaud’s cognitive epistemology thought for a homologous object. This referential congruence artifice sought to establish the possibility of transition of the approaches, without hierarchy, but with the clear implication that the demonstrated alternative could easily be introduced in initial disciplines of Electromagnetism, typically taken in the first cycle of Physics and Engineering courses, contributing to the resumption of progression of the subject in advanced modules.

Keywords:
Conceptual bridges; Tensorial calculus; Derivation; Maxwell’s equations; Lorentz transformations


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