2003/11/10 by Tomislav Ivezić, Tomislav Ivezic, Ivezic, Tomislav
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Numerical methods for differential equations #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0311043
REVTeX 4, 20pages
arxiv created 2003/11/10 · openalex publication_date 2003/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper it will be exactly proved both in the geometric algebra and tensor formalisms that the usual Maxwell equations with the three-dimensional (3D) vectors of the electric and magnetic fields, Ebold and Bbold respectively, are not, contrary to the general opinion, Lorentz covariant equations. Consequently they are not equivalent to the field equations with the observer independent quantities, the electromagnetic field tensor Fsupab (tensor formalism) or with the bivector field F (the geometric algebra formalism). Different 4D algebric objects are used to represent the standard observer dependent and the new observer independent electric and magnetic fields. The proof of a fundamental disagreement between the standard electromagnetism and the special relativity does not depend on the character of the 4D algebric object used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EsubHL and BsubHL and the abstract tensors, the 4-vectors Esupa and Bsupa. All these quantities are defined without reference frames. Such field equations are in a complete agreement with experiments.