dorsal/arxiv
View SchemaThe Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations
| Authors | Tomislav Ivezic |
|---|---|
| Categories | |
| ArXiv ID | physics/0409118 |
| URL | https://arxiv.org/abs/physics/0409118 |
| DOI | 10.1007/s10701-005-6484-y |
| Journal | Found.Phys. 35 (2005) 1585-1615 |
Abstract
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebric objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebric objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors E_{Hv} and B_{Hv} and the abstract tensors, the 4-vectors E^{a} and B^{a}. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D E and B and their ST.
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"abstract": "In this paper the Lorentz transformations (LT) and the standard\ntransformations (ST) of the usual Maxwell equations (ME) with the\nthree-dimensional (3D) vectors of the electric and magnetic fields, E and B\nrespectively, are examined using both the geometric algebra and tensor\nformalisms. Different 4D algebric objects are used to represent the usual\nobserver dependent and the new observer independent electric and magnetic\nfields. It is found that the ST of the ME differ from their LT and consequently\nthat the ME with the 3D E and B are not covariant upon the LT but upon the ST.\nThe obtained results do not depend on the character of the 4D algebric objects\nused to represent the electric and magnetic fields. The Lorentz invariant field\nequations are presented with 1-vectors E and B, bivectors E_{Hv} and B_{Hv} and\nthe abstract tensors, the 4-vectors E^{a} and B^{a}. All these quantities are\ndefined without reference frames, i.e., as absolute quantities. When some basis\nhas been introduced, they are represented as coordinate-based geometric\nquantities comprising both components and a basis. It is explicitly shown that\nthis geometric approach agrees with experiments, e.g., the Faraday disk, in all\nrelatively moving inertial frames of reference, which is not the case with the\nusual approach with the 3D E and B and their ST.",
"arxiv_id": "physics/0409118",
"authors": [
"Tomislav Ivezic"
],
"categories": [
"physics.gen-ph"
],
"doi": "10.1007/s10701-005-6484-y",
"journal_ref": "Found.Phys. 35 (2005) 1585-1615",
"title": "The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations",
"url": "https://arxiv.org/abs/physics/0409118"
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