2000/12/20 by Tomislav Ivezic
Physics and Astronomy · #physics.class-ph #gr-qc #physics.gen-ph
published as Found.Phys. 31 (2001) 1139-1183 · 27 pages, 4 figures, conference IARD 2000, to be published in Foundations of Physics
arxiv created 2000/12/20 · arxiv updated 2009/11/30
Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based geometric quantities comprising both components and a basis. This approach we call the ''true transformations (TT) relativity.'' It is compared with the usual covariant approach, which mainly deals with the basis components of true tensors. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from ''3+1'' space and time, e.g., the synchronously determined spatial length. This formulation is called the ''apparent transformations (AT) relativity.'' The spacetime length is considered in the ''TT relativity'' and spatial and temporal distances in the ''AT relativity.'' It is also found that the usual transformations of the three-vectors of the electric and magnetic fields \QTRbfE and \QTRbfB are the AT. The Maxwell equations with Fab are written in terms of the 4-vectors of the electric Ea and magnetic Ba fields. The covariant Majorana electromagnetic field 4-vector Ψa is constructed by means of 4-vectors Ea and Ba and the covariant Majorana formulation of electrodynamics is presented. A Dirac like relativistic wave equation for the free photon is obtained.