"True Transformations Relativity" and Electrodynamics
  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 $\QTR{bf}{E}$ and $\QTR{bf}{B}$ are the AT. The Maxwell equations with $F^{ab}$ are written in terms of the 4-vectors of the electric $E^{a}$ and magnetic $B^{a}$ fields. The covariant Majorana electromagnetic field 4-vector $\Psi ^{a}$ is constructed by means of 4-vectors $E^{a}$ and $B^{a}$ and the covariant Majorana formulation of electrodynamics is presented. A Dirac like relativistic wave equation for the free photon is obtained. 
Tomislav Ivezic