engleski

"True transformations relativity" and electrodynamics

Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach, which we call the "true transformations (TT) relativity." In this approach a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor (when no basis has been introduced) or equivalently by a coordinate-based geomtric quantity comprising both components and a basis (when some basis has been introduced). This invariant approach is compared with the usual covariant approach, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference. 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 lenght. This formulation is called the "apparent transformations (AT) relativity." It is shown that the principal difference between these approaches arises from the difference in the concept of sameness of a physical quantity for different observers. This difference is invesitgated considering the spacetime length 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 (3-vectors) of the electric and magnetic field E and B are the AT. Furthermore it is proved that the Maxwell equations with the electromagneti field tensor F^ab and the usual Maxwell equations with E and B are not equivalent, and that the Maxwell equationwith E and B do not remain unchanged in form when the Lorentz transformations of the ordinary derivative operators and the AT of E and B are used. 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 phi^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.

true transformations relativity; electrodynamics

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