The invariant formulation of special relativity, or the "true   transformations relativity", and electrodynamics
  In the invariant approach to special relativity (SR), which we call the ''true transformations (TT) relativity,'' a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor or equivalently by a coordinate-based geometric quantity comprising both components and a basis. This invariant approach differs both from 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,.and 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 noncovariant formulation of SR is called the ''apparent transformations (AT) relativity.'' The principal difference between the ''TT relativity'' and the ''AT relativity'' arises from the difference in the concept of sameness of a physical quantity for different observers. In the second part of this paper we present the invariant formulation of electrodynamics with the electromagnetic field tensor F^{ab}, and also the equivalent formulation in terms of the four-vectors of the electric E^{a} and magnetic B^{a} fields. 
Tomislav Ivezic