On the possibility of a relativistic correction to the E and B fields around a current-carrying wire

It is well known that electric and magnetic fields may change when they are observed from different frames of reference. For example, the motion of a charged probe particle moving parallel to a current-carrying wire would be described by utilizing different electric or magnetic fields, depending on from which frame of reference the system is observed and described. To describe the situation in all frames by utilizing the theory of relativity, one has to first describe the situation in one particular frame, and this choice in the case of a current-carrying wire is the topic of this paper. Specifically, I consider the question of in which frame the current carrying wire is neutral. The importance of relaxation processes is emphasized. As an example, I examine a specific alternative to the standard choice, and consider its theoretical and experimental validity. An outcome of alternative approaches is that in the rest frame of a wire, running a current introduces also an electric field by giving rise to a minute charge. Present day experimental sensitivities, specifically those of cold ions, may be able to differentiate between the observable signatures predicted by the different approaches.