Moving dipoles and the relativity of simultaneity

Abstract

An observer moving parallel to a current-carrying wire detects an electric field due to the Lorentz transformation directed either toward or away from the wire, depending on the relative motion of observer and current. The accepted interpretation of this situation as viewed from the observer’s rest frame is that there is a net linear charge density on the wire. The Lorentz contraction of the separation of fixed ions and charge carriers is different due to their different speeds in the observer’s frame. The idea that a net charge exists on a wire in a reference frame moving parallel to the wire leads to the expectation that there is a charge separation seen on a moving current loop, resulting in paradoxes, such as that proposed by Mansuripur. I argue that the apparent charge on a current-carrying wire is due to a misinterpretation of the Lorentz transformation and is a consequence of the relativity of simultaneity. Given this insight, the nature of the fields of moving dipoles and the nature of the magnetization–polarization tensor are investigated.