This paper analyses magnetosphere-ionosphere (MI) coupling from a perspective that is independent of inertial reference frame, explicitly acknowledging the role of the principle of relativity in MI coupling. For the first time in the context of MI coupling, we discuss the literature on the low-velocity limit of the theory of special relativity applied to electrodynamics. In many MI coupling theories, a particular low-velocity limit applies, known as the “magnetic limit”. Two important consequences of the magnetic limit are: 1) Maxwell’s equations cannot contain a displacement current and be consistent with the magnetic limit and 2) the magnetic field is not modified by currents created by charge densities in motion, thus charge density is approximately zero. We show how reference frame-independent descriptions of MI coupling require that ion-neutral relative velocities and ion-neutral collisions are key drivers of the physics. Electric fields, on the other hand, depend on reference frame, and can be zero in an appropriate frame. Currents are independent of reference frame and will flow when the electric field is close to zero. Starting with the same momentum equations that are typically used to derive Ohm’s law, we derive an equation that relates the perpendicular current to collisions between ions and neutrals, and electrons and neutrals, without reference to electric fields. Ignoring the relative motion between ions and neutrals will result in errors exceeding 100% for estimates of high latitude Joule heating during significant geomagnetic storms when ion-neutral velocity differences are largest near the initiation of large-scale ion convection.