Abstract

This article discusses a selection of problems that ensue from (over-)using local description in inherently global situations. Two cases, discussed here, are Faraday's law of induction and the kinship of the Michelson-Morley and Sagnac interferometer experiments. Conceptual predicaments created by standard (local) approaches are first discussed in setting the stage for learning how to deal with the differentiation of integral expressions describing global situations. Once the results thereof have been secured, the business of repair begins. The global Faraday induction law gives rise to the source-free Maxwell equations as well as the Lorentz force law. The Michelson and Sagnac experiments end up in unified description, invoking minimal relativity precepts, here shared by special and general theory: i.e., constancy of the speed of light. The latter premise is valid for both, as long as gravity profiles remain "flat" on an astronomical scale. All of which brings us to the local concept of the Weber potential, which, after the revision by Phipps, is not only compatible with, but a sine qua non for a relativity view of E&M theory. Its application improves the logic and precision of the Sommerfeld-Dirac view of hydrogen fine structure. These efforts at conceptual integration make the Lorentz group a much more abstract item than hitherto perceived.