Generalised Maxwell theories - theoretical structure and experimental tests

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The electromagnetic field is one of the most important system in physics. All the information we are receiving and all measurements we are doing rely on electrodynamics. Though the Maxwell equations provide an extremely successful description of all electromagnetic phenomena there are reasons to reconsider this theory: (i) The standard formulation of electrodynamics leads to severe problems in the self-force problem (radiation reaction) of charged point particles. One derives unphysical pre-acceleration as well as run-away solutions. (ii) In constructive axiomatic approaches to establish the space-time geometry of General (and Special) Relativity the unique properties of light play an essential role. Any modification of the phenomena of electrodynamics will also be directly related to a modified space-time geometry. This is also related to (iii) the search for a theory of Quantum Gravity. Since according to our present understanding General Relativity and Quantum Theory are theoretically not compatible, a new theory combining the geometric and quantum aspects of our world has to be different from at least one of these theories what, for consistency, also would change the Maxwell equations. Accordingly, it is of utmost importance to find out whether the equations underlying all electromagnetic phenomena are the well-known Maxwell equations or whether one has to take into account modifications.Accordingly, we have to discuss all possible modifications in a structured way and then to explore the experimental significance of these modifications. Thereby we will proceed in a systematic way in that we discuss non-linear, non-local and non-homogeneous extensions of the Maxwell equations. For these modifications we discuss wave propagation, stationary solutions for point sources, the equation of motion for charged particles including self-force, the hydrogen atom, and the Equivalence Principle for electromagnetically bound systems. Whereas the planned investigation is theoretical, it will also be of high relevance in view of experiments: It will provide additional or new interpretations of experiments that have already been done, and it will also suggest new experiments dedicated to particular aspects of the Maxwell equations. If it turns out that there might be modifications of these equations all measurements and observations have to be re-interpreted.Orléans and Bremen are amongst the most active groups worldwide in this research area. This project will benefit from a mixture of common and complementary expertise. Both groups are connected to top-level international collaborations. The coordinators, additional applicants together with further co-workers will be a strong collaborating team in order to work on the proposed work plan.