From the classical self-force problem to the foundations of quantum mechanics and beyond

Classical electrodynamics and general relativity are successful non-theories: Plagued by the self-force problem, both are ill defined yet extremely practical. The paradox of a `practical non theory' is resolved in the current paper by showing that the experimentally valid content of classical electrodynamics can be extracted from a set of axioms, or constitutive relations, circumventing the ill-definedness of the self-force. A concrete realization of these constitutive relations by a well defined theory of testable content is presented, and it is argued that all previous attempts to resolve the self-force problem fail to do so, thus, at most, turning a non-theory into a theory - which is not classical electrodynamics. The proposed theory is shown to be compatible with the statistical predictions of quantum mechanics, thus providing an (observer independent) ontology in a `block universe' formulation. A straightforward generally covariant extension of the proposed theory of classical electrodynamics leads to a well defined general relativity incorporating matter, suggesting new interpretations of some astronomical observations. A tentative model of subatomic physics is sketched, which is based on the proposed theory of classical electrodynamics alone. Thus the failure to properly address the century old classical self-force problem may be at the crux of modern physics.