On conceptual issues in classical electrodynamics: Prospects and problems of an action-at-a-distance interpretation

Some conceptual issues in the foundations of classical electrodynamics concerning the interaction between particles and fields have recently received increased attention among philosophers of physics. After a brief review of the debate, I argue that there are essentially two incompatible solutions to these issues corresponding to F.A. Muller's distinction between the extension and the renormalization program. Neither of these solutions comes free of cost: the extension program is plagued with all problems related to extended elementary charges, the renormalization program works with point charges but trades in the notorious divergences of the field energies. The aim of this paper is to bring back into the discussion a third alternative, the action-at-a-distance program, which avoids both the riddles of extended elementary charges as well as the divergences although it admittedly has other problems. It will be discussed, why action-at-a-distance theories are actually not a far cry from particle–field theories, and I will argue that the main reasons for rejecting action-at-a-distance theories originate in certain metaphysical prejudices about locality and energy conservation. I will broadly suggest how these concepts could be adapted in order to allow for action at a distance.