This protracted development simplified the underlying concepts. Subsequently, the study of electromagnetic phenomena divides rather neatly into two parts. The first is concerned with bodies. In addition to such mechanical concepts as 'space', 'time', 'mass', and 'force', one adds a new distinctively electromagnetic concept, 'charge'. Classical electromagnetism includes the assumption that macroscopic bodies are made up of atoms and molecules, that atoms have electrons, that charged particles produce electrostatic fields, that charged particles in motion produce magnetic fields. Further properties depend on grouping bodies as insulators or conductors; dielectric, paramagnetic, ferromagnetic, etc., and measuring resistance, electrical polarizability, and related properties (See Cook, 1975, chaps. 9‑12). The details are not our immediate concern. The pertinent point is the conceptual framework. It is still the familiar world of macroscopic objects, supplemented by the new properties required to explain and systematize electromagnetic phenomena. However, it also includes the assumption that macroscopic bodies are made up of atoms, and that atoms have parts which are held together by electrical forces. It does not include any detailed models of the atom.
The second component is the electromagnetic field. In place of ontological assumptions concerning a substratum it became customary to treat the electromagnetic field as a separate entity. The interaction between the field and matter hinges on the principle of minimal electromagnetic coupling. Charges produce fields and fields act on charges: an electric field on an electric charge; a magnetic field on a moving charge. The electric and magnetic fields were accepted as real because they are measurable. This leads to a familiar ontological interpretation of electrodynamics based on the reality of the electromagnetic field. This may be given the strong ontological interpretation that the field is local, i. e. the field at a point is determined only by its immediate environment, and deterministic. We will briefly consider three subsequent developments that have a bearing on the interpretation of classical electrodynamics.
In 1931 L. Landau and R. Peierls, both working at Bohr's Institute, wrote a paper questioning the logical consistency of quantum field theory. The essential problem was the effect of vacuum fluctuations and radiation reactions on the point‑sized particles used to define the electromagnetic field. Bohr, who had come to accept quantum field theory as the only reasonable interpretation of the light‑quantum hypothesis, worked with Léon Rosenfeld on a paper establishing the conceptual consistency of quantum field theory.17 The paper is not concerned with field theory as such or even with actual measurements, but with the conceptual consistency of the assumptions concerning measurement. In place of point‑sized test particles one must assume particles, particles whose dimensions are sufficiently large compared to atomic dimensions that the charge may be treated as a constant over the surface. Since one is assuming a classical particle, one may also assume classical models, e.g., a rigid particle which may be attached to springs to measure momentum, or to a rigid frame to measure position. They conclude that the continuous distribution of energy in space is an idealization valid only in the limit in which quantum effects, such as vacuum fluctuations, are negligible. Thus, the continuous electromagnetic field is an idealization of classical macroscopic descriptions. As such it does not supply a basis for a microscopic ontology, e.g., whether the electromagnetic field is ultimately continuous or discrete.
17 The papers by Landau and Peierls and the two papers by Bohr and Rosenfeld are translated in Wheeler, 1983, Sect. IV. An analysis of the Bohr-Rosenfeld argument is given in Darrigol, 1991.