As the title indicates, I'm not sure if Maxwell's equations or Gauss' law indicate that charged bodies are the source of the EM fields. This is question comes from the reading of this paper.
As Mario Bunge (one of the physicists quoted in the paper) stated in his Foundation of Physics (1967):
the source hypothesis is an extra assumption: as our axiom systems show, fields and currents are conjoined but not causally associated: Only field changes are causally associated with charged bodies in case there are any in the region considered. [...] Both in CEM and in GR the “source”-free field equations have infinitely many nontrivial solutions, in particular waves. In short, the source hypothesis is an extra assumption that may but need not be made – not any more than its converse, the sink hypothesis. Consequently there is no reason to discard the “advanced” F’s, particularly as they need not be interpreted as advanced fields. [...] For example, j(x’, t+) might be interpreted as the current at x’, t+ associated with the field F+; i.e., F+ might be regarded as the part of the field that reacts on the current and influences its value at a later instant. Consequently the total solution (4.18) could be interpreted as describing both the action of the currents on the field and the latter’s reaction on the former. Whether or not this interpretation holds water is here immaterial: the point is that some of the difficulties of CEM are of a semantic nature and some of them are caused by tacit and controvertible assumptions such as that the charges produce fields but not conversely – a hypothesis that is clearly absent from the axiom basis of CEM.
Or, as Gustavo Romero points out in this paper, in reference to Bunge's view:
Bunge’s analysis of the electromagnetic field is remarkably lucid. Among other Issues, he points out that theory does not properly contain the hypothesis that charges are the sources of the field. Strictly speaking, electromagnetic theory is a theory of the interactions between fields and charged particles. The hypothesis that charges are sources of the field must be added to the Maxwell equations in order to discard the advanced contributions (determined by future events) to the solutions of the inhomogeneous Dalambertian equation. This is done by means of the application of the principle of causality. This hypothesis is logical, ontological and epistemologically independent from the rest of the theory. Something similar happens with the general theory of relativity: the hypothesis that matter is the cause of the curvature of spacetime (gravitational field) is a posteriori.
In another book, Matter and Mind, Bunge wrote:
The electromagnetic field that remains in a region of space after all the electric charges have been neutralized, and all the electric currents have been switched off, is a concrete though tenuous thing.
What are your thoughts on this? Is the "source hypothesis" an a posteriori addition to interpret the equations? Do the EM field exist even when there are no charged bodies to "create it"? Am I or the authors (or maybe, I'm misinterpreting the authors) not seeing something?