  We show that in the Maxwell-Lorentz theory of classical electrodynamics most
initial values for fields and particles lead to an ill-defined dynamics, as
they exhibit singularities or discontinuities along light-cones. This
phenomenon suggests that the Maxwell equations and the Lorentz force law ought
rather to be read as a system of delay differential equations, that is,
differential equations that relate a function and its derivatives at different
times. This mathematical reformulation, however, leads to physical and
philosophical consequences for the ontological status of the electromagnetic
field. In particular, fields cannot be taken as independent degrees of freedom,
which suggests that one should not add them to the ontology.
