Conceptual problems in classical electrodynamics: No more toils and trouble?

•The familiar version of the Lorentz force law results in an inconsistency in CED.•The Abraham model does not solve all conceptual problems of CED.•The familiar point particle theory is inconsistent.

In previous work I have argued that classical electrodynamics is beset by deep conceptual problems, which result from the problem of self-interactions. Symptomatic of these problems, I argued, is that the main approach to modeling the interactions between charges and fields is inconsistent with the principle of energy–momentum conservation. Zuchowski (2013) reports a formal result that shows that the so-called ‘Abraham model' of a charged particle satisfies energy–momentum conservation and argues that this result amounts to a refutation of my inconsistency claim. In this paper I defend my claims against her criticism and argue that she has succeeded neither in refuting my inconsistency argument nor in showing that the conceptual problems of classical electrodynamics have been solved.