  This paper follows in the tradition of direct-action versions of
electromagnetism having the aim of avoiding a balance of infinities wherein a
mechanical mass offsets an infinite electromagnetic mass so as to arrive at a
finite observed value. Given that, in this respect the direct-action approached
ultimately failed because its initial exclusion of self-action was found to be
untenable in the relativistic domain, this paper continues the tradition
considering instead a version of electromagnetism wherein mechanical action is
excluded and self-action is retained. It is shown that the resulting theory is
effectively interacting due to the presence of infinite forces. A vehicle for
the investigation is a pair of classical point charges in a positronium-like
arrangement for which the orbits are found to be self-sustaining and naturally
quantized.
