  We re-visit the problem of two (oppositely) charged particles interacting
electromagnetically in one dimension with retarded potentials and no radiation
reaction. The specific quantitative result of interest is the time it takes for
the particles to fall in towards one another. Starting with the
non-relativistic form, we answer this question while adding layers of
complexity until we arrive at the full relativistic delay differential equation
that governs this problem. That case can be solved using the Synge method,
which we describe and discuss.
