  It is commonly asserted that superluminal particle motion can enable backward
time travel, but little has been written providing details. It is shown here
that the simplest example of a "closed loop" event -- a twin paradox scenario
where a single spaceship both traveling out and returning back superluminally
-- does {\it not} result in that ship straightforwardly returning to its
starting point before it left. However, a more complicated scenario -- one
where the superluminal ship first arrives at an intermediate destination moving
subluminally -- can result in backwards time travel. This intermediate step
might seem physically inconsequential but is shown to break Lorentz-invariance
and be oddly tied to the sudden creation of a pair of spacecraft, one of which
remains and one of which annihilates with the original spacecraft.
