A photon scatters off an electron. Or perhaps an electron scatters off a photon. Or perhaps an electron and photon scatter. Whatever you choose to call it, the electron absorbs the photon and a little later, emits a photon. This is the diagram:

The horizontal axis is meant to be the time axis, although one may imagine the figure has having two spacial dimensions.

The above is the sane process.

An insane process can occur as well: the electron emits a new photon, then absorbs the original photon. This diagram illustrates three versions of the process. Recall that the horizontal axis is the time axis. The units are chosen so that the slope of something going the speed of light is one, or the angle is 45 degrees.

The first diagram is literally what I described. You might recognize it as a version of the opening of my story about the USS FTL0476. In the middle version of the process, the electron emits the photon, then goes back in time to pick up the other photon.

Of course, a particle can't go back in time. (A little later, it's earlier?) The electron drawn as going back in time is really a positron going forward in time. First, the photon pair-produces an electron and a positron. Then the positron annihilates the original electron, producing a new photon.

That's the version of the events of the USS FTL0476 according to the alien freighter.