Some of the most accurate optical clocks in the world use single trapped ions. Even though these ions are trapped and cooled down to ultracold temperatures, relativistic effects are very important: because of the relativistic Doppler shift, the motion of clock ions can lead to sizeable systematic errors (compared to the 18th decimal place, anyway). Estimating the size of these systematics is especially complicated when there are background gas collisions, which can knock the clock ions into entangled states of their internal and motional degrees of freedom.

In this informal seminar, I will provide a simple introduction to the basic problem, and present some recent work where I have tried to unravel this tangled mess. A happy outcome of this analysis is that we may not have to fear the 'ghosties and beasties' that bump against trapped atoms in optical clocks.