  We have previously shown (arXiv:1912.00033) that three approaches to
relational quantum dynamics -- relational Dirac observables, the Page-Wootters
formalism and quantum deparametrizations -- are equivalent. Here we show that
this `trinity' of relational quantum dynamics holds in relativistic settings
per frequency superselection sector. We ascribe the time according to the clock
subsystem to a POVM which is covariant with respect to its (quadratic)
Hamiltonian. This differs from the usual choice of a self-adjoint clock
observable conjugate to the clock momentum. It also resolves Kucha\v{r}'s
criticism that the Page-Wootters formalism yields incorrect localization
probabilities for the relativistic particle when conditioning on a Minkowski
time operator. We show that conditioning instead on the covariant clock POVM
results in a Newton-Wigner type localization probability commonly used in
relativistic quantum mechanics. By establishing the equivalence mentioned
above, we also assign a consistent conditional-probability interpretation to
relational observables and deparametrizations. Finally, we expand a recent
method of changing temporal reference frames, and show how to transform states
and observables frequency-sector-wise. We use this method to discuss an
indirect clock self-reference effect and explore the state and temporal
frame-dependence of the task of comparing and synchronizing different quantum
clocks.
