  Observables in quantum gravity are famously defined asymptotically, at the
boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate
system or suitably dressing the field operators, an approximate, "quasi-local"
approach is also possible, that can give account of the measurements performed
by a set of observers living inside the spacetime. In particular, one can
attach spatial coordinates to the worldlines of these observers and use their
proper times as a time coordinate. Here we highlight that any such local
formulation has to face the relativity of the event, in that changing frame (=
set of observers) implies a reshuffling of the point-events and the way they
are identified. As a consequence, coordinate transformations between different
frames become probabilistic in quantum gravity. We give a concrete realization
of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can
be defined operationally with geodesics anchored to the boundary. We describe
different ways to do so, each corresponding to a different frame, and compute
the variances of the transformations relating some of these frames. In
particular, we compute the variance of the location of the black hole horizon,
which appears smeared in most frames. We then suggest how to calculate this
effect in Einstein gravity, assuming knowledge of the wavefunction of the
metric. The idea is to expand the latter on a basis of semiclassical states.
Each element of this basis enjoys standard/deterministic coordinate
transformations and the result is thus obtained by superposition. As a
divertissement, we sabotage the familiar Lorentz boosts by adding to Minkoswki
spacetime a quantum superposition of gravitational waves and compute the
probabilistic transformation to a boosted frame in linearized gravity. Finally,
we attempt to translate the relativity of the event in the language of dressed
operators.
