  In general relativity, the description of spacetime relies on idealised rods
and clocks, which identify a reference frame. In any concrete scenario,
reference frames are associated to physical systems, which are ultimately
quantum in nature. A relativistic description of the laws of physics hence
needs to take into account such quantum reference frames, through which
spacetime can be given an operational meaning.
  Here, we introduce the notion of a spacetime quantum reference frame,
associated to a quantum particle in spacetime, and we give a manifestly
covariant formulation of physical laws from the perspective of such a quantum
reference frame. In particular, we consider a system of $N$ relativistic
quantum particles in a weak gravitational field, and introduce a timeless
formulation in which the global state of the $N$ particles appears "frozen",
but the dynamical evolution is recovered in terms of relational quantities. We
describe both the external and the internal degrees of freedom of the
particles. The external degrees of freedom are used to fix the quantum
reference frame via a transformation to the local frame of the particle such
that the metric is locally flat at the origin of the quantum reference frame.
The internal degrees of freedom are used as clocks keeping the proper time in
the local frame of the particle. We then show how the remaining particles
evolve dynamically in the relational variables from the perspective of the
quantum reference frame. The construction proposed here includes the
Page-Wootters mechanism for non interacting clocks when the external degrees of
freedom are neglected. Finally, we find that a quantum superposition of
gravitational redshifts and a quantum superposition of special-relativistic
time dilations can be observed in the quantum reference frame.
