  Alternative approaches to the study of the quantum-gravity problem are
handling the role of spacetime very differently. Some are focusing on the
analysis of one or another novel formulation of "empty spacetime", postponing
to later stages the introduction of particles and fields, while other
approaches assume that spacetime should only be an emergent entity. We here
argue that recent progress in the covariant formulation of quantum mechanics
suggests that empty spacetime is not physically meaningful. We illustrate our
general thesis in the specific context of the noncommutative Snyder spacetime,
which is also of some intrinsic interest, since hundreds of studies were
devoted to its analysis. We show that empty Snyder spacetime, described in
terms of a suitable kinematical Hilbert space, is discrete, but this is only a
formal artifact: the discreteness leaves no trace on the observable properties
of particles on the physical Hilbert space.
