  Noncommutative spacetimes are a proposed effective description of the
low-energy regime of Quantum Gravity. Defining the microcausality relations of
a scalar quantum field theory on the $\kappa$-Minkowski noncommutative
spacetime allows us to define for the first time a notion of light-cone in a
quantum spacetime. This allows us to reach two conclusions. First, the majority
of the literature on $\kappa$-Minkowski suggests that this spacetime allows
superluminal propagation of particles. The structure of the light-cone we
introduced allows to rule this out, thereby excluding the possibility of
constraining the relevant models with observations of in-vacuo dispersion of
Gamma Ray Burst photons. Second, we are able to reject a claim made in [Phys.
Rev. Lett. 105, 211601 (2010)], according to which the light-cone of the
$\kappa$-Minkowski spacetime has a "blurry" region of Planck-length thickness,
independently of the distance of the two events considered. Such an effect
would be hopeless to measure. Our analysis reveals that the thickness of the
region where the notion of timelike and spacelike separations blurs grows like
the square root of the distance. This magnifies the effect, e.g. in the case of
cosmological distances, by 30 orders of magnitude.
