  We investigate a connection between recent results in 3D quantum gravity,
providing an effective noncommutative-spacetime description, and some earlier
heuristic descriptions of a quantum-gravity contribution to the fuzziness of
the worldlines of particles. We show that 3D-gravity-inspired spacetime
noncommutativity reflects some of the features suggested by previous heuristic
arguments. Most notably, gravity-induced worldline fuzziness, while
irrelevantly small on terrestrial scales, could be observably large for
propagation of particles over cosmological distances.
