Predictive description of Planck-scale-induced spacetime fuzziness

Several approaches to the quantum-gravity problem predict that spacetime should be “fuzzy,” but so far these approaches have been unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been proposed on the basis of semiheuristic arguments and, in particular, involves an irreducible Planck-scale contribution to the uncertainty of the energy of a particle. These arguments also inspired a rather active phenomenological program that looks for the blurring of images of distant astrophysical sources that would result from such energy uncertainties. Here we report the first ever physical characterization of spacetime fuzziness derived constructively within a quantum picture of spacetime, the one provided by spacetime noncommutativity. Our results confirm earlier heuristic arguments suggesting that spacetime fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances. However, we find no Planck-scale-induced lower bound on the uncertainty of the energy of particles; we observe that this changes how we should picture a quantum spacetime, and it also imposes a reanalysis of the associated phenomenology.