Predictive description of Planck-scale-induced spacetime fuzziness

TL;DR

This paper provides a constructive quantum characterization of spacetime fuzziness using noncommutative geometry, confirming its potential observability over cosmological distances without imposing a lower bound on particle energy uncertainty.

Contribution

It offers the first physical, constructive description of Planck-scale spacetime fuzziness within a quantum spacetime model, challenging previous heuristic assumptions.

Findings

Spacetime fuzziness could be observable over cosmological distances.

No Planck-scale lower bound on particle energy uncertainty.

Reevaluation of phenomenological models of quantum spacetime.

Abstract

Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been proposed on the basis of semi-heuristic 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 programme looking for blurring of images of distant astrophysical sources that would result from such energy uncertainties. We here 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, and we observe that this changes how we should picture a quantum spacetime and also imposes a reanalysis of the associated phenomenology.