Nuclear Physics B (Oct 2017)

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

  • Gianluca Calcagni,
  • Michele Ronco

DOI
https://doi.org/10.1016/j.nuclphysb.2017.07.016
Journal volume & issue
Vol. 923, no. C
pp. 144 – 167

Abstract

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We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.