Abstract
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within the framework of multifractional theories, whose key assumption is an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared. This sole ingredient is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements that was reported in studies combining quantum mechanics and general relativity heuristically. This allows us to fix two free parameters of the theory and leads, in one of the scenarios we contemplate, to a value of the ultraviolet dimension which had already found support in other quantum-gravity analyses. We also formalize a picture such that fuzziness originates from a fundamental discrete scale invariance at short scales and corresponds to a stochastic spacetime geometry.
Highlights
Introduction and main goalThe landscape of quantum gravity (QG) looks like a variegated compound of approaches that start from different conceptual premises and use different mathematical formalisms
We here put forward and motivate the conjecture that dimensional flow is directly related to the presence of limitations on the measurability of distances close to the Planck length Pl = Gh /c3, a feature which has been of interest for QG research for decades [40,41,42,43,44,45,46,47]
Note that (1) is uniquely determined parametrically as soon as dimensional flow is switched on and is slow in the IR [52]. This means that different models of quantum gravity can predict different values of the parameters αμ and ∗, but the general form of the measure as a parametric profile are the same and given by (1)
Summary
The landscape of quantum gravity (QG) looks like a variegated compound of approaches that start from different conceptual premises and use different mathematical formalisms (see, e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]). Understanding its origin is just as important as looking for its physical characterization, needed to relate the flow of dimensions to physical observables. It has been shown that, in some cases, spacetime fuzziness could be investigated in ongoing and forthcoming experiments, even if the fuzziness is introduced at the Planck scale. This was first explored in analyses of the interferometers used for gravity-wave searches [48,49,50], and more recently is focusing mainly on the implications of fuzziness for the formation of halo structures in the images of distant quasars [48,51]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
