One problem in most theories of quantum gravity is getting a quantum scale of spacetime at very small sizes, especially the Planck scale (of about 10-33 meters), to expand into a smooth spacetime fabric at large scales (as predicted by general relativity). Benedetti's study of spacetime in two different configurations shows that applying quantum groups to spacetime results in differences in how spacetime behaves, based on the scale that it's being examined.
Specifically, Benedetti's work shows a possible link between quantum groups (which have noncommutative geometries, where xy does not equal yx) with some approaches to quantum gravity such as causal dynamical triangulations and exact renormalization group. These sort of connections between different approaches may mean that insights gained in one approach can help propel new insights in another approach, so they are significant to the development of quantum gravity theories and will hopefully bring scientists closer to a more complete understanding of how gravity will behave at quantum levels.
- PhysOrg.com - Spacetime May Have Fractal Properties on a Quantum Scale
- Cornell ArXiv - Fractal Properties of Quantum Paper (abstract and click on PDF link to view the paper)