Jesse van der Duin and Renate Loll: Effective topology of quantum spacetime

According to long-standing folklore, spacetime at Planckian distances bears no resemblance to the spacetime of classical general relativity, but instead is some kind of “quantum foam”, due to strong quantum fluctuations. Turning this handwaving concept into physical theory requires a nonperturbative, quantitative modelling of quantum gravity and spacetime near the Planck scale, which for a long time was out of reach. The advent of an operational framework for lattice quantum gravity, based on causal dynamical triangulations (CDT), has opened the door to such investigations. Inspired by topological data analysis (TDA), we have developed and tested a new class of quantum observables that allows us to measure topological features of quantum spacetime, such as those associated with microscopic wormholes. The key idea is to investigate the Betti numbers of coarse-grained path integral histories as a function of a coarse-graining scale. In two dimensions our analysis verifies the previously established fractal nature of nonperturbative Lorentzian and Euclidean quantum gravity, paving the way for investigations in four dimensions. (Based on arXiv:2510.05693 and arXiv:2510.05695.)