Abstract:
Quantum gravity is the art of showing that quantum theory and general relativity are not fundamentally incompatible, all the way to the Planck scale. It turns out that a highly fruitful strategy is to use nothing but good old quantum field theory, without any exotic ingredients, and adapt it to the situation where spacetime geometry is dynamical. It has taken us a while to address the underlying technical and conceptual challenges, but the good news is that we now have charted a path toward a theory of quantum gravity which is unitary, essentially unique and can produce "numbers" beyond perturbation theory. I will introduce the approach of Causal Dynamical Triangulations (CDT), which is to quantum gravity what lattice QCD is to nonabelian gauge theory. Its nonperturbative toolbox has allowed us to go where other approaches cannot (yet) and to extract quantitative results on quantum observables at or near the Planck scale. They reveal promising evidence for both genuine quantum effects and the existence of a classical limit, reflecting the mathematical richness of the underlying "random geometry". A breakthrough result of CDT quantum gravity in four dimensions is the emergence, from first principles, of a nonperturbative quantum spacetime with de Sitter-like properties. I will summarize these findings, highlight some structural challenges and discuss the future prospects of quantum gravity.
