Abstract

What does empty spacetime look like on the very smallest scale? This fascinating and age-old question still awaits resolution by a quantum formulation of Einstein's theory of General Relativity. Although qualitative pictures of a fluctuating "quantum foam" at this tiny Planck scale have been around for almost 50 years, we still lack a quantitative microscopic model which at the same time reproduces our ordinary four-dimensional spacetime on large scales. I will describe the intriguing new view of spacetime that emerges from assembling sub-Planckian geometric building blocks into a finite-size universe. The underlying method of Causal Dynamical Triangulations is elegant and minimalist, and based on a quantum superposition principle and a microcausality postulate. The building rules of this dynamical model of quantum gravity are completely explicit and have enabled us to create a piece of quantum universe on a desktop computer and study some of its physical properties. Taking a closer look at its microscopic geometry reveals an entirely non-classical, fractal space of dimension two instead of the expected four, offering a tantalizing glimpse of the quantum structure of spacetime beyond the world view of 20th century physics.