Abstract: We analyze the double slit interference of a mesoscopic particle. I give an introduction to the spin foam/group field theory approach to non-perturbative quantum gravity. I try to convey the general ideas and motivations, the basic construction of spin foam models and the idea of a simplicial third quantization of gravity leading to group field theories. I use the 3d case a simplified example to illustrate explicitely the procedures and the type of mathematics used, and the structure of the resulting models. I also highlight the relation with other approaches to quantum gravity, like matrix models, loop quantum gravity, Regge calculus and dynamical triangulations.