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.