Everett's many worlds interpretation (MWI) is one of the most widely discussed topics in contemporary fundamental science, yet discussions of it often remain at a superficial and qualitative level. The goal of this talk is to convince you that a more quantitative discussion is needed and possible using tools from statistical mechanics. To this end, I start by introducing the MWI and its problems. I then review the decoherent histories formalism, which allows to address various problems of the MWI. Based on it, the following two (mostly numerical) results are discussed.
First, I argue that the basic mechanism of decoherence are slow and coarse observables of isolated non-integrable many-body systems. Those show exponentially suppressed interference effects as a function of the particle number of the system, if probed a few times.
However, things start to change drastically for very long histories (e.g., many repetitions in a quantum coin flip experiment). The "branches" of the many worlds "tree" then suddenly acquire a non-trivial structure, with decoherence surviving only on a very small subset of branches. Remarkably, those surviving classical branches are exactly those that sample frequencies according to Born's rule.