The preferred basis problem in the many-worlds interpretation of quantum mechanics: why decoherence does not solve it

We start by very briefly describing the measurement problem in quantum mechanics and its solution by the Many Worlds Interpretation (MWI). We then describe the preferred basis problem, and the role of decoherence in the MWI. We discuss a number of approaches to the preferred basis problem and argue that contrary to the received wisdom, decoherence by itself does not solve the problem. We address Wallace's emergentist approach based on what he calls Dennett's criterion, and we compare the logical structure of Wallace's argument that the Hilbert space structure and the unitary dynamics should be considered a complete description of the physics of the universe with the logical structure of the EPR argument against the completeness of quantum mechanics. Then, we consider the nature of so-called "high level emergent facts" and Dennett's criterion in Wallace's approach and we discuss the implications of its non-reductive nature. Finally, we conclude that (contrary to the received wisdom) the MWI is not a straightforward interpretation of pure quantum mechanics that doesn't add anything to it. Whether or not it is more parsimonious than other quantum mechanical theories (such as the GRW theory and Bohm's theory) depends on the details of the additions.