to solve foundational issues, one must check if decoherence accomplishes these two facts. Below we will show in detail why decoherence in fact does *not* explain the suppression of macroscopic interference nor selects a preferred basis. Therefore, decoherence is unable to solve the measurement problem and to explain the emergence of classicality. In order to fully back up these claims (sections \[si\] and \[pb\] below), we will start with some necessary preliminary material.

The standard formalism and the measurement problem
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In order to properly discuss the merits of decoherence as a tool to solve foundational problems in quantum mechanics, it is very useful to start by considering first the standard interpretation and, in particular, by being explicit about what it consists of. The standard interpretation of quantum mechanics, for which we mean something along the lines of the version of Dirac [@Dirac], von Neumann [@von] or what one usually finds in contemporary textbooks, can be summarized as follows:

-   The physical states of quantum systems are represented, at all times, by unit vectors in an appropriate Hilbert space.

-   The physical properties of the system are represented by Hermitian operators.

-   The time evolution of the system is governed 