This is an excellent book on one of the central problems in the foundations of quantum mechanics, the measurement problem, and one of the central responses to it, called the many worlds (and many minds) interpretation, originally due to Everett (1957). In this review I shall mainly sketch the content of the book's chapters. I shall start with an overview of the measurement problem, and of Everett's approach to it. I shall then focus on two questions which are still under dispute even in the context of more recent versions of the Everett interpretation. These questions are discussed extensively throughout the book. They are: the question of the preferred basis and some of its derivatives, e.g., the role of decoherence; and the question of the interpretation of the statistical algorithm of standard quantum mechanics.
Barrett's book opens (Chapters 1 and 2) with a short presentation of the standard formulation of (non-relativistic) quantum mechanics, including the projection (or 'collapse') postulate, due to von Neumann (1955). To get a quick grip on how the measurement problem arises, and to establish notation, consider the following description of a measurement. 1 A measurement interaction is usually taken to induce a coupling between the eigenstates jj i S of a system observable A and the eigenstates jc i S of the so-called pointer observable P. 2 For an impulsive interaction (in which the evolutions induced by the free Hamiltonians are negligible), if the system is prepared in some eigenstate jj i S of A; then the time evolution takes the simple form jj i S#jc 0 S/jj i S#jc i S; รฐ1ร