Many worlds and modality in the interpretation of quantum mechanics: An algebraic approach

Many world interpretations (MWIs) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MIs) which state that quantum mechanics does not provide an account of what “actually is the case,” but rather deals with what “might be the case,” i.e., with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why—even though both interpretations share the same formal structure—MI fall pray of Kochen–Specker-type contradictions while MWI escape them.