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

TL;DR

This paper develops an algebraic framework to analyze the modal aspects of the many worlds interpretation of quantum mechanics and compares it with modal interpretations, explaining why MWI avoids certain contradictions.

Contribution

It introduces a formal algebraic approach to compare MWI and MI, clarifying why MWI avoids Kochen-Specker contradictions unlike MI.

Findings

MWI considers all superposition terms as actual

MI deals with possibilities rather than actualities

MWI avoids Kochen-Specker contradictions

Abstract

Many worlds interpretations (MWI) 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 (MI) 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 (KS) type contradictions while MWI escape them.