Interpreting the modal Kochen-Specker theorem: possibility and many worlds in quantum mechanics

TL;DR

This paper explores the physical interpretation of the Modal Kochen-Specker theorem within quantum mechanics, analyzing how possibilities and actualities are constrained in the many-worlds interpretation using orthomodular lattices.

Contribution

It provides a novel interpretation of the MKS theorem by connecting modal logic, quantum possibilities, and the many-worlds framework.

Findings

The MKS theorem constrains the actualization of quantum properties.

Distinction between classical and quantum notions of possibility clarified.

Implications for the relation between possible and actual realms in quantum mechanics.

Abstract

In this paper we attempt to physically interpret the Modal Kochen- Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of "possibility" in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible realms.