A model-theoretic interpretation of environmentally-induced superselection

Abstract

Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely quantum-mechanically. It is shown that einselection can only generate classical systems if the "environment" is assumed \textit{a priori} to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures (POVMs) acting on a global quantum state. It is shown that this re-formulation enables a natural interpretation of apparently-classical systems as virtual machines that requires no assumptions beyond those of classical computer science.