Consistent quantum mechanics admits no mereotopology

TL;DR

This paper argues that the common assumption of well-defined Hilbert spaces for physical systems in quantum mechanics is unjustified, as such partitions are only consistent when systems do not interact, challenging standard views.

Contribution

It demonstrates that the assumption of well-defined Hilbert spaces for physical systems is physically unwarranted, especially in the presence of interactions.

Findings

Hilbert space partitions require non-interacting components

Standard assumptions about system Hilbert spaces are unjustified

Implications for quantum system composition and interpretation

Abstract

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.