Is mereology empirical? Composition for fermions

TL;DR

This paper investigates the formal structure of quantum systems, specifically fermions, under permutation invariance, proposing that non-entangled fermionic assemblies challenge classical mereology, raising interpretative questions about quantum composition.

Contribution

It explores how permutation invariance as a representational redundancy affects the formalism of quantum systems and their composition, especially for fermions, challenging classical mereological notions.

Findings

Fermionic assemblies not entangled challenge classical mereology

Permutation invariance impacts the formal representation of quantum systems

Non-entangled fermionic assemblies serve as counterexamples to classical composition theories

Abstract

How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation invariance reflects a representational redundancy in the formalism. Under such a proposal, it is far from obvious how a constituent quantum system is represented. Consequently, it is also far from obvious how quantum systems compose to form assemblies, i.e. what is the formal structure of their relations of parthood, overlap and fusion. In this paper, I explore one proposal for the case of fermions and their assemblies. According to this proposal, fermionic assemblies which are not entangled -- in some heterodox, but natural sense of 'entangled' -- provide a prima facie counterexample to classical mereology. This result is puzzling; but, I argue, no more intolerable than any other available interpretative option.