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The British Journal for the Philosophy of Science

Wavefunction Mereology

Isaac Wilhelm

Published Feb 25, 2025• 1 citation
Publisher

Abstract

I propose and defend an analysis of the parthood relation among quantum wavefunctions. Roughly put, according to the analysis, one wavefunction is part of another just in case the latter can be projected onto the former. This analysis brings mereology into closer contact with contemporary physics, implies many standard mereological principles, challenges some traditional mereological presuppositions, and supports compelling answers to long-standing questions about parthood.

DOI
10.1086/735531

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I propose and defend an analysis of the parthood relation among quantum wavefunctions. Roughly put, according to the analysis, one wavefunction is part of another just in case the latter can be projected onto the former. This analysis brings mereology into closer contact with contemporary physics, implies many standard mereological principles, challenges some traditional mereological presuppositions, and supports compelling answers to long-standing questions about parthood.
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.
This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.
We assess the possibilities offered by Hilbert space fundamentalism, an attitude towards quantum physics according to which all physical structures (e.g. subsystems, locality, spacetime, preferred observables) should emerge from minimal quantum ingredients (typically a Hilbert space, Hamiltonian, and state). As a case study, we first mainly focus on the specific question of whether the Hamiltonian can uniquely determine a tensor product structure, a crucial challenge in the growing field of quantum mereology. The present paper reviews, clarifies, and critically examines two apparently conflicting theorems by Cotler et al. and Stoica. We resolve the tension, show how the former has been widely misinterpreted and why the latter is correct only in some weaker version. We then propose a correct mathematical way to address the general problem of preferred structures in quantum theory, relative to the characterization of emergent objects by unitary-invariant properties. Finally, we apply this formalism in the particular case we started with, and show that a Hamiltonian and a state are enough structure to uniquely select a preferred tensor product structure.
One recent debate in philosophy of physics has centered whether quantum particles are individuals or not. The received view is that particles are not individuals and the standard methodology is to approach the question via the structure of quantum theory. I challenge both the received view and the standard methodology. I contend not only that the structure of quantum theory is not the right place to look for conditions of individuality that quantum particles may or may not satisfy, but also that there is an important role for traditional metaphysics to play. Consequently, my work brings together the philosophy of physics and traditional metaphysics literatures to shed new light on the debate over the individuality of quantum particles. I defend a set of conditions of individuality and argue that quantum particles satisfy these conditions thereby defending the view that particles are individuals in opposition to the received view. I also challenge a second feature of the standard methodology insofar as I challenge the significance of the Principle of the Identity of Indiscernibles in terms of which much discussion in the philosophy of physics literature is framed. My work is significant in a number of additional ways as well. My work implies that the dominant explanation for quantum statistics in terms of non-individuality is incorrect and it also undermines the ontic-structural realists metaphysical underdetermination challenge to the scientific realist.
This paper investigates quantized mereology, which merges quantum information theory with classical mereology, the formal analysis of the part-whole relationship. It emphasizes that information about crisp mereological relations is captured by classical bits, whereas mereological vagueness involves the use of quantum bits, or qubits, to capture mereological information. Transitioning from classical bits to qubits offers a new understanding of part-whole relations among entities that are subject to mereological vagueness. This paper methodically studies the quantized mereology that arises from the classical RCC5 formalism, one of the most widely studied formalisms in Qualitative Reasoning (QR), a subfield of Artificial Intelligence. The argument is made that this method can be extended to quantize more sophisticated QR formalisms, mirroring how strategies are used in physics to transition from classical to quantum systems. The study explores: (i) the conversion of bits to qubits while understanding that these (qu)bits convey mereological information; (ii) the representation of qubit states via set partitions, acknowledging that set theory aligns more closely with classical logic than with the complex vector spaces employed in quantum physics; (iii) demonstrating that classical QR formalisms can be seen as special cases within quantized formalisms; and (iv) showing that qubits more effectively encapsulate information about vague phenomena.