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Towards a Tensor Product Structure-Grounded Mereology.

Matías Pasqualini1, Sebastian Fortin2

  • 1CONICET, Instituto de Investigaciones "Dr. Adolfo Prieto", Universidad Nacional de Rosario, Rosario 2000, Argentina.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary
This summary is machine-generated.

Quantum mereology, based on tensor product structures (TPSs), does not follow classical partitions. This research shows TPSs lack lattice structure, challenging classical composition interpretations and requiring a non-classical framework.

Keywords:
Hilbert spacemereologyquantum mechanicstensor product

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Area of Science:

  • Quantum mechanics
  • Mereology
  • Mathematical physics

Background:

  • Classical mereology relies on extensionality and lattice structures for composition.
  • Previous work suggested quantum mereology might align with classical extensionality using tensor product structures (TPSs).

Purpose of the Study:

  • To develop a systematic framework for quantum mereology using Hilbert space tensor product structures (TPSs).
  • To investigate the structural properties of the space of TPSs and compare them to classical mereology.

Main Methods:

  • Analysis of the space of all possible tensor product structures for a given Hilbert space.
  • Demonstration of the absence of a canonical meet operation within this space.
  • Examination of the implications for the weak supplementation principle.

Main Results:

  • The space of TPSs lacks the lattice-theoretic structure of classical partitions.
  • A canonical meet operation is absent, violating a natural extension of the weak supplementation principle.
  • Quantum mereology based on TPSs exhibits non-extensional behavior.

Conclusions:

  • Quantum mereology, even when TPS-based, is inherently non-extensional.
  • The notion of 'part' in quantum mereology is strongly decomposition-relative.
  • A formally richer, non-classical mereological framework is necessary for quantum composition.