Anatomical Review of "Heading towards an Algebraic Heisenberg Cut": Sectorisation, Self-Decoherence, and the Algebraic Foundations of the Quantum–Classical Transition

Syed Muntasir Mamun

Published Jun 8, 2026• 0 citations

Abstract

This review provides a detailed anatomical dissection of the recent paper by Van Den Bossche and Grangier (2025), which advances an algebraic approach to the quantum measurement problem grounded in von Neumann's theorems on infinite tensor products (ITP). The target work models photon polarisation detection via avalanche photodiodes (APDs), demonstrating that sectorisation of the Hilbert space and effective self-decoherence emerge dynamically through the exponential growth of the electron avalanche, even in the absence of conventional environmental baths. I evaluate the mathematical structure, physical idealisations, and philosophical commitments of the CSM (Contexts, Systems, Modalities) framework within which the argument is embedded. Strengths include the controlled treatment of the infinite limit, explicit computation of sector-parameter convergence, and the proposal of an "algebraic Heisenberg cut". Limitations centre on model idealisation, the persistent role of infinity for full orthogonality, and limited engagement with experimental constraints or competing interpretations. The review situates the contribution against leading global research in decoherence, consistent histories, many-worlds, and algebraic quantum theory. Epistemological and ontological implications are drawn, particularly regarding contextuality, the co-fundamentality of quantum and classical realms, and the status of modalities as primary ontology. Also available on Academia.edu: https://www.academia.edu/attachments/133038530/download_file?s=portfolio

DOI: 10.5281/zenodo.22991397

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