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arXiv:2202.10928 · Studies in History and Philosophy of Science Part A

Towards noncommutative quantum reality

Otto C. W. Kong

Published Feb 24, 2022• 10 citations
arXivHTMLPDF
DOI
10.1016/j.shpsa.2022.02.002

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An experiment that would measure noncommuting quantum-mechanical observables without collapsing the wave function has been recently proposed by Y. Aharonov, J. Anandan, and L. Vaidman [Phys. Rev. A 47, 4616 (1993)]. These authors argue that this ``protected measurement'' may give an indication on ``the reality of the wave function.'' We show that the proposed experiment admits a much simpler interpretation: it is an experiment in which the quantum system is (assumed to be) in an eigenstate of the observable being measured. As such, the fact that no collapse occurs is trivial and can be understood without the need of the concept of ``protective'' devices. We argue that the experiment does not provide a way for measuring noncommuting observables without a collapse, does not bear on the issue of the ``reality of the wave function,'' and does not add any particular insight into our understanding (or nonunderstanding) of quantum mechanics.
We present a Hilbert space framework in which observed reality is defined as the image of a noncommutative operator cascade acting on an admissible configuration space. The cascade consists of three physically motivated filters: formation, interaction, and persistence, with formation decomposed into a hard projector (structural admissibility) and a soft weighting operator (thermodynamic and dynamical accessibility). An ordering commutator is introduced to quantify the noncommutativity of the cascade, along with a scalar diagnostic that measures the degree of structural competition between filters. Using a constrained three-qubit model, we show that the constraint operator determines whether the system exhibits nontrivial filter tension or collapses into an effectively commuting structure. In one sector, the filters act on misaligned subspaces and produce a weighted superposition; in another, they align and reduce observed reality to a single configuration. This provides a minimal, computable model of constraint-dependent structural selection in Hilbert space and establishes noncommutativity as a structural indicator of complexity. This work is part of the Carroll Wells Gradient (CWG) framework, which explores how persistence, constraint, and information shape structure across physical systems.