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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2601.18856 |
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| _version_ | 1866914330784563200 |
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| author | Pronskikh, Vitaly |
| author_facet | Pronskikh, Vitaly |
| contents | The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while the theoretical description employs a noncommutative operator algebra with continuous unitary symmetry. This change of mathematical structure constitutes the core of the ``cut'': a necessary interface from group-based kinematics to set-based counting. In the Operationally Induced Preferred Basis (OIPB) framework, the basis relevant for recorded outcomes is not fixed by the system Hamiltonian but induced by the measurement interface -- the detector channel together with its coarse-grained readout. The Born rule follows from Gleason-type uniqueness (Gleason for projections in $d>2$ and Busch's extension for POVMs including $d=2$), as the unique probability measure consistent with additivity over exclusive events and basis-independence of the unitary sector. A compact qubit-pointer model yields an induced unsharp POVM $E_{\pm}=\frac12(\mathbb{1}\pmησ_z)$ with sharpness $η$ fixed by pointer resolution, explicitly demonstrating detector-induced basis selection. OIPB aligns with decoherence and operational theories while diverging from collapse models (no spontaneous reductions) and the Many-Worlds Interpretation (no ontological branching). Empirical distinctions arise through POVM tomography, Wigner-friend incompatibility tests, and superposition stability bounds. Nested-observer paradoxes are resolved by a non-composability lemma: joint assignment of outcome propositions is possible only if a joint instrument exists. This relocates the origin of randomness to the stochasticity of the interface rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operationally induced preferred basis in unitary quantum mechanics Pronskikh, Vitaly Quantum Physics The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while the theoretical description employs a noncommutative operator algebra with continuous unitary symmetry. This change of mathematical structure constitutes the core of the ``cut'': a necessary interface from group-based kinematics to set-based counting. In the Operationally Induced Preferred Basis (OIPB) framework, the basis relevant for recorded outcomes is not fixed by the system Hamiltonian but induced by the measurement interface -- the detector channel together with its coarse-grained readout. The Born rule follows from Gleason-type uniqueness (Gleason for projections in $d>2$ and Busch's extension for POVMs including $d=2$), as the unique probability measure consistent with additivity over exclusive events and basis-independence of the unitary sector. A compact qubit-pointer model yields an induced unsharp POVM $E_{\pm}=\frac12(\mathbb{1}\pmησ_z)$ with sharpness $η$ fixed by pointer resolution, explicitly demonstrating detector-induced basis selection. OIPB aligns with decoherence and operational theories while diverging from collapse models (no spontaneous reductions) and the Many-Worlds Interpretation (no ontological branching). Empirical distinctions arise through POVM tomography, Wigner-friend incompatibility tests, and superposition stability bounds. Nested-observer paradoxes are resolved by a non-composability lemma: joint assignment of outcome propositions is possible only if a joint instrument exists. This relocates the origin of randomness to the stochasticity of the interface rules. |
| title | Operationally induced preferred basis in unitary quantum mechanics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.18856 |