Operationally induced preferred basis in unitary quantum mechanics

TL;DR

This paper introduces the Operationally Induced Preferred Basis framework, which explains measurement outcomes in unitary quantum mechanics without collapse, emphasizing the role of the measurement interface and providing testable empirical distinctions.

Contribution

It proposes a new basis selection mechanism induced by measurement interfaces, diverging from collapse and Many-Worlds interpretations, and offers a formal mathematical framework with empirical implications.

Findings

The Born rule derived from Gleason-type measures.

A qubit-pointer model demonstrating detector-induced basis selection.

Empirical tests proposed through POVM tomography and Wigner-friend experiments.

Abstract

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 $E_{\pm}=\frac12(\mathbb{1}\pm\eta\sigma_z)$ with sharpness $\eta$ 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.