Operator Outcome Measures and the Squared-Norm Form: A Structural Admissibility Result (IM-E004, v0.3)

Anders Nils Gunnar Widgren

Published Feb 16, 2026• 0 citations

Abstract

This document is part of the Informational Mechanics (IM) framework and is published in the IM-E (Measurement & Operators) series within the IM v0.3 corpus. The paper analyzes the structural status of outcome weights in quantum measurement under admissibility constraints. Rather than modifying quantum mechanics or deriving new dynamical laws, it formalizes the operator-defined conditions under which outcome weights must be proportional to the squared norm of state amplitudes. Building on the mathematical uniqueness result established in IM-B002, the analysis shows that orthogonal additivity, invariance under unitary transformations, and minimal regularity conditions constrain admissible strength functionals to the squared-norm form. The result is structural and regime-bounded: it applies within quantum-mechanical regimes where operator-defined observables and comparability are physically implementable. The paper introduces no new axioms, collapse models, hidden variables, or empirical fits. Its contribution is operational and classificatory, clarifying the admissibility conditions under which squared-amplitude outcome weights retain scientific meaning while avoiding unwarranted ontological extrapolation.

DOI: 10.5281/zenodo.18661572

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