The Physics of Unresolved Uncertainty: Quantum Mechanics as a Theory of Potentiality

We propose a reformulation of quantum mechanics as a theory of unresolved uncertainty. The framework is formulated in the language of complex-valued measure theory, regarded as a pre-probabilistic counterpart of ordinary probability theory. In this formulation, additivity, conditioning, independence, mixtures, transition kernels, and temporal divisibility retain natural linear forms at the potentiality level, while non-classical probability-level features such as interference arise from the nonlinear Born map. Measurement is described as Bayesian-type conditioning of potentialities on actualized information, and non-selective measurement as the replacement of coherent potentiality by statistical mixtures of conditional branches. Mixed states, decoherence, composite systems, entanglement, and Bell-type correlations are also given a unified potentiality-level interpretation. The resulting formulation is empirically equivalent to standard quantum mechanics, but it makes explicit a pre-probabilistic description of physical reality that is usually implicit in the Hilbert-space formalism.