The Physics of Unresolved Uncertainty: Quantum Mechanics as a Theory of Potentiality
Abstract
We propose a reformulation of quantum mechanics as a theory of unresolved uncertainty. This theory of potentiality 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 potentiality branches. Mixed states, decoherence, composite systems, entanglement, and Bell-type correlations are also given a unified potentiality-level interpretation. The density matrix is interpreted as a coherence kernel whose off-diagonal blocks encode retained phase relations. For pure bipartite states, potentiality independence is shown to be equivalent to factorization of the Born distribution in every pair of local contexts. 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.
Related
- What is Physics For? Why Classical Physics is not the Limit of Quantum Mechanics
- Reverse Physics for Quantum Mechanics
- Mass weighting algorithm optimizes Fourier-based physics-informed neural network in adhesive contact mechanics
- Mechanics Cognitive Diagnostic: Testing Fine-Grained Learning Objectives in Introductory Physics
- Models and Measures of Statistical Physics and Sociophysics for Fracture Mechanics and Earthquake Dynamics: An Introduction
BibTeX
@misc{martellini2026physics,
title = {{The Physics of Unresolved Uncertainty: Quantum Mechanics as a Theory of Potentiality}},
author = {Lionel Martellini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23745},
eprint = {2607.23745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23745},
}
RIS
TY - UNPB
TI - The Physics of Unresolved Uncertainty: Quantum Mechanics as a Theory of Potentiality
AU - Lionel Martellini
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2607.23745
UR - https://arxiv.org/abs/2607.23745
AB - We propose a reformulation of quantum mechanics as a theory of unresolved uncertainty. This theory of potentiality 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 potentiality branches. Mixed states, decoherence, composite systems, entanglement, and Bell-type correlations are also given a unified potentiality-level interpretation. The density matrix is interpreted as a coherence kernel whose off-diagonal blocks encode retained phase relations. For pure bipartite states, potentiality independence is shown to be equivalent to factorization of the Born distribution in every pair of local contexts. 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.
ER -