What does this research mean for the field?

Quantum measurement outcomes and Born rule statistics can be deterministically derived from conserved geometry and Hamiltonian flow on a compact symplectic manifold, eliminating the need for stochastic collapse or multiple-world postulates. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

To provide an ontological, deterministic formulation of geometric quantum mechanics that explains definite measurement outcomes and derives Born rule frequencies without invoking stochastic collapse or many-worlds interpretations.

September 2, 2026Open Access

An Ontological Completion of Geometric Quantum Mechanics

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Authors

ZBZayn BloreHong Kong Metropolitan University

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Implication

Theoretical framework demonstrates deterministic measurement outcomes in geometric quantum mechanics, indicating Born rule statistics emerge naturally from conserved symplectic geometry.

Key Points

To provide an ontological, deterministic formulation of geometric quantum mechanics that explains definite measurement outcomes and derives Born rule frequencies without invoking stochastic collapse or many-worlds interpretations.
Represented physical reality as a single deterministic trajectory evolving under Hamiltonian flow on a compact symplectic manifold.
Used a toric moment map to project the Fubini–Study reference measure on complex projective state space onto a uniform measure across the probability simplex.
Formulated mathematical relationships between quantum interference visibility and the dynamical separation of contextual outcome sectors.
Demonstrated that state-dependent barycentric region volumes equal squared state amplitudes (|ψ|²), deriving Born rule statistics from conserved geometry rather than axioms.
Identified a quantitative correspondence between interference visibility V and outcome region separation I, showing V ≈ 1 − I in the macroscopic limit as I → 1.
Established that finite, measure-preserving Constraint-Surface Dynamics complies with Bell, Kochen–Specker, Fine, and PBR theorems while providing falsifiable empirical predictions.

Cite This Study

Zayn Blore (2026) studied this question.

synapsesocial.com/papers/6a97e2c5c562ede874ec71be https://doi.org/10.5281/zenodo.22199330

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Implication

Theoretical framework demonstrates deterministic measurement outcomes in geometric quantum mechanics, indicating Born rule statistics emerge naturally from conserved symplectic geometry.

An Ontological Completion of Geometric Quantum Mechanics

Discussion

Member takes

Implication

Key Points

Cite This Study

An Ontological Completion of Geometric Quantum Mechanics

Discussion

Member takes

Implication

Key Points

Cite This Study

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