IMM Paper 4: Born Rule from Projection Measures

Three conditions (basis invariance, orientation independence, projection-integration stability) force μ(αm)=|α|²μ(m) without assuming Hilbert space (Theorem). Under Hilbert Embeddability Ansatz and six explicit Gleason conditions, P(i)=|⟨i|ψ⟩|² follows uniquely (Proposition). Ansatz labeled with bilateral operational consequences. Soler's theorem pathway to deriving the Ansatz identified. Qubit case (dim H=2) explicitly excluded.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-14
DOI
https://doi.org/10.5281/zenodo.20365728
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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preprint

IMM Paper 4: Born Rule from Projection Measures

Travis Bergen
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

IMM Paper 4: Born Rule from Projection Measures

Travis Bergen
preprint en

Abstract

Three conditions (basis invariance, orientation independence, projection-integration stability) force μ(αm)=|α|²μ(m) without assuming Hilbert space (Theorem). Under Hilbert Embeddability Ansatz and six explicit Gleason conditions, P(i)=|⟨i|ψ⟩|² follows uniquely (Proposition). Ansatz labeled with bilateral operational consequences. Soler's theorem pathway to deriving the Ansatz identified. Qubit case (dim H=2) explicitly excluded.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Quantum Mechanics and Applications
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IMM Paper 4: Born Rule from Projection Measures — Travis Bergen · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS