| _version_ | 1866901254409551872 |
|---|---|
| author | Longmire, James (JD) |
| author_facet | Longmire, James (JD) |
| contents | <p>We present a derivation of the Born rule from the ontological constraints imposed by the Three Fundamental Laws of Logic (L₃) within the Logic Realism Theory (LRT) framework. The central argument proceeds through five stages: (1) L₃ constraints at the vehicle level require that physical systems possess determinate dispositions toward measurement outcomes; (2) these dispositions must satisfy vehicle‑weight invariance—probability assignments cannot depend on the descriptive decomposition chosen; (3) vehicle‑weight invariance, combined with finite additivity, yields the premises of Gleason‑type theorems; (4) Gleason’s theorem then forces the trace form μ(P) = Tr(ρP) for all projectors; (5) for pure states, this reduces to the Born rule p = |⟨φ|ψ⟩|².[Attachment] We provide both an intuitive derivation chain and a formal axiom presentation (A1–A7) suitable for rigorous development. The derivation is non‑circular: L₃ constraints are conceptually and logically prior to the probability measure they entail. We situate this result within the quantum reconstruction literature and discuss implications for foundational physics.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18756374 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Deriving the Born Rule from Logical Constraint: A Logic Realism Theory Approach Longmire, James (JD) Born rule; Gleason's theorem; logic realism; Logic Realism Theory; quantum foundations; quantum reconstruction; probability; measurement problem <p>We present a derivation of the Born rule from the ontological constraints imposed by the Three Fundamental Laws of Logic (L₃) within the Logic Realism Theory (LRT) framework. The central argument proceeds through five stages: (1) L₃ constraints at the vehicle level require that physical systems possess determinate dispositions toward measurement outcomes; (2) these dispositions must satisfy vehicle‑weight invariance—probability assignments cannot depend on the descriptive decomposition chosen; (3) vehicle‑weight invariance, combined with finite additivity, yields the premises of Gleason‑type theorems; (4) Gleason’s theorem then forces the trace form μ(P) = Tr(ρP) for all projectors; (5) for pure states, this reduces to the Born rule p = |⟨φ|ψ⟩|².[Attachment] We provide both an intuitive derivation chain and a formal axiom presentation (A1–A7) suitable for rigorous development. The derivation is non‑circular: L₃ constraints are conceptually and logically prior to the probability measure they entail. We situate this result within the quantum reconstruction literature and discuss implications for foundational physics.</p> |
| title | Deriving the Born Rule from Logical Constraint: A Logic Realism Theory Approach |
| topic | Born rule; Gleason's theorem; logic realism; Logic Realism Theory; quantum foundations; quantum reconstruction; probability; measurement problem |
| url | https://doi.org/10.5281/zenodo.18756374 |