Invariant Magnitude from Phase-Bearing Summaries: The Quadratic Necessity
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2026
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| _version_ | 1866901805966819328 |
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| author | Searcy, Kenneth |
| author_facet | Searcy, Kenneth |
| contents | <p>Born-like squared magnitude is forced by stable composition, not assumed from physics. This paper derives a Born-like squared-magnitude rule as a representational necessity in a pre-physical program. Building on prior results that force (1) plural incompatible stabilization criteria, (2) route dependence with cancellation-capable summaries (phase-like structure), and (3) the need for a stable nonnegative "yield" map, we formalize a yield function rho from summaries to nonnegative real numbers under minimal requirements: phase invariance, additivity over exclusive outcomes, multiplicativity under independent composition, and symmetry under balanced regrouping (no preferred exclusive coordinates).</p> <p>Under mild regularity, multiplicativity restricts rho to a power-law family, and regrouping invariance uniquely selects the quadratic case. The result is a squared-magnitude extraction rule obtained without assuming Hilbert spaces, wavefunctions, inner products, dynamics, hbar, or measurement postulates. The paper concludes by identifying the next forced pressures toward complex realization and norm-preserving (unitary-like) evolution.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18420896 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Invariant Magnitude from Phase-Bearing Summaries: The Quadratic Necessity Searcy, Kenneth Born rule squared magnitude quadratic norm Quantum physics Quantum Theory probability phase invariance measurement problem quantum foundations pre-physical foundations order theory <p>Born-like squared magnitude is forced by stable composition, not assumed from physics. This paper derives a Born-like squared-magnitude rule as a representational necessity in a pre-physical program. Building on prior results that force (1) plural incompatible stabilization criteria, (2) route dependence with cancellation-capable summaries (phase-like structure), and (3) the need for a stable nonnegative "yield" map, we formalize a yield function rho from summaries to nonnegative real numbers under minimal requirements: phase invariance, additivity over exclusive outcomes, multiplicativity under independent composition, and symmetry under balanced regrouping (no preferred exclusive coordinates).</p> <p>Under mild regularity, multiplicativity restricts rho to a power-law family, and regrouping invariance uniquely selects the quadratic case. The result is a squared-magnitude extraction rule obtained without assuming Hilbert spaces, wavefunctions, inner products, dynamics, hbar, or measurement postulates. The paper concludes by identifying the next forced pressures toward complex realization and norm-preserving (unitary-like) evolution.</p> |
| title | Invariant Magnitude from Phase-Bearing Summaries: The Quadratic Necessity |
| topic | Born rule squared magnitude quadratic norm Quantum physics Quantum Theory probability phase invariance measurement problem quantum foundations pre-physical foundations order theory |
| url | https://doi.org/10.5281/zenodo.18420896 |