Paper T14: A Classical Derivation of the Born Rule from Angular Coherence Filtering Probability as Real-Valued Path Volume in a Rotational Lattice
Year: 2025
Type: article
Abstract: Here we present a classical, non-circular route to the Born rule in which outcome frequencies arise from real path volume on a rotating SU(2) lattice (“Holospheres”). In this framework, particles are angular phase structures that propagate only when local rotational compatibility is satisfied; most candidate routes are filtered by a mechanical gate, and the surviving coherence-preserving paths set outcome weights. In the continuum limit this classical lattice reproduces the standard SU(2) overlap on S^3: the real coherence functional cos(Δ/2) (with 4π spinor holonomy) leads to observable intensity |cos(Δ/2)|² and “dark nodes” at Δ=π, 3π—so Born’s squaring appears as a physical intensity law, not a postulate. To avoid circularity, the selection mode on S² is obtained from classical angular elasticity with O_h symmetry (infinitesimal rail pinning), not from quantum harmonics. We then validate emergence numerically using an icosahedral sphere mesh and the cotangent Laplace–Beltrami operator with a proper mass matrix. The discrete rail eigenmode converges to the continuum target sin(θ)cos(φ), and the eigenvalue to the l=1 value (λ→2). Best-fit power laws show high-order convergence: E_shape ≈ h^4.41 and E_born ≈ h^4.47, with small, structureless residuals—confirming that the Born map emerges from classical geometry without building in quantum structures. The coherence gate is fixed by SU(2) geometry: θ_c = 2α and ε_c = 2α² (derived in Paper 49), and is approximately scale-invariant under coarse-graining. “Collapse” is S^3-mixing into the dark-node set (globally), or a local gate breach (|Δθ|>θ_c). A two-defect ring provides a concrete micro-mechanism for the 2π sign flip / 4π closure but is not required for the |·|² law itself. The program yields falsifiable predictions (gate-induced anisotropies and lattice-spacing effects at femtometer scales). Code and convergence data are provided to enable independent replication.
Author: Sarnowski, Michael
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893321469
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