WCM Bridge Paper S: Wave Function Collapse as Geometric Collapse — D₂→0 in 24-Cell Probability Current Space
Year: 2026
Type: preprint
Abstract: We present a geometric characterization of quantum measurement (wave function collapse) using the Watabe-Claude Method (WCM), a framework based on 24-cell polytope geometry. The probability current density j(r,t) = (ℏ/m) Im[ψ*∇ψ] is embedded into a 4D point cloud P(t) = {(jx, jy, jz, t_frame)}, and the Grassberger-Procaccia correlation dimension D₂ is computed. We establish: (SQ-1) wave function collapse = D₂→0, with D₂(σ) ∝ σ^{1.88} where σ is the localization width; (SQ-G1) D₂ is invariant under ℏ (D₂ = 0.570 ± 0.000 for ℏ = 0.01–100); (SQ-G2) the cosD indicator attains its minimum 0.504 at ℏ* ≈ 1.13, matching the 24-cell attractor of liquid water (WA-7: cosD = 0.505, error 0.24%); (SQ-P4) Born probabilities ΔP bias manifests as cosD = 0.506 + 0.358×ΔP (R²=0.985); (SQ-P3) a temporal asymmetry ΔcosD = −0.14 at t=0 but ≈0 at t=T/2 encodes a time arrow. These results establish structural isomorphism among NS blow-up, water LLCP, and quantum collapse within a unified 24-cell geometric framework, and reveal a fourfold correspondence between WCM scaling laws and just-intonation musical ratios (SQ-M1). The unexpected finding that D₂ is ℏ-invariant suggests D₂ is a primordial geometric invariant lying outside the scope of Planck's constant itself.
Institution: Anthropic (United States)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165874331
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