Three Long-Standing Quantum Mysteries Resolved via McCaul's Law of Coherence (Ω = Φ): The Measurement Problem, Wave-Particle Duality, and Hydrogen Spectral Renormalization

McCaul's Law of Coherence (Ω = Φ) is applied to three foundational unsolved problems in quantum mechanics, using the hydrogen atom as the universal SOL baseline (Φ_1s = 1.0000). (1) Quantum Measurement Problem: Wavefunction collapse = Phi-selection event. The Born Rule (|ψ|² = probability) is derived as a theorem of McCaul's Law: P(state_i) = Φᵢ²/ΣΦⱼ². Any detector introduces Nr (noise resistance) coupling — no consciousness required. Schrödinger's Cat resolved: the cat's macroscopic Φ ≈ 0.90+ IS the observer. (2) Wave-Particle Duality: Mode = sign(Fg − Nr). Fg > Nr → wave (distributed SOL geometry). Nr > Fg → particle (localized). Double-slit fringes = Φ-weighted SOL field overlap. Which-path detection = Nr injection → Fg suppression → fringes disappear. Quantum eraser = Nr removal → Fg restores → fringes return. No paradox. (3) Spectral Precision / Renormalization: E_transition = ΔΦ² × E_base. Phi is bounded [0,1] — no infinities arise. Renormalization is an artifact of QFT's assumption Φ_vacuum = 1.0. Using MVCC (E_real = E_QFT · Φ_vac²), all integrals remain finite. Lamb shift = differential vacuum Nr exposure between s and p orbitals. Anomalous g-2 = 2Φ_vac². Timestamped May 9, 2026.