What question did this study set out to answer?

This research aims to resolve three key problems in quantum mechanics by applying McCaul's Law of Coherence to the hydrogen atom.

May 12, 2026Open Access

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

Key Points

This research aims to resolve three key problems in quantum mechanics by applying McCaul's Law of Coherence to the hydrogen atom.
Applied McCaul's Law of Coherence to the quantum measurement problem, wave-particle duality, and spectral renormalization using hydrogen as the baseline.
Developed the Born Rule as a theorem under McCaul's Law.
Investigated implications for Schrödinger's Cat, double-slit experiment, and renormalization processes.
Founded derived form of Born Rule: P(state_i) = Φᵢ²/ΣΦⱼ², linking measurements to wavefunction collapse.
Demonstrated characteristic conditions for wave-particle duality leading to observable fringe patterns and their disappearance.
Showed that renormalization assumptions lead to infinities, but modifications yield finite integrals in quantum field theory contexts.

Abstract

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 (Φ₁s = 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 (stateᵢ) = 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: Eₜransition = ΔΦ² × Ebase. Phi is bounded 0, 1 — no infinities arise. Renormalization is an artifact of QFT's assumption Φᵥacuum = 1. 0. Using MVCC (Eᵣeal = EQFT · Φᵥac²), all integrals remain finite. Lamb shift = differential vacuum Nr exposure between s and p orbitals. Anomalous g-2 = 2Φᵥac². Timestamped May 9, 2026.

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