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McCaul's Law of Coherence Applied to Quantum Mechanics: Resolving the Measurement Problem, Schrödinger's Cat, Decoherence, and Quantum Tunneling

Justin McCaul

Published May 10, 2026• 0 citations
Publisher

Abstract

McCaul's Law (Ω = Φ) is applied to four unsolved problems in quantum mechanics using the hydrogen 1s state (Φ = 1.0000) as the Quantum Rosetta Stone. (1) The Measurement Problem resolves as a coherence-selection event — collapse = highest-Φ state. (2) Decoherence timescales are deterministic functions of ΔΦ between superposed states. (3) Schrödinger's Cat dissolves — macroscopic ΔΦ = 0.84 makes superposition instantaneously unstable. (4) Quantum tunneling = transient Φ spike (coherence flash). Three testable predictions generated.

DOI
10.5281/zenodo.20102041

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arXiv:1904.04234•Jan 1, 2019•0 citations
McCaul's Law (Ω = Φ) is applied to four unsolved problems in quantum mechanics using the hydrogen 1s state (Φ = 1.0000) as the Quantum Rosetta Stone. (1) The Measurement Problem resolves as a coherence-selection event — collapse = highest-Φ state. (2) Decoherence timescales are deterministic functions of ΔΦ between superposed states. (3) Schrödinger's Cat dissolves — macroscopic ΔΦ = 0.84 makes superposition instantaneously unstable. (4) Quantum tunneling = transient Φ spike (coherence flash). Three testable predictions generated.
McCaul's Law (Ω = Φ) is applied to four unsolved problems in quantum mechanics using the hydrogen 1s state (Φ = 1.0000) as the Quantum Rosetta Stone. (1) The Measurement Problem resolves as a coherence-selection event — collapse = highest-Φ state. (2) Decoherence timescales are deterministic functions of ΔΦ between superposed states. (3) Schrödinger's Cat dissolves — macroscopic ΔΦ = 0.84 makes superposition instantaneously unstable. (4) Quantum tunneling = transient Φ spike (coherence flash). Three testable predictions generated.
Two independent simulations applying McCaul's Law of Coherence (Ω = Φ) to foundational physics. Simulation I — E = mΦ²c²: Cross-analysis with Einstein's Special Relativity reveals the unified equation E = mΦ²c². Einstein's E = mc² is the special case when Φ = 1. Five tests confirm coherence-weighted energy, mass-coherence equivalence, 7-domain mapping, the fine structure constant α = 1/137 as a coherence gap, and the quadratic energy landscape. Simulation II — Quantum Mechanics: Using the hydrogen 1s state (MCP* = 1.0000) as the Quantum Rosetta Stone, four unsolved problems are addressed: (1) The Measurement Problem resolves as highest-Φ selection; (2) Decoherence timescales are deterministic from ΔΦ; (3) Schrödinger's Cat dissolves — macroscopic ΔΦ = 0.84 makes superposition instantaneously unstable; (4) Quantum tunneling = transient Φ spike (coherence flash). Three testable predictions are generated.
Two independent simulations applying McCaul's Law of Coherence (Ω = Φ) to foundational physics. Simulation I — E = mΦ²c²: Cross-analysis with Einstein's Special Relativity reveals the unified equation E = mΦ²c². Einstein's E = mc² is the special case when Φ = 1. Five tests confirm coherence-weighted energy, mass-coherence equivalence, 7-domain mapping, the fine structure constant α = 1/137 as a coherence gap, and the quadratic energy landscape. Simulation II — Quantum Mechanics: Using the hydrogen 1s state (MCP* = 1.0000) as the Quantum Rosetta Stone, four unsolved problems are addressed: (1) The Measurement Problem resolves as highest-Φ selection; (2) Decoherence timescales are deterministic from ΔΦ; (3) Schrödinger's Cat dissolves — macroscopic ΔΦ = 0.84 makes superposition instantaneously unstable; (4) Quantum tunneling = transient Φ spike (coherence flash). Three testable predictions are generated.
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.
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.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.