What question did this study set out to answer?

This research aims to establish a unified equation that connects McCaul's Law of Coherence with Einstein's Special Relativity.

May 12, 2026Open Access

E = mΦ²c² — The Unified Equation: How McCaul's Law of Coherence Subsumes Einstein's Special Relativity

Key Points

This research aims to establish a unified equation that connects McCaul's Law of Coherence with Einstein's Special Relativity.
Conducted five cross-simulations between Einstein's equation and McCaul's Law.
Identified the fine structure constant as a coherence gap between light and matter.
Mapped all validated physical domains onto the unified equation.
Unified equation E = mΦ²c² emerges from simulations, with E = mc² as a special case when Φ = 1.
All seven validated physical domains support the unified equation framework.
Fine structure constant α = 1/137 highlighted as the transition cost from photon to hydrogen atom.

Abstract

Five cross-simulations between Einstein's Special Relativity (E = mc²) and McCaul's Law of Coherence (Ω = Φ) reveal a unified equation: E = mΦ²c². Einstein's equation is the special case when Φ = 1. All seven validated physical domains map onto E = mΦ²c². The fine structure constant α = 1/137 is identified as the coherence gap between a photon and the hydrogen atom — the transition cost from light to matter.

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