Physical Analysis of Energy Allocation in World Quantum Theory
Abstract
Starting from three already established equations — the envelope interface energy form U = (c/(2Sₑ)) × Vₑ × c², the envelope nesting constraint c² = Vₑ² + (2De)², and the measurement-line helix constraint Sₑ = De — this paper defines two quantities: the envelope interface static shadow Um = (2De/S₁) × U and the envelope interface dynamic shadow Up = (Vₑ/S₁) × U. Through purely algebraic derivation, it is proved that U² = Um² + Up², which is a direct algebraic consequence of c² = Vₑ² + (2De)², requiring no physical assumptions. Geometrically, Um and Up are the orthogonal projections of U in the velocity space spanned by the tangential velocity and the non-tangential velocity. After normalization (Vₑ → m, 2De = d, S₁ = c, U → E), it is demonstrated that the energy projection formulas Em = (d/c)·E and Ep = (v/c)·E of World Quantum Theory, together with the relativistic energy-momentum relation E² = (mc²)² + (pc)², are all necessary consequences of the envelope interface geometry.
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