On the Emergence of the Orthogonal Decomposition Formula of World Quantum Theory from Envelope Interface Nesting Structure

One of the core postulates of World Quantum Theory (WQT) is that the internal rotational velocity of the world quantum satisfies the orthogonal decomposition c² = v² + d², where c is the total velocity, v is the tangential component, and d is the radial component. This formula is introduced as a postulate in WQT, and its physical origin is not explained. Starting from the envelope interface nesting structure, this paper demonstrates that this formula is not an independent assumption, but rather the natural cancellation of the spatial scale factor K in the macro-rotation coordinate system. This paper defines two types of rotation: the rotation of the parent envelope surface is called internal rotation, and the rotation of the radial-line envelope surface is called macro-rotation. The radial velocity of the parent envelope surface exists in the form K·c, where c is a constant fundamental velocity and K is the instantaneous spatial scale factor that varies with the expansion and contraction of the parent envelope surface. In the real parent coordinate system, the total velocity of the radial-line envelope surface is K·c, and the three orthogonal components are K·Ve, K·Se, and K·De, satisfying (Kc)² = (KVe)² + (KSe)² + (KDe)² = K²(Ve² + Se² + De²). However, the entire space of the radial-line envelope surface expands and contracts synchronously with K, making it unable to perceive the existence of K—the K² on both sides of the equation naturally cancels, yielding c² = Ve² + Se² + De² in the macro-rotation coordinate system. From the Survey Line Spiral constraint Se = De, we naturally obtain c² = v² + d². For the radial-line envelope surface, the highest frequency of its space of existence is fₚ (Planck frequency), and its own macro-rotation frequency is f_w. However, in the real parent envelope surface coordinate system, the true frequency of the radial-line envelope surface is fₚ × f_w.