Unified Theory of Cosmic Holism and Fundamental Interactions:A Grand Unified Model Based on Cosmic-Scale Zero-Point Fluctuations, Left-Handed Quaternion Multiplication, and Dual Operators

This paper systematically constructs a mathematical physics grand unified theoretical framework based on the holistic view of the universe. The framework is centered on six fundamental axioms: the Cosmic Holism Axiom, the Vacuum Duality Axiom, the Entanglement-Geometry-Medium Equivalence Axiom, the Algebraic Hierarchy Correspondence Axiom, the Cosmic-Scale Zero-Point Fluctuation Axiom, and the Dual Universe Generation Axiom. Within this framework, the fundamental commutation relations of quantum mechanics are generalized into three pairs of dual operators: time-energy, space-momentum, and angle-angular momentum, forming the basis for the Quantum Relativistic STEM unified equations. The imaginary unit is endowed with physical reality, corresponding to concepts such as imaginary time, imaginary space, imaginary mass, and imaginary energy, rigorously proven in Theorem 3.4. The four fundamental interactions are unified under the algebraic hierarchy of real numbers, complex numbers, and quaternions: gravity corresponds to the real unit 1 (like masses attract), electromagnetism corresponds to the complex unit \(i\) (like charges repel), the strong interaction corresponds to the quaternion imaginary units \(I, J, K\) (color confinement), and the weak interaction emerges as a relativistic effect of color charge interactions. The Left-Handed Multiplication Rule is rigorously formalized in Definition 4.2, and its equivalence to the chirality of the weak interaction is proven in Theorem 4.2. From this, the weak mixing angle in the pure color charge limit is rigorously derived to be \(30^\circ\) , with the electromagnetic correction yielding the precise expression \(\theta_W = 30^\circ \times \sqrt{1 - \sqrt{\alpha}} + \mathcal{O}(\alpha)\), which aligns remarkably with the experimental value of \(28.74^\circ\).