The Big Bang: From Singularity Big Bang to Zero-Point Big Bang

The traditional Big Bang theory (Singularity Big Bang) successfully explains the evolution of the universe but fails to account for the origin of the singularity itself. This paper presents a comprehensive and mathematically rigorous theoretical framework—the Zero-Point Big Bang hypothesis—positing that the universe originates from a zero-point quantum fluctuation at the most fundamental level, producing fully dual universes: a positive-mass matter universe and a negative-mass antimatter universe (or a positive-mass antimatter universe and a negative-mass matter universe). This framework, built upon extended fundamental operator equations of quantum mechanics and the Quantum Relativistic STEM equations,naturally incorporates expanded physical quantities such as positive/negative time, real/imaginary space, and positive/negative energy. We construct rigorous models of fully dual and semi-dual universes, proving that when a fully dual universe undergoes annihilation, it returns completely to zero. Through a detailed analysis of negative-mass universe stability using complex manifold theory, general relativity, and quantum field theory, we demonstrate three independent stability mechanisms: geometric separation via Euclidean signature barriers, gravitational field cancellation at equal densities, and quantum orthogonality through superselection rules. These mechanisms guarantee that positive and negative mass universes can coexist without catastrophic runaway motion. Furthermore, we establish a rigorous mathematical mapping between fundamental interaction charges (electric, color) and the imaginary units of complex numbers and quaternions, thereby explaining phenomena like like-charge repulsion and color confinement. The special quaternion constraints are derived from first principles through the chiral projection operator, eliminating any ad-hoc assumptions.