Metric Gap Physics: A Topological Framework for Spacetime Singularities, Tachyonic Metric Gradients, and Scale-Inversion Duality

AbstractModern theoretical physics faces an impasse regarding spacetime singularities, negative-rootmathematical breakdowns at extreme velocities, and the conceptual chasm betweenmacrocosmic event horizons and quantum subatomic boundaries. In this work, we introducethe framework of Metric Gap Physics, a novel theoretical model that reformulatesspatiotemporal geometry through a foundational 1+1 topological gap. By establishing thePlanck-derived metric speed boundary as an absolute physical accessibility limit, we resolvethe crisis of imaginary values and eliminate classical singularities without unphysical infinities.Furthermore, we reformulate Special Relativity into a comprehensive topological framework,successfully deriving elementary particle charges from tachyonic metric gradients andestablishing mass as an emergent, scale-inverted phenomenon via precise metric velocityregimes. Crucially, the model yields profound testable implications for quantum mechanics,demonstrating that quantum entanglement and non-local correlations emerge naturally as amanifestation of an implicated time-structure folded in frequency domains. Finally, weestablish a robust scale-inversion duality demonstrating that the universe functions as aninverted black hole, wherein any gravitational horizon yields a "Megatom" structure composedof negative and positive metric masses—directly analogous to the micro-atomic architectureconstituted by negative and positive metric electrical charges. This reveals that macro-scalecosmic acceleration originates directly from the metric gap rooted in the quantum realm,thereby offering a unified physical model that seamlessly bridging subatomic metric topologyand extreme gravitational horizons.