Why the Direct-Sum Approximation Breaks at Boundaries: Interference, ER Bridges, and Large-Scale Asymmetry

This work examines the limits of the direct-sum approximation commonly used in quantum theory and related frameworks. While direct-sum formulations assume exact separability of state spaces and the absence of inter-sector interference, this assumption is shown to be unstable once boundary conditions are treated dynamically. In this study, the Einstein–Rosen bridge is reinterpreted as a physical point at which potential barriers collapse, leading to unavoidable inter-sector coupling. Under this reinterpretation, exact direct-sum separability ceases to hold near structural boundaries, resulting in effective symmetry breaking without violating fundamental physical laws. The framework provides a natural conceptual explanation for observed large-scale asymmetries, such as hemispherical anisotropy in the Cosmic Microwave Background, and suggests that direct-sum structures should be regarded as conditional approximations rather than fundamental principles.