A Geometric Interpretation of Quantum Entanglement via Rotation-Induced Radial Structure: Phenomenological Visualization of Correlations from Spatial Phase Organization

Abstract Quantum entanglement gives rise to correlations between measurements performed on spatially separated systems that cannot be explained by classical local models. These correlations are well confirmed experimentally and are described quantitatively by the standard formalism of quantum mechanics. Their physical interpretation, however, remains a subject of continuing discussion in the foundations of quantum theory. The present work contributes to this discussion by proposing a phenomenological geometric visualization of entanglement correlations based on spatial phase organization associated with rotational symmetry of quantum states. Within this interpretation, the phase structure of certain quantum states is represented by a sinusoidal radial phase pattern, here described using a radial-wave representation. Subsystems originating from the same preparation process may therefore be represented as sharing a common geometric phase relationship established during state preparation. The framework presented here does not modify the mathematical formalism of quantum mechanics, introduce hidden variables, or attempt to circumvent Bell’s theorem. Instead, it provides a geometric interpretation of correlations already predicted by the quantum formalism. In particular, the familiar cosine correlation observed in Bell-type experiments appears naturally within the geometric representation. A representative illustrative model is presented to demonstrate the internal consistency of the geometric representation. Within this representation, the familiar cosine correlation observed in Bell-type experiments emerges naturally from the phase relationships defined by the geometric construction. Possible conceptual implications are briefly discussed, while detailed physical applications are left for future investigation.