Quantum Entanglement as Structural Non-Closure: A TNA Perspective

Quantum entanglement violates Bell inequalities experimentally, ruling out locally closed descriptions of physical systems. This violation is not dynamical—no superluminal signaling occurs—but structural: the global quantum state cannot be reconstructed from local properties. We formalize this failure of local closure using the Theory of Axiomatic Necessity (TNA), where coherent systems require irreducible external structural support (N₁) beyond their locally observable domain (N₀). Entanglement provides a physical instantiation of this principle: the global wavefunction plays a role structurally analogous to N₁, enabling coherence without operating causally. This framework unifies quantum non-separability with similar structural limits in mathematics, machine learning, and social systems, demonstrating that local closure is not merely difficult but impossible for coherent systems.