Non-Separability as a Structural Principle: From Classical Integrability to Quantum Complementarity

Persistent attempts to interpret quantum theory in terms of classical separability have obscured the structural origins of non-separable phenomena in modern physics. This paper argues that non-separability is not an exclusively quantum feature, but the culmination of a structural transition already implicit in the breakdown of integrability in classical mechanics. Building on insights from Poincaré, Planck, Einstein, and Bohr, the analysis traces how global separations fail under generic dynamics and how fundamental constants encode obstructions to arbitrary decomposition. Complementarity and contextuality are then reinterpreted as emergent structural constraints arising from mutually defining dynamical and observational frameworks, rather than as fundamental postulates. This perspective situates quantum theory within a broader structural continuum and aligns naturally with contemporary relational and structural realist approaches to physical theory.