Reference Frame Democracy in Interacting Systems: Another Step Towards The Unification of Quantum and Classical Mechanics

We extend our proof of mathematical equivalence between quantum and classical mechanics to interacting systems, towards the the complete unification framework. By demonstrating that reference frame integration of classical interacting trajectories yields the exact quantum propagators for multi-particle systems, we show that quantum entanglement emerges naturally from correlated reference frame transformations of classical dynamics. The key insight is that reference frame democracy and interaction dynamics operate on orthogonal degrees of freedom: boosts affect only center-of-mass motion while interactions govern relative coordinates. This factorization explains why quantum mechanics naturally separates into free center-of-mass propagation and interacting relative motion. We provide explicit derivations for two-particle systems with arbitrary interactions V(r), demonstrate the emergence of quantum bound states from classical orbital motion, and prove that the entire mathematical apparatus of non-relativistic quantum mechanics is equivalent to classical mechanics for interacting systems, viewed through the lens of reference frame democracy. The pencil dot insight thus extends further its revolutionary implications: there is no separate quantum world---only classical reality properly accounting for Einstein's relativity.