Complementarity as interaction-dependent decomposition: a relational mechanism for a foundational Quantum principle

This paper proposes that quantum complementarity arises from interaction-dependent tensor-product-structure (TPS) selection. Different measurement interactions impose distinct decompositions on the joint system–apparatus Hilbert space, each stabilizing a different pointer algebra through decoherence. Complementary descriptions emerge when the TPS induced by one interaction is incompatible with another, so no single coupling can realize both observable algebras simultaneously. The framework stays within standard quantum mechanics, requiring no new postulates. A minimal qubit model demonstrates how incompatible measurement couplings stabilize different subsystem splits and suppress coherence pathways needed for alternative descriptions. The account clarifies Bohr's original claim that phenomena depend on the whole experimental arrangement, grounding it in interaction geometry rather than interpretive principle. Testable predictions include tunable complementarity regimes, TPS interference revival, and multi-detector incompatibility thresholds.