Relational Prohibition of Spatial Superposition: A Proof by Contradiction within Relational Quantum Theory

This paper presents a proof by contradiction demonstrating that within Relational Quantum Theory (RQT), objects with high relational density cannot exist in spatial superposition. Unlike standard decoherence interpretations, where macroscopic superpositions are merely "unobservable" due to rapid environmental entanglement, RQT asserts that spatial superposition is logically forbidden for objects with dense internal relational networks. The key argument proceeds as follows: For an object to exist in spatial superposition |O_A⟩ + |O_B⟩, three conditions must be satisfied simultaneously: (1) identical internal relations (object identity), (2) different external relations (distinct positions), and (3) orthogonality of states (superposition requirement). We demonstrate that these conditions are mutually contradictory for objects where internal and external relations form a coupled network. The result offers a testable prediction distinguishing RQT from standard quantum mechanics: objects of equal mass but different internal relational density (e.g., crystal vs. confined gas) should exhibit different decoherence times, even in identical external environments.