Extended Relational Quantum Dynamics (RQD): Wavefunctions as Intrinsic Relational States

We develop an extended formulation of Relational Quantum Dynamics (RQD) in which the quantum wave function is treated as an intrinsic relational entity rather than an external absolute state. Building on enriched category theory and related advanced frameworks, we formalize RQD using higher-category structures and presheaf/topos-theoretic tools to rigorously capture the web of relations between quantum systems (observers and observed). In this enriched formalism, each pair of quantum systems is associated with a relational Hilbert space and state vector, and higher-category morphisms naturally represent multi-observer interactions. We incorporate information-theoretic “awareness” measures such as mutual information and integrated information into the theory, allowing a quantitative gauge of relational knowledge or consciousness where applicable. We show that the Born rule for outcome probabilities emerges internally from the relational structure, consistent with Gleason’s theorem, and that quantum contextuality (no observer-independent values) is built in by construction. Using presheaf models, we demonstrate that no global hidden-variable state can exist across all observers, aligning with the Kochen–Specker theorem. The extended RQD remains empirically equivalent to standard quantum mechanics in ordinary scenarios, but it provides a richer language to address exotic setups. We explore novel experimental scenarios, including designs where quantum computers serve as controllable “observers.” We review recent work in quantum computation and relational interpretations, and propose how multi-observer interference experiments and quantum information protocols can test the relational framework.