Quantum mechanics as observer-induced quotient graph dynamics

Abstract A discrete ontological reconstruction of quantum mechanics based on a graph-theoretical model with deterministic cyclic dynamics is proposed. The approach is based on the hypothesis that the standard formalism of quantum theory emerges as an effective relational description of the dynamics of a closed finite system from the perspective of an endogenous (internal) observer. Within this holistic framework, the observer acts simultaneously as the subject and the object of measurement. The self-referential nature of an internal observer imposes fundamental limitations on access to the complete ontological description, giving rise to a specific form of informational incompleteness. It is shown that the physically accessible states for an internal observer are exclusively equivalence classes of macroscopically indistinguishable ontological states. Therefore, factorization of the dynamics with respect to indistinguishable ontological states becomes the conceptual core of the description of physical reality. Using a basic model as an example, we demonstrate how the factorization of ontological trajectories induced by informational incompleteness naturally leads to the emergence of complex amplitudes and the Born rule. It is shown that the geometry of the edge space of a complete graph realizes a discrete phase space on which the action of the Heisenberg–Weyl group is induced. As a physical verification of the proposed formalism, a graph-theoretical interpretation of two-photon interference in the Hong–Ou–Mandel effect is presented.