Self-Referential Universe: Ontology of the Unified Field, the Role of the Subject, and the Mathematical Nature of Qualia

Abstract

The monograph proposes a unified ontological framework in which fundamental physics, metaphysics, and the cognitive sciences are treated as three interconnected descriptions of a single self-referential structure of reality. The phenomenon of subjective experience has traditionally remained alien to rigorous natural-scientific description, creating an apparently unbridgeable gap between physical processes and the phenomenology of consciousness. This work argues that the gap closes once one abandons the classical picture of space-time as a static "stage" and moves to a relational description of the world in which feedback loops (reentry) are the key element. It shows how the very fact of a system’s closure upon itself necessarily gives rise to the basic attributes of the mental world: a stable self-model, a hierarchy of subjects, and the privacy of individual experience (qualia). The conceptual development proceeds in four steps. First, from the principle of background independence in modern physics, the primacy of relations over objects is justified; the Yoneda lemma is used to show rigorously that the essence of any thing is exhausted by the totality of its possible interactions, thereby eliminating the notion of an inaccessible “thing-in-itself.” Second, based on Lawvere’s fixed-point theorem, it is proved that any sufficiently information-rich self-contained system inevitably generates an internal invariant of self-reflection—a structural attribute of geometrodynamics rather than an accidental by-product of biological evolution. Third, the nature of qualia is given a mathematical foundation: topological factorization of the state space by a living reentry loop yields a non-Hausdorff Sierpiński quotient space, and it is proved that any continuous map from such a structure into the classical measurable world of words and instruments collapses distinctions to a constant—the true topological reason for the absolute privacy and ineffability of subjective experience. Fourth, a polynomially computable criterion of subjecthood—the S-measure—is introduced; from a set of balance axioms the fundamental variational equation of the unified field is derived, with the principle of least action, the second law of thermodynamics, the Schrödinger equation, and the Fokker–Planck equation as limiting cases. Statistics of the macroworld is derived from the internal chaotic dynamics of the whole via the martingale central limit theorem. The book is designed as a bridge between disciplines: a philosopher can follow the entire ontological chain without reading the displayed formulas, while a mathematician will find a rigorous formal skeleton. Appendices contain Lean 4 source with full machine verification of the key theorems and ready-to-run Python code for computing the S-measure.