We observe that there exists a presumed ontology, on the basis of which a dynamical theory is formulated. Extracting the essence of the ontology underlying classical mechanics, we revise it suitably to accommodate quantum mechanics seamlessly. The revision goes through two stages: First, we elaborate the concept of “state” as the propensity of an object to arouse events on discerners. Second, we integrate the position and momentum spaces into a single entity, related via the Fourier transform. Based on this revised ontology, quantum mechanics is deduced naturally without relying upon any artificial assumptions like the “quantum condition” or mathematical apparatuses like the Hilbert space and self-adjoint operators. In consequence, such thorny issues as the “measurement problem” are shown to either resolve or simply disappear.
We observe that there exists a presumed ontology, on the basis of which a dynamical theory is formulated. Extracting the essence of the ontology underlying classical mechanics, we revise it suitably to accommodate quantum mechanics seamlessly. The revision goes through two stages: First, we elaborate the concept of “state” as the propensity of an object to arouse events on discerners. Second, we integrate the position and momentum spaces into a single entity, related via the Fourier transform. Based on this revised ontology, quantum mechanics is deduced naturally without relying upon any artificial assumptions like the “quantum condition” or mathematical apparatuses like the Hilbert space and self-adjoint operators. In consequence, such thorny issues as the “measurement problem” are shown to either resolve or simply disappear.
This work presents a rigorous derivation of quantum mechanics from purely a priori ontological principles, a result not previously achieved within a single self-contained framework. Beginning with the apodictically certain proposition "I am"—immune to all doubt through performative contradiction—we establish through necessary deduction the Principle of Ontological Continuity (POC): Being is continuous and cannot cease or arise ex nihilo. From this single ontological foundation, the complete mathematical structure of quantum mechanics emerges as necessary consequence. We demonstrate that any mathematical representation of ontological continuity must have Hilbert space structure, that ontological conservation necessarily implies unitary evolution, and that the Schrödinger equation follows via Stone's theorem as mathematical necessity, not empirical postulate. The Born rule is derived through three independent converging arguments (Gleason's theorem, direct conservation requirements, and Zurek's envariance), establishing quantum probability as ontological necessity rather than interpretative supplement. Classical foundational problems—wave function collapse, the measurement problem, Bell's non-locality—are resolved without additional assumptions. Collapse emerges as effective description of decoherence; the observer is reconceptualized as self-aware subsystem without ontological dualism; Bell violations confirm ontological unity rather than presenting paradox. Quantum phenomena—superposition as ontological potentiality, tunneling as manifestation of continuity, Pauli exclusion as consequence of ontological structure—are shown to be necessary rather than mysterious. The work establishes quantum mechanics with apodictic certainty mediated through deductive necessity, demonstrating that quantum reality could not have been otherwise. This monograph integrates foundational ontology, mathematical formalism, and resolution of interpretative problems within unified self-contained framework. It deliberately closes at non-relativistic quantum mechanics, establishing stable foundation for future extensions (quantum field theory, general relativity, quantum gravity, normative ethics).
This paper develops the epistemological foundation underlying the spectral reduction of the Riemann Hypothesis presented in RFC-132. Rather than proposing a new analytic proof or an explicit operator construction, RFC-133 addresses a more fundamental question:Why must such an operator exist at all? We introduce the concept of the questionless state—an epistemological zero preceding observation, measurement, and formulation. Within this framework, observation itself is interpreted as an operator action, and stability of existence is shown to require self-adjointness. As a consequence, self-adjoint operators are not optional mathematical tools, but unavoidable structural necessities imposed by the act of observation. The paper reframes the long-standing difficulty of explicitly constructing a Hilbert–Pólya operator. Failure to write down such an operator is interpreted not as non-existence, but as expressive inaccessibility: a limitation of representation rather than ontology. In this view, non-constructive operator existence is not a weakness, but the strongest possible resolution of certain spectral problems. RFC-133 provides the epistemological and ontological closure of the Riemann Operator Program. Together with RFC-132, it establishes both the sufficiency and the necessity of operator existence for resolving the Riemann Hypothesis, while remaining fully consistent with modern operator theory and quantum mechanics. Keywords:Riemann Hypothesis, Operator Theory, Self-Adjointness, Hilbert–Pólya Program, Observation, Epistemology, Quantum Measurement, Non-Constructive Proofs
This paper presents a unified conceptual framework — the Dual-Aspect Coin Framework (DACF) — for understanding the nature of quantum fields, quantum objects, classical reality, hierarchical emergence, and the precise relationship between mathematics and physical reality. The framework proposes a three-stage ontology as the foundation of physical existence. The first stage is the germinating stage — quantum fields as pure potentiality, neither static nor flow, prior to any dual-aspect expression, permanently beyond mathematical formulation. The second stage is actualisation — the emergence of a real physical entity when all probability conditions simultaneously converge and are fulfilled. The third stage is the coin — the actualised quantum object carrying two irreducible co-constitutive faces, a static face and a flow face — the first appearance of dual-aspect reality. From this actualised coin, hierarchical emergence proceeds through successive stabilisation events, building from quantum objects through composite particles, atoms, molecules, and macroscopic classical reality. The framework further establishes that mathematical symbols are static formulations and equations are mathematical representations of flow — tools consciousness uses to formulate what has already actualised. Critically, the Schrödinger equation and all quantum mechanical formalism operate exclusively in the post-actualisation domain. The germinating stage is identified as a permanent and structural boundary of mathematical knowledge — not a technical limitation awaiting future resolution but an absolute ontological boundary arising from the fact that the germinating stage is prior to the very conditions that make mathematics possible. This framework resolves wave-particle duality, the measurement problem, the quantum-to-classical transition, and the unre
We introduce an ontology of objects and events that is particularly well suited for several interpretations of quantum mechanics. It leads to an important revision of the notion of matter and its implications. Within this context one can show that systems in entangled states present emergent new properties and downward causation where certain behavior of parts of the system are only determined by the state of the whole. Interpretations of quantum mechanics that admit such an event ontology solve the problem of emergence.
Abstract Metaphysicians should pay attention to quantum mechanics, but not because it provides definitive answers to many metaphysical questions. The theory itself is remarkably silent on the nature of the physical world, and the various interpretations of the theory on offer present conflicting ontological pictures. Rather, quantum mechanics is essential to the metaphysician because it reshapes standard metaphysical debates and opens up unforeseen new metaphysical possibilities. Even if quantum mechanics provides few clear answers, there are good reasons to think that any adequate understanding of the quantum world will result in a radical reshaping of our classical worldview in some way or other. Whatever the world is like at the atomic scale, it is almost certainly not the swarm of particles pushed around by forces that is often presupposed. This book guides readers through the theory of quantum mechanics and its implications for metaphysics in a clear and accessible way. The theory and its various interpretations are presented with a minimum of technicality. The consequences of these interpretations for metaphysical debates concerning realism, indeterminacy, causation, determinism, holism, and individuality (among other topics) are explored in detail, stressing the novel form that the debates take given the empirical facts in the quantum domain. While quantum mechanics may not deliver unconditional pronouncements on these issues, the range of possibilities consistent with our knowledge of the empirical world is relatively small—and each possibility is metaphysically revisionary in some way.