The Identification of a Viable Ontology for Quantum Mechanics: A Self-Consistent Framework in Which the Postulates of Quantum Theory Are Derived and Its Mysteries Dissolved
For a century, the postulates of quantum mechanics have been taken as irreducible axioms. Bohr, von Neumann, and Feynman each concluded that asking for physical mechanisms underlying the Born rule, wavefunction collapse, or the Pauli exclusion principle constitutes a category error. This consensus was never proved — it was an inference from the failure ofknown attempts.This paper challenges that consensus by exhibiting a candidate framework — Modular Entropic Gravity (MEG) — built on four geometric axioms, in which the six foundational postulates of quantum mechanics are derived consequences and the five standard mysteries of quantum theory have precise physical explanations reducible to classical mechanisms. We make a precise logical claim, not an empirical one. We do not assert that MEG is the correct final theory. We assert that it is internally consistent: its derivations are valid within the framework, no quantum postulate appears as a hidden input, and the programme is non-circular in a precise sense — it derives the probabilistic and interpretive postulates of textbook quantum mechanics from a deeper operator-algebraic level plus the MEG axioms.Several derivations have open steps, all identified explicitly. These concern the technical completion of MEG as a specific theory and do not affect the existence argument: a frame-work of this kind demonstrably can be constructed, as MEG shows. Whether MEG is the correct such framework is an empirical question. That a coherent framework of this kind exists is established here.
For a century, the postulates of quantum mechanics have been taken as irreducible axioms. Bohr, von Neumann, and Feynman each concluded that asking for physical mechanisms underlying the Born rule, wavefunction collapse, or the Pauli exclusion principle constitutes a category error. This consensus was never proved — it was an inference from the failure ofknown attempts.This paper challenges that consensus by exhibiting a candidate framework — Modular Entropic Gravity (MEG) — built on four geometric axioms, in which the six foundational postulates of quantum mechanics are derived consequences and the five standard mysteries of quantum theory have precise physical explanations reducible to classical mechanisms. We make a precise logical claim, not an empirical one. We do not assert that MEG is the correct final theory. We assert that it is internally consistent: its derivations are valid within the framework, no quantum postulate appears as a hidden input, and the programme is non-circular in a precise sense — it derives the probabilistic and interpretive postulates of textbook quantum mechanics from a deeper operator-algebraic level plus the MEG axioms.Several derivations have open steps, all identified explicitly. These concern the technical completion of MEG as a specific theory and do not affect the existence argument: a frame-work of this kind demonstrably can be constructed, as MEG shows. Whether MEG is the correct such framework is an empirical question. That a coherent framework of this kind exists is established here.
The postulates of quantum mechanics — complex Hilbert space structure, unitary evolution, the Born rule, definite measurement outcomes, the canonical commutation relations, and the Pauli exclusion principle — have traditionally been taken as axioms. In this work we show that, within the framework of Modular Entropic Gravity (MEG), these structures admit a unified derivation from four geometric axioms governing the informational structure of the quantum vacuum.The framework is non-circular: its inputs are operator-algebraic structures of quantum field theory — including modular Hamiltonians, the JLMS identity, and the Bisognano–Wichmann theorem — which are defined independently of any probability interpretation. The probabilistic and dynamical rules of textbook quantum mechanics then arise as an infrared effective description of this underlying structure.The six results are obtained in logical order: (Q1) the emergence of complex structure from the entropion mass gap; (Q2) the L2 Hilbert space and Schrödinger equation from the long-wavelength limit of the vacuum propagator; (Q3) the Born rule from a relative entropy identity combined with the PLES–Petz correspondence; (Q4) definite measurement outcomes from PLES boundary conditions imposed by classical apparatus; (Q5) the canonical commutation relations from modular flow via the Bisognano–Wichmann and Araki reconstruction; and (Q6) the Pauli exclusion principle from the Z3 topological structure of the MEG vacuum.Three of these results (Q1, Q2, Q5) are established as complete theorems within the framework. The remaining three (Q3, Q4, Q6) are structurally complete derivations in which the underlying mechanism is fully identified, and any remaining conditions concern either formal infinite-dimensional extension or quantitative refinement.The paper therefore presents a coherent and non-circular programme in which the postulates of quantum mechanics are reconstructed from a smaller set of underlying principles, together with an explicit account of the remaining technical steps required for complete formalisation.
For a century, quantum mechanics has been the most accurately tested theory ever written — and the least understood. It predicts the electron's magnetism to one part in ten trillion, yet no one can quite say why a measurement yields a single definite result, why outcomes appear random, or why two particles far apart are correlated more tightly than any classical theory allows. This paper offers one reading of all three. The deeper description of Nature, we propose, is six-dimensional: ordinary spacetime plus two non-spatial geometric directions — a scale dimension, carrying the resolution at which a question is asked, and a phase dimension, carrying the gauge phase that locks matter to force. In that fuller geometry the underlying state is deterministic and constitutionally real, as Einstein hoped — with no complex phase for quantum chance to be written in; it is not, as Bell's theorem requires of any such theory, local. What a four-dimensional observer sees is its projection; every measurement is unavoidably an average over the two hidden directions — the averaging a century of physics has called collapse. Read this way, the century-old measurement problem becomes three precise questions, each answered by a theorem, and one further question — why outcomes fall in exactly the proportions Born's rule predicts — whose dynamical realization is closed at the relaxation level, as a stated conditional theorem, with one named analytic step remaining. We claim no new laboratory prediction where quantum mechanics already succeeds; we offer a picture in which its deepest strangeness is the shape of a shadow, and the dice — rolled in an imaginary unit made by the same projection — are thrown in two directions our senses can never turn to face. Part of the GG-Theory program, a series of preprints developing a six-dimensional geometric framework and its consequences for particle physics, cosmology, and open-system dynamics. The complete series is available at https://preprints.arisaka-gg.org/
Title Ontological Uniqueness of Quantum Mechanics: A Pre-Quantum Classification Theorem Description This work addresses one of the most fundamental questions in theoretical physics: Why does nature employ quantum mechanical structure rather than alternative mathematical frameworks? We prove a rigorous classification theorem showing that quantum mechanics is not one possible theory among many, but the unique mathematical structure compatible with ontological continuity—the principle that "being cannot cease to be." Unlike previous approaches that either interpret quantum mechanics within its existing formalism (many-worlds, Bohmian mechanics) or derive it from operational measurement axioms (Gleason, Hardy, Chiribella-D'Ariano-Perinotti), this work operates at a pre-quantum logical level: we classify which geometric structures are ontologically admissible before introducing any quantum formalism. Main Result: Any theory satisfying minimal ontological requirements—continuity of being, compositional independence of subsystems, and reversibility of closed-system evolution—must describe the space of identity-classes as complex projective space ℂℙⁿ equipped with the Fubini–Study metric. Complex Hilbert space, unitary dynamics, the Schrödinger equation, and the Born rule emerge as necessary geometric consequences, not as postulates. Alternative structures (real or quaternionic projective spaces, non-homogeneous manifolds) are proven ontologically inadmissible through rigorous exclusion arguments. Key Contributions: Rigorous derivation showing that ontological composition forces a symplectic structure, which combined with homogeneity and isotropy uniquely determines Kähler geometry, selecting ℂℙⁿ as the only admissible space. Complete defense against circularity concerns, with detailed appendices showing that the axioms assume no quantum structure—they are purely ontological requirements for coherent continuous being. Systematic distinction from Gleason/Kochen-Specker theorems and operational axiomatizations, clarifying that this work classifies geometries before quantum mechanics, not constraints within it. Testable predictions in cosmology (Hubble tension resolution, matter fluctuation scaling) and quantum foundations (decoherence rates in molecular interferometry), while rigorously separating structural necessity from empirical determination. Significance: This work transforms quantum mechanics from an empirically successful but conceptually mysterious framework into an ontologically inevitable structure—comparable to Einstein's geometrization of gravity. It shows that quantum structure has no alternative: it is the only mathematical form compatible with coherent, continuous, compositional being. The manuscript includes comprehensive technical appendices with full geometric proofs, axiom justifications, and comparative analysis with existing foundational approaches. Suitable for researchers in quantum foundations, mathematical physics, philosophy of physics, and differential geometry. Document Status: Preprint submitted to Foundations of Physics (January 2026). Related Work: This work is part of the Law of Continuity of Being (LCS) research program, which derives physical and ethical structures from fundamental ontological principles. See author's ORCID profile for related publications. Open Access: This preprint is made available under CC BY 4.0 license to facilitate discussion and feedback from the research community prior to peer review.
The Born rule — the identification of measurement probability with the squared modulus of quantum amplitudes — has resisted derivation from deeper principles for a century. Every attempt within the Hilbert space framework faces the same structural obstacle: complex amplitudes and real probabilities are different kinds of mathematical objects, and connecting them requires either a new postulate or a covert assumption that smuggles in the probability structure being derived.We argue that in Modular Entropic Gravity (MEG), this obstacle does not arise. The MEG state-to-field map (Axiom 1) sends any quantum mixture ρ = |α|2ρA + |β|2ρB with orthogonal branches to the entropy field configuration Sρ = |α|2SA + |β|2SB . The Born weights |α|2 and |β|2 appear directly as convex coefficients of a real field decomposition — not as complex amplitudes requiring conversion. The factorisation of the measurement map through the coarse-graining channel (established in prior work) guarantees that measurement outcomes respect this convex structure, and we prove a readout faithfulness propositionestablishing that an unbiased branch-resolving apparatus produces outcome frequencies equal to the convex coefficients.The traditional Born rule problem — how do complex amplitudes become real probabilities? — is not answered in MEG. It is rendered unnecessary. In a framework where the physical description is a real entropy field whose branch decomposition carries the Born weights as mixture fractions, the amplitude-to-probability conversion is not a measurement postulate but a feature of the representation change from Hilbert space to entropy field. We directly confront the objection that this merely relocates the Born rule into the density matrix, and show that the relocation changes its logical status: from a postulate connecting two categorically different mathematical objects to an inherited structural property of the physical state representation. The information-geometric results of the MEG programme — the Petz recovery fidelity F 2 = |α|2 and the PLES–Petz equilibrium coincidence — are reinterpreted as independent confirmations of the consistency of this convex structure.
The axiomatic foundations of quantum mechanics, while operationally successful, obscure the underlying physical reality. This work introduces a mechanical topological ontology intended to provide a causal basis for the theory. We propose a single postulate: that a fundamental fermion is the 0-dimensional boundary of a 1-dimensional, massive, string-like object topologically anchored to a dynamic vacuum field. From this postulate, we argue that the core structures of single-particle relativistic quantum mechanics can be understood as derivable theorems. First, we construct the object’s state space by identifying two independent, binary properties—a local, vibrational/topological duality (spin) and a global, orientational duality (matter/antimatter)—whose tensor product naturally yields the 4-component Dirac spinor. Second, we show that the requirement of relativistic consistency uniquely determines the algebraic operators (gamma matrices and their Clifford algebra) and the lowest-order dynamical law, leading to the Dirac equation as a theorem of consistency. Third, we demonstrate that the non-relativistic Schrödinger and Pauli equations emerge as its correct low-energy limits, where the quantum potential V (x) is identified with a local variation in the object’s rest mass. Finally, we argue that the foundational tenets of quantum measurement—the spin-1/2 property, the probabilistic Born rule, and the correlations of entanglement—can be reframed as necessary consequences of the object’s intrinsic topology and interaction mechanics. This framework thus offers a path toward demoting the axioms of quantum theory to derivable theorems, aiming to resolve its long-standing paradoxes by providing a clear and coherent physical picture.
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).