This paper proposes a theoretical framework—Relational Theory—based on dynamic relational networks, in which discrete spacetime serves as the fundamental ontology, while continuous geometry and gravity emerge as macroscopic statistical phenomena. This framework unifies the description of matter, spacetime, and gravity, aiming to bridge the theoretical divide between quantum field theory and general relativity, while providing a discrete spacetime physical substrate for the orthodox prob abilistic interpretation of quantum mechanics. The fundamental ontology of the universe is defined as the evolution of a dynamic relational network, where nodes represent fundamental quantum units of space, edges correspond to adjacency relations between units, and matter manifests as complex probability amplitude excitation modes propagating on the network. The framework is built upon two foundational axioms: the matter field undergoes unitary evolution driven by the graph Lapla cian operator, and the network topology dynamically reconfigures in response to the matter energy density, with links undergoing continuous generation and decay, while matter evolution exhibits the discrete alternating character of “annihilation here, creation there.”Under the mean-field continuum limit, the two axioms respectively evolve into a Schr¨odinger equation describing matter propagation in curved space and a link density equation characterizing the response of spacetime geometry to matter distribution. These two sets of equations form a self-consistent feedback mechanism in which matter and spacetime geometry mutually constrain each other. The study demonstrates that grav ity is not a fundamental interaction, but rather a statistical emergent entropic force driven by the inhomogeneous spatial distribution of network link density.This paper further proposes a dynamic relational network interpretation, circumventing the collapse paradox of the Copenhagen interpreta tion, the universe-splitting problem of the many-worlds interpretation, and the non-locality dilemma of hidden variable theories. It provides an underlying topological explanation for wave function evo lution, the measurement problem, and the origin of quantum probability. The laws of black hole thermodynamics and the fundamentals of the holographic principle can all be reasonably explained within this microscopic topological framework. The paper systematically verifies the mathematical self-consistency of the model, distinguishes rigorously derived conclusions from conjectures awaiting verification, and demonstrates the feasible pathways for numerical simulation tests and astronomical observational corroboration.
This paper proposes a theoretical framework—Relational Theory—based on dynamic relational networks, in which discrete spacetime serves as the fundamental ontology, while continuous geometry and gravity emerge as macroscopic statistical phenomena. This framework unifies the description of matter, spacetime, and gravity, aiming to bridge the theoretical divide between quantum field theory and general relativity, while providing a discrete spacetime physical substrate for the orthodox prob abilistic interpretation of quantum mechanics. The fundamental ontology of the universe is defined as the evolution of a dynamic relational network, where nodes represent fundamental quantum units of space, edges correspond to adjacency relations between units, and matter manifests as complex probability amplitude excitation modes propagating on the network. The framework is built upon two foundational axioms: the matter field undergoes unitary evolution driven by the graph Lapla cian operator, and the network topology dynamically reconfigures in response to the matter energy density, with links undergoing continuous generation and decay, while matter evolution exhibits the discrete alternating character of “annihilation here, creation there.”Under the mean-field continuum limit, the two axioms respectively evolve into a Schr¨odinger equation describing matter propagation in curved space and a link density equation characterizing the response of spacetime geometry to matter distribution. These two sets of equations form a self-consistent feedback mechanism in which matter and spacetime geometry mutually constrain each other. The study demonstrates that grav ity is not a fundamental interaction, but rather a statistical emergent entropic force driven by the inhomogeneous spatial distribution of network link density.This paper further proposes a dynamic relational network interpretation, circumventing the collapse paradox of the Copenhagen interpreta tion, the universe-splitting problem of the many-worlds interpretation, and the non-locality dilemma of hidden variable theories. It provides an underlying topological explanation for wave function evo lution, the measurement problem, and the origin of quantum probability. The laws of black hole thermodynamics and the fundamentals of the holographic principle can all be reasonably explained within this microscopic topological framework. The paper systematically verifies the mathematical self-consistency of the model, distinguishes rigorously derived conclusions from conjectures awaiting verification, and demonstrates the feasible pathways for numerical simulation tests and astronomical observational corroboration.
Abstract This article does not claim to present a successful theory of quantum gravity. Instead, it undertakes a systematic and self-aware survey of the research program aiming to derive both quantum mechanics and general relativity from a purely relational network, based on a set of minimal ontological postulates. The framework rests on three axioms: (1) physical reality consists of nodes without intrinsic properties and their symmetric relations; (2) the relation strengths are non-negative and symmetric, with the total information capacity conserved as an ensemble expectation; (3) local evolution is restricted to redistribution of relations within triads. We honestly display and rigorously distinguish the conceptual achievements from the essential obstacles of this framework. On the quantum side, we obtain solid conceptual progress: the Born rule, unitary evolution, and topological nonlocality of entanglement all emerge naturally as representation-theoretic consequences of the statistical description of a finite information capacity network. This strongly suggests that the mathematical structure of quantum mechanics may be a generic feature of the statistical representation of any complex informational system satisfying “finite information + local relational evolution.” On the gravitational side, however, we encounter chasms that current mathematical and conceptual tools cannot bridge. A central contribution of this article is to clearly label these obstacles as fundamental open scientific problems: the conflict between a positive-definite relational ontology and the target of pseudo-Riemannian signature (signature problem); the missing coarse-graining procedure from a discrete network to a smooth manifold (coarse-graining problem); and the disharmony between external algorithmic time and emergent physical time (time problem). We argue that these are not technical details unique to this framework, but core challenges that any “spacetime from relations” program must confront. The article positions itself as a “conceptual cartography”—it precisely delineates the known boundaries of this research program, exposes the fatal rift often bypassed in mainstream discourse, and transforms all unresolved issues into a formal invitation for future investigation.
General relativity and quantum mechanics rely on fundamentally incompatible conceptions of spacetime: the former treats spacetime as a smooth, dynamical entity, while the latter presupposes a fixed background on which quantum states evolve. This work introduces the Collapse Spacetime Model (CSM), a foundational framework in which spacetime itself is not fundamental but emerges from discrete ontological transition events (OTEs)—objective, irreversible acts of actualization that generate localized spacetime structure. Within CSM, quantum state reduction is reinterpreted as one particular manifestation of a more general ontological transition, rather than as an anomaly within unitary dynamics. A central refinement, the Multiplicity of Spacetime Hypothesis (MSH), proposes that physical systems construct their own partial spacetimes, with the classical spacetime continuum arising from stable intersections among these locally generated structures. Constants such as the speed of light are interpreted as invariant structural ratios of spacetime co-generation, rather than as fundamental properties of matter or signals. The model aligns conceptually with causal set theory, emergent network geometry, and collapse-based approaches, while offering a unified ontological account of spacetime emergence, time’s passage, and the relational origin of geometry. CSM reframes physical reality as a becoming universe, providing a coherent foundation for quantum gravity, cosmology, and the philosophy of time, while deliberately postponing detailed dynamical and mathematical formalization to future work.
A Trinary Relational Framework for Physics: Information, Energy, and Emergent Spacetime presents a foundational theoretical model in which relations, rather than isolated objects, are treated as the primary constituents of physical reality. The paper proposes a trinary ontology in which any minimal physical existence consists of two systems and the relation between them, with the relation itself carrying physical significance. From this basis, it develops a relational formalism linking informational structure to energy, mass, decoherence, time, gravity, and discrete geometry. The framework introduces a non-Markovian, threshold-based update mechanism in which physical change occurs only when accumulated relational drive overcomes stability resistance. Within this model, decoherence is reinterpreted as an objective structural phase transition rather than an observer-dependent collapse, black hole singularities are replaced by maximum-density stability walls, and gravitational time dilation is derived as informational update-impedance. The paper also argues that discrete geometric spectra emerge from resonance-selected relational structure, yielding an area-first ontology that can generate bounded volumetric primitives without presupposing background spacetime. In addition to its ontological and mathematical proposals, the paper outlines a route toward explaining the Standard Model mass hierarchy in terms of informational complexity, local constraint structure, and pathway adjacency. It further advances falsifiable predictions, particularly in quantum decoherence, discrete area quantization, and black hole evaporation, with several proposed tests designed to be accessible using current or near-term experimental technology. Overall, the work is an attempt to construct a unified, information-first relational physics in which many longstanding foundational problems, including the measurement problem, emergent classicality, temporal asymmetry, and singularity formation, arise from a single underlying mechanism: the thresholded updating of relational information.
## Title The Relational Closure Framework: From Relations to Matter via Causal Consistency ## Authors Mingdong He (Independent Researcher, ORCID: 0009-0009-5176-7571) ### Overview This deposit contains the complete source code and compiled PDF of the Relational Closure Framework (RCF) version 2.0C, a relational approach to the foundations of physics developed as a candidate contribution to Hilbert's sixth problem (the axiomatization of physics). The framework proposes that the universe is constituted by **relations** rather than objects. Stable relations form **closures** (self-consistent cycles); closures generate topological invariants (holonomies); and these invariants underpin all physical structures—conservation laws, the least-action principle, the Born rule, dimension, geometry, and matter—as emergent phenomena of the closure network at different scales. ### What is new in v2.0C Version 2.0C introduces a **causal consistency principle**: physical existence requires causal consistency as a precondition, not as a consequence of continuous spacetime. What appears as continuity is reinterpreted as **pseudo-continuity**—the statistical artifact of mutually constraining discrete closures. This reframing dissolves (rather than solves) the continuum-limit problem that has obstructed discrete approaches to physics for decades. Key new results in v2.0C: 1. **Causal consistency as physical precondition** — The speed of light is derived as the enforcement mechanism for causal consistency (not an arbitrary postulate). 2. **Randomness from constraint gaps** — Quantum probability arises naturally from the incompleteness of discrete constraints, not from an axiom. 3. **Wave function as constraint-gap envelope** — The wave function exists because the network is discrete; it "waves" because holonomy phases interfere; it is non-classical because it carries probability, not energy. 4. **Schrödinger equation from pseudo-continuity** — Via the Madelung transformation, the Schrödinger equation is shown to emerge from: (i) holonomy action stationarity (Hamilton–Jacobi), (ii) constraint-gap-induced probability density, and (iii) Noether conservation (continuity equation). The quantum potential is interpreted as the signature of pseudo-continuity failure. 5. **Fields as long-range constraint mechanisms** — All fundamental fields are intrinsically long-range because causal consistency is a global requirement. The de Sitter entropy (~10^122) is conjectured as the information-theoretic capacity bound on causal constraints. ### Core results (retained from v1.2) - A **generalized Noether theorem**: conservation is identified with the kernel of the exchange map, derived from axioms without assuming symmetry. - A **least-action principle**: the action is proved to be necessarily a function of closure holonomies; δS = 0 is equivalent to a non-abelian Kirchhoff law; the continuum limit recovers Maxwell and Yang–Mills equations. - The **Born rule**: stochasticity arises from the observer as an open dynamical system (Nakajima–Zwanzig); the square law |α|² is forced by the Gleason–Busch theorem under finite additivity. - The **Z₃–γ₅ algebraic correspondence**: a strict algebraic identity linking the minimal relational closure (3-cycle) to the Dirac chirality operator. - A **quantum error correction correspondence**: the Gauss-law operator is structurally identical to the toric-code stabilizer; vacuum stability is topologically protected. ### AI use disclosure This manuscript was prepared with the assistance of AI language models (Claude/ChatGPT/Gemini families) for typesetting, reference formatting, and consistency checking. All theoretical content—axioms, proofs, conjectures, and the causal consistency principle—is the sole intellectual contribution of the author. AI tools were used as a writing assistant, not as a source of scientific ideas.
We propose a unified physical framework in which four-dimensional spacetime vacuum is the unique physical reality, and all quanta are its localized topological excitations. Matter particles correspond to stable knot-like configurations, while radiation quanta correspond to weak propagating ripples of the same substrate. From this single ontological commitment, we derive: (1) wave–particle duality is resolved—particle behavior belongs to the localized excitation, wave behavior to the disturbance field it generates in spacetime; (2) double-slit interference arises from coherent superposition between a quantum's newly sourced disturbance and its own historical disturbance field, not from ontological self-superposition; (3) the wave function is a statistical tool encoding ensemble distributions of trajectories modulated by disturbance feedback, and collapse is epistemic convergence rather than a physical process; (4) quantum entanglement corresponds to Planck-scale topological connectivity (microscopic Einstein–Rosen bridges), preserving relativistic causality; (5) gravity is the macroscopic accumulation of universal but individually weak quantum–vacuum couplings, explaining both its microscopic weakness and macroscopic dominance without requiring a graviton; (6) the four fundamental interactions are differentiated coupling modes of quanta to one spacetime vacuum field; and (7) apparent dark matter and dark energy are reinterpreted as collective topological curvature and large-scale vacuum self-relaxation, respectively. We formulate falsifiable predictions at both laboratory and cosmological scales, including disturbance–corpuscle separation interferometry, tunable decoherence threshold measurements, and galaxy rotation–topology correlations. The framework compresses the conventional axiomatic structure of quantum mechanics and cosmology into one master axiom and eliminates at least twenty-eight independent interpretive assumptions.
The core dilemma of modern physics stems from two unproven ontological presuppositions: that spacetime is an innate container preceding matter, and that matter is an entity composed of indivisible particles. These presuppositions have led to the fundamental split between general relativity and quantum mechanics, giving rise to a series of century-old unsolved problems such as wave-particle duality, the quantum measurement paradox, the nature of gravity, and dark matter and dark energy. Based on the sole unfalsifiable first principle that "the essence of cognition is succession", this paper deduces a complete ontological system through pure a priori reasoning: the authentic physical world consists solely of one-dimensional successive rays and their transverse coupling relations; time is the successive extension of rays, space is the network of coupling relations, matter is the steady state of closed coupling, and all interactions are different manifestations of coupling actions. Particles are not authentically existing entities, but rather point-like endpoint phenomena presented in the observer's phenomenal world when two rays undergo an all-or-nothing coupling. Based on this framework, this paper uniformly explains all core phenomena in both the microscopic quantum domain and the macroscopic relativistic domain in one go, resolves all traditional physical paradoxes at the ontological level, achieves the ontological unification of the four fundamental forces, and proposes three falsifiable core predictions. This paper demonstrates that all theories of traditional physics are approximate descriptions of the authentic physical world at the phenomenal level, and their fundamental error lies in mistaking "coupling endpoints" for "primitive entities", thereby reversing the causal relationship. Cognitive Succession Ontology provides a logically consistent and universally unified ultimate foundation for physics.