This work introduces and formalizes Horizon Monism, a foundational relational research program built upon minimal ontology. It postulates a timeless, scale-free, geometry-free totality of relations \mathfrak{R}, together with a collection of irreducible first-person referential anchors. All observable physical phenomena emerge from a single core constraint: finite distinguishability. Each referential anchor carries a non-injective information extraction map, which induces reference-dependent equivalence relations. These partition the underlying relational totality into quotient spaces of effectively distinguishable states. Non-commutative algebraic structures (quantumness), effective time and its arrow, Lorentzian spacetime geometry together with gravity, and gauge interactions all arise homologously as effective descriptions for observers confined within finite referential horizons. We rigorously demonstrate that finite equivalence classes equipped with relation groupoids yield non-commutative C^*-algebras. A four-point classical toy model further illustrates that incompatible extraction operations can naturally produce non-commutativity, serving as a mathematical prototype for the horizon-based origin of quantum structures. We clearly separate three tiers of statements: constructively proven mathematical results, hypothetical emergence mechanisms, and low-energy effective phenomenology. The Standard Model gauge group and particle spectra are treated as low-energy emergent features to be derived in future work, rather than fundamental axioms. This framework avoids circular reasoning by not presupposing time, probability, spacetime geometry or quantum states at the ontological level, offering a falsifiable relational pathway toward quantum gravity.
This work introduces and formalizes Horizon Monism, a foundational relational research program built upon minimal ontology. It postulates a timeless, scale-free, geometry-free totality of relations \mathfrak{R}, together with a collection of irreducible first-person referential anchors. All observable physical phenomena emerge from a single core constraint: finite distinguishability. Each referential anchor carries a non-injective information extraction map, which induces reference-dependent equivalence relations. These partition the underlying relational totality into quotient spaces of effectively distinguishable states. Non-commutative algebraic structures (quantumness), effective time and its arrow, Lorentzian spacetime geometry together with gravity, and gauge interactions all arise homologously as effective descriptions for observers confined within finite referential horizons. We rigorously demonstrate that finite equivalence classes equipped with relation groupoids yield non-commutative C^*-algebras. A four-point classical toy model further illustrates that incompatible extraction operations can naturally produce non-commutativity, serving as a mathematical prototype for the horizon-based origin of quantum structures. We clearly separate three tiers of statements: constructively proven mathematical results, hypothetical emergence mechanisms, and low-energy effective phenomenology. The Standard Model gauge group and particle spectra are treated as low-energy emergent features to be derived in future work, rather than fundamental axioms. This framework avoids circular reasoning by not presupposing time, probability, spacetime geometry or quantum states at the ontological level, offering a falsifiable relational pathway toward quantum gravity.
Horizon Monism proposes a unified theoretical framework in which quantum structure, operational time, and spacetime geometry emerge from finite reference horizons embedded within a single, scale-free relational–interaction totality. Rather than treating spacetime, fundamental time, and quantum probabilities as primitive, the framework investigates their possible reconstruction through finite distinguishability, relational compression, and effective projection structures. The paper establishes a strict mathematical hierarchy of finite-horizon resolutions, deriving monotonic distinction deficits and a directed fine-to-coarse order as a candidate foundation for operational time. This construction is extended to multiple reference horizons through order-preserving transport and conditional shared-blindness theorems. Within a conditionally constructed complex groupoid algebra, the minimal noncommutative effective structure is identified as M₂(ℂ). Projection compression is shown to generate noncommuting effective operators, while smoothly varying projections induce connection curvature. Under specified geometric conditions, this curvature reconstructs the Levi-Civita curvature of an emergent Lorentzian spacetime. Explicit de Sitter and nonlinear Green-spectral constructions provide conditional examples of Einstein geometry and stable nonvanishing projected curvature. A further reconstruction of quantum probability establishes that normalized, context-independent, coarse-graining-consistent effect assignments admit a unique density-matrix representation, recovering the Born rule for pure states. The Principle of Minimal Sufficient Realization is additionally applied to a restricted class of Standard-Model-type representations, yielding conditional minimality results for color, fermion generations, and Higgs structure. The framework distinguishes exact mathematical theorems from conditional physical realizations. Its principal unresolved questions concern the microscopic origin of quantum probability consistency, physical state selection, continuum dynamics, and experimentally distinguishable predictions. Horizon Monism is presented as a mathematical and theoretical research program toward the possible co-emergence of quantum physics and gravitation.
This treatise develops Informational Monism as a unified ontological architecture for emergent spacetime, quantum records, and bounded agency. It rejects the premise of an ontologically primary spatiotemporal container populated by localized particles, and treats physical reality instead as a coarse-grained, error-corrected rendering of a deeper informational state. Reality is organized across three tiers: an unmanifest Meta-Background; a low-dimensional Code Circuit carrying a global unitary description; and a rendered bulk in which embodied observers encounter classical spacetime, matter, and records. Within this architecture, the treatise offers interpretive accounts of three central problems in foundational physics. Bell correlations are read through joint commitment at the boundary rather than through bulk signalling. Quantum measurement is treated as the actualization of a single irreversible record under a question-and-commitment discipline that preserves Born neutrality. Black-hole information is handled through complexity-resolved conservation: fine-grained unitarity may be preserved while remaining inaccessible to resource-bounded decoders. A Minimal Core of six postulates supports these proposals without modifying the predictive apparatus of quantum mechanics. Broader extensions — including the Horizon Model of the Dynamic Absolute, the Principle of Super-Balance, and the conservation of meaning — are developed separately and marked as dependent on further postulates. The work distinguishes direction from status in the arrow of time, states labelled conjectures and conditions of revision, and presents a research programme with near-, mid-, and far-term horizons. The result is not a claim of final theory, but a systematic non-dualistic framework in which geometry, record formation, accessibility, and agency can be discussed within one architecture. Keywords: Informational Monism; emergent spacetime; holographic principle; quantum measurement; Bell non-locality; black hole information; complexity; Super-Balance; philosophy of physics; foundations of quantum mechanics
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.
The Transreflective Dimensional Model (MTD) is reformulated as a speculative pre-spatiotemporal relational framework rather than as a completed theory of quantum gravity or a direct unification of quantum mechanics and general relativity. The central hypothesis is that observable physical distinctions need not correspond to primitive distinctions in the fundamental ontology. The fundamental domain, denoted by X, is assumed to admit multiple relational manifestations without any manifestation possessing a privileged ontological status as an “original.” Observable properties, subsystem decomposition, and potentially spacetime itself are treated as emergent structures associated with context-dependent manifestations of X. The paper introduces a minimal set of postulates and investigates their mathematical consequences. A quotient construction is shown to remain compatible with a classical Boolean theory, demonstrating that pre-spatiotemporality, relational emergence, and transreflective equivalence alone are insufficient to recover quantum mechanics. A groupoid-based realization is developed as a candidate mathematical representation of reversible transreflective relations, while a non-globality condition is examined as a route to contextual nonclassicality. The analysis establishes several no-go results: the present MTD postulates do not uniquely derive quantum mechanics, the Born rule, purification, general relativity, or the Standard Model. MTD 2.0 therefore does not claim a Theory of Everything. It is presented as a mathematically explicit foundational research framework and as a starting point for investigating whether transreflective principles can generate independently testable physical structure.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.
This manuscript presents a conservative mathematical framework investigating whether observable multiplicity and distinguishability in physical theories can emerge from a more primitive, undifferentiated starting point. A singular foundational state SSS is defined as a minimal-ontology entity lacking internal partitions, while interpretation operators III are introduced as structural maps that induce differentiated state spaces M=I(S)M = I(S)M=I(S). The paper develops the formal properties of these operators using moderate operator algebra, category theory, and structural analysis, and situates the framework alongside established programs in quantum reconstruction, operator-algebraic foundations, information-theoretic approaches, and relational quantum mechanics. Connections are drawn between interpretive non-commutativity and contextuality, and between induced multiplicity and the emergence of classical state identity in measurement theory. This is an exploratory theoretical contribution intended to motivate further mathematical development. It does not propose empirical modifications to quantum mechanics, but provides a structural model for understanding how distinctions, state-space geometry, and observable outcomes may be generated rather than postulated. The framework may have relevance for foundational studies in quantum information, measurement, generalized probabilistic theories, and the structure of operator families underlying physical state differentiation.