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.
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.
Does Physical Existence Require Predefined Identity, Position, or Distance? This paper investigates a foundational possibility: physical entities may exist without possessing fully defined relational identities, positions, or measurable distances. It proposes that these properties become physically meaningful through relational structures capable of representing the information that defines them. The framework explores two applications of this principle. In quantum physics, it examines the indistinguishability of identical particles, fermionic antisymmetry, bosonic occupation multiplicity, and entanglement through the distinction between physical existence and relational identity. In emergent geometry, it proposes that spatial distinction can precede measurable distance, with metric structure arising from a larger network of physical relations. The mathematical development introduces a weighted relational network and employs graph Laplacians, Green functions, spectral dimension, and effective resistance to investigate the emergence of geometric structure. A relational compensation principle motivates preliminary equilibrium conditions and dynamical models. An initial numerical experiment shows that a localized perturbation can produce a nonlocal structural response across the network. Although this result does not yet reproduce a gravitational law, it provides a concrete starting point for investigating field-like behavior within the proposed framework. The central contribution is a common relational foundation for quantum identity and emergent spacetime geometry, supported by mathematical constructions and preliminary numerical investigation. The work does not claim a completed unification of quantum mechanics and general relativity. Open challenges include deriving a unique network dynamics, three-dimensional space, the Born rule, and gravitational field equations. The principal research question is whether a single relational dynamics can yield quantitative, testable predictions in both quantum physics and emergent spacetime geometry.
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.
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.
Quantum phenomena are traditionally described as states evolving in spacetime, yet the zero–proper–time behavior of massless systems points to a different architecture—one in which propagation is not fundamental. Motivated by this observation, we develop a relational framework in which physical processes are represented not as trajectories but as relations between contexts and outcomes. The central object is a relational amplitude function R:B×O→C, organized as a fiber bundle whose slices R_b are selected by experimental contexts. Expressed entirely in standard mathematical terms—probability theory, quantum amplitudes, and fiber‑bundle structure—this relational architecture is precise and unambiguous. Interference, entanglement, and measurement emerge as geometric properties of slice selection rather than as dynamical evolution of a spacetime system. Interference arises when a slice contains multiple coherent contributions; entanglement arises from the non‑factorization of the relational object; and measurement corresponds to a context update rather than a physical collapse. The geometry of zero proper time motivates a shift from a spacetime ontology to a relational one, yielding a unified, non‑spatiotemporal account of quantum phenomena. The result is a structurally simple and conceptually coherent reformulation of quantum mechanics that dissolves long‑standing paradoxes and clarifies the relational foundations from which spacetime events arise. This is version 1.0 of the manuscript. Authors' note (October 2026). This is the original March 2026 manuscript, preserved unchanged as the starting point of an ongoing research program. It is a conceptual proposal, not a set of established results: the framework reformulates the standard quantum formalism in relational language and does not derive it. The proofs of Theorems 5.3 (entanglement) and 5.5 (no-signaling) require additional assumptions that the paper does not state, and claims that the framework “dissolves” the measurement problem or is “complete” should be read as aspirations. The original motivation subsequently led to investigations of geometric, analytic, and measurement-theoretic questions under more explicit assumptions. One such development is The Lorentz-Analytic Exterior: A Conditional Mathematical Framework (Version 2, October 2026), which examines related geometric and analytic structures without relying on the original paper’s zero-proper-time argument as a derivation of quantum mechanics. This later work does not validate the original manuscript’s unsupported claims. https://doi.org/10.5281/zenodo.23400176
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.