13-Apr-2026(V1.0): Gamma-DG and the Quantum–Spacetime Bridge: Toward a Unified Structural Theory This paper develops an original structural framework, Gamma-DG, for the quantum–spacetime bridge. The central problem is not merely how to connect a quantum-primitive foundational layer and a relativistically readable spacetime layer, but how to describe a controlled, admissible, and structurally coherent passage between these distinct regimes. The paper formulates a unified perspective in which bridge formation, bridge validation, and bridge culmination are treated as successive aspects of a single theoretical program. Core I and Core II provide the foundational basis of the framework, while the present paper focuses on the minimal structural ideas needed for the current synthesis.
13-Apr-2026(V1.0): Gamma-DG and the Quantum–Spacetime Bridge: Toward a Unified Structural Theory This paper develops an original structural framework, Gamma-DG, for the quantum–spacetime bridge. The central problem is not merely how to connect a quantum-primitive foundational layer and a relativistically readable spacetime layer, but how to describe a controlled, admissible, and structurally coherent passage between these distinct regimes. The paper formulates a unified perspective in which bridge formation, bridge validation, and bridge culmination are treated as successive aspects of a single theoretical program. Core I and Core II provide the foundational basis of the framework, while the present paper focuses on the minimal structural ideas needed for the current synthesis.
This work presents a conceptual and representational framework aimed at clarifying the structural relationships among established physical theories across relativistic, quantum, and cosmological regimes. Rather than proposing new dynamical laws, particles, or experimentally testable predictions, the manuscript focuses on how existing physical descriptions may be consistently interpreted within a unified representational structure. The proposed Dual-Spacetime Projection Framework distinguishes between an underlying descriptive domain and an observed effective spacetime, connected through a scale-dependent projection. This distinction is intended as a formal and interpretative tool, not as an ontological claim about the existence of multiple physical spacetimes. Within this perspective, several foundational features of modern physics—such as Lorentz invariance, finite signal propagation, quantum uncertainty, and large-scale cosmological behavior—are discussed as consequences of representational structure rather than as independent postulates. The manuscript is positioned as a contribution to the foundations of theoretical physics, offering a coherent conceptual lens for organizing and interpreting existing theories. It is intended for readers interested in foundational questions, conceptual unification, and the representational aspects of physical law, and does not rely on experimental data or numerical simulation.
This work presents a unified theoretical framework that aims to bridge relativity and quantum mechanics through a single structural principle: delayed realization. Instead of assuming spacetime, time evolution, or quantum states as primitive entities, the framework introduces a pre-geometric definability network in which relational differences are initially undefined and become stabilized through nonlinear dynamics. The emergence of spacetime is then reinterpreted as the stabilization of definable differences, while the present is not given a priori but selected via delayed consistency over histories. Within this formulation, quantum phenomena arise naturally when multiple realization candidates coexist, producing interference structures governed by a variational principle. In the low-defect limit, the framework recovers effective relativistic geometry and field-theoretic behavior, including emergent gravitational curvature and gauge structures. A central contribution of this work is the formulation of a unified definability action, combining stabilization, curvature minimization, delayed consistency, and informational structure into a single variational framework. Under appropriate coarse-graining, this action yields structures consistent with Einstein field equations, quantum amplitudes, and gauge invariance as different regimes of the same underlying mechanism. This paper does not claim a fully closed mathematical unification of all physical sectors. Instead, it provides a coherent structural framework in which spacetime emergence, present realization, quantum probability, and effective field dynamics are organized as manifestations of a single principle. The framework is intended as a foundational step toward a deeper unification of physics, where time, geometry, and probability are not assumed, but emerge from the stabilization and realization of definable relational structures.
Release V1.0 This preprint is the second part of the time-core series in the Gamma–Dynamic Geometry (Gamma-DG) programme.In Time-Core I (Kawanishi, 2025), time was treated as a structural object equipped with three basic roles—absolute, relative, and undefined—and organised into layers, Brūri regions, gates, and clock layers over a core time axis TcoreTcore. That framework provided an axiomatic backbone for multi-layer time, including a minimal “arrow of time’’ derived from monotone role levels along gate chains. Time-Core II: Brūri Regions and Branching Traces extends this architecture by introducing internal state spaces, dynamics, and state-annotated traces on time layers. Each layer is enriched with an abstract state space and a local time-evolution relation, and gates are equipped with state-transition relations. On top of this, the paper defines state-annotated traces that follow a single event through time and across layers while respecting the original gate axioms. Within this extended setting, Brūri regions—points where multiple layers are simultaneously visible—naturally support branching families of traces that emanate from undefined layers and end in different absolute layers. This yields a minimal, structural model of “measurement-like’’ behaviour without committing to any specific physical or probabilistic interpretation. The paper also presents relativistic-style Rel–Rel configurations (e.g., Earth vs.\ ISS viewpoints) and uses them as conceptual templates for gravitational and multi-clock scenarios. Finally, the work sketches Spin-like labels and measurement-like selection on families of branches, preparing the ground for fully fledged Spin/Brūri structures in future parts of Gamma-DG. Time-Core II should be regarded as a time-core foundations layer: a template designed to host concrete models for intuition, quantum/relativistic/gravitational viewpoints, and number-theoretic applications (such as Collatz and Goldbach) in subsequent work.
This paper explores the fundamental nature of spacetime from the perspective of emergent causal structures, rooted in quantum mechanical principles. We propose a theoretical framework that treats spacetime not as a pre-existing background, but as a collective phenomenon arising from the interaction of quantum causal relations. By analyzing the constraints of causality and quantum coherence, we derive key implications for the emergence of classical spacetime geometry and the limits of local realism. Our results suggest a new way to bridge quantum mechanics and gravitational theory, providing a foundation for future studies in quantum gravity and spacetime physics.
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.