This work introduces a resolution-dependent geometric framework—Quantum Fractal Geometry (QFG)—in which the effective physical description of systems depends explicitly on observational scale. Within this framework, entangled quantum systems are modelled as unified geometric structures at deep resolution, characterised by a scale-dependent metric g_{μν}(ℓ) and a geometric phase field φ(x,ℓ) valued on S¹. Measurement is interpreted as a resolution-dependent projection of this unified structure onto detector-scale observables. A symmetry-constrained coarse-graining map is introduced as the minimal fixed point of resolution flow, identifying antipodal phase configurations (S¹ → S¹/ℤ₂). Under isotropy, continuity, and convex-linearity, the quantum correlation function E(a,b) = −cos(θ_a − θ_b) is recovered as the unique rotationally invariant statistic compatible with the projection structure, saturating the Tsirelson bound. Within QFG, Bell inequality violation arises not from nonlocal signalling or measurement dependence, but from the failure of scale-independent separability. Locality (in the operational no-signalling sense) and measurement independence are preserved. The framework further outlines a programme for deriving the Born rule from resolution-induced measure structure and identifies falsifiable predictions, including resolution-dependent deviations from ideal cosine correlations. This work should be understood as establishing the minimal geometric structure required for the QFG interpretation of Bell correlations, with full dynamical derivations deferred to future work.
This work introduces a resolution-dependent geometric framework—Quantum Fractal Geometry (QFG)—in which the effective physical description of systems depends explicitly on observational scale. Within this framework, entangled quantum systems are modelled as unified geometric structures at deep resolution, characterised by a scale-dependent metric g_{μν}(ℓ) and a geometric phase field φ(x,ℓ) valued on S¹. Measurement is interpreted as a resolution-dependent projection of this unified structure onto detector-scale observables. A symmetry-constrained coarse-graining map is introduced as the minimal fixed point of resolution flow, identifying antipodal phase configurations (S¹ → S¹/ℤ₂). Under isotropy, continuity, and convex-linearity, the quantum correlation function E(a,b) = −cos(θ_a − θ_b) is recovered as the unique rotationally invariant statistic compatible with the projection structure, saturating the Tsirelson bound. Within QFG, Bell inequality violation arises not from nonlocal signalling or measurement dependence, but from the failure of scale-independent separability. Locality (in the operational no-signalling sense) and measurement independence are preserved. The framework further outlines a programme for deriving the Born rule from resolution-induced measure structure and identifies falsifiable predictions, including resolution-dependent deviations from ideal cosine correlations. This work should be understood as establishing the minimal geometric structure required for the QFG interpretation of Bell correlations, with full dynamical derivations deferred to future work.
This work presents a comprehensive theoretical formulation of Quantum Fractal Geometry (QFG), a framework in which spacetime is fundamentally resolution-dependent. The apparent distinction between quantum and classical physics emerges from a single geometric principle: observer resolution as a structural parameter. The paper develops the formal mathematical foundations of QFG, including the definition of resolution-dependent metrics, a projection operator governing information accessibility, and the derivation of key physical results. These include the emergence of the Born rule from projection covariance, the recovery of the Einstein field equations as an infrared limit, and the Schrödinger equation as a dual flow correspondence. The framework provides a unified geometric interpretation of entanglement, black hole entropy, and gravitational structure, and introduces the Curvature Texture Index (CTI) as a measurable prediction linking multiscale geometric structure to astrophysical observables. A companion empirical study tests the CTI prediction using observational data from supermassive black hole host galaxies. All predictions are formulated with explicit falsifiability criteria, enabling experimental validation or refutation.
This paper presents a structural interpretation of quantum measurement within the Scalar Drag Emergence Framework (SDEF), in which physical systems are described in terms of corridor morphology and an ancestry field governing coherence and constraint. In this formulation, measurement is defined as a mapping from an underlying structural configuration to observable outcomes under imposed constraints. Particles are interpreted not as fundamental entities, but as localized realizations of this mapping. Observable probabilities arise from the geometry of projection between structure and constraint, rather than from intrinsic randomness of independent objects. Entanglement is reinterpreted as the non-separability of corridor morphology, and Bell correlations emerge naturally from the non-factorizability of the mapping process. The framework reproduces standard quantum predictions, including the cosine correlation law and maximal Bell violation, as a consequence of symmetry. Quantum mechanics is identified as a symmetry-dominant regime corresponding to spatially uniform ancestry, in which transport remains non-selective and structural selection is inactive. Beyond this regime, the framework predicts structured, anisotropic deviations from ideal behavior in non-equilibrium or high-energy environments. This work does not modify quantum mechanics, but provides a coherent structural basis for understanding measurement, entanglement, and correlation within a unified conceptual model.
Bell’s theorem constrains theories in which joint measurement outcomes can be expressed as factorizable functions of local measurement settings and shared hidden variables. Experimental violations of Bell inequalities therefore exclude a broad class of separable local models. The present work develops a complementary geometric interpretation within the Geometric Monism (GM) framework. In GM, entangled fermionic systems are modeled not as independent localized particles, but as multiple accessible nodes of a single continuous torsional standing-wave structure embedded in a 5-dimensional manifold governed by a universal Planck stiffness (κT=c4/G). Within this framework, the assumption of factorizability underlying Bell inequalities natively fails, because the physical state of the system is globally defined and not decomposable into independent local subsystems. We provide a geometric derivation of the −cos(θ) quantum correlation and a continuum-mechanics analogue for Born's Rule via spatial boundary projections. We further propose that quantum computational scaling (Ω∼2N) may be interpreted as arising directly from the available orientational embeddings of these non-separable topologies. The claims are presented as a dynamic geometric reinterpretation compatible with established quantum correlations rather than a replacement for quantum field theory (QFT), since QFT remains an extremely effective approach for the description of interactions between entities. However, the underlying axioms of QFT do not support the description of the entities themselves due to the abandonment of continuity and the violation of the first law of thermodynamics.
We develop a metric-measure geometric reinterpretation of quantum entanglement in which nonlocal correlations are encoded in the intrinsic geometry of composite state space rather than in dynamical propagation. Using the Bures metric and CPTP coarse-graining semigroups, we define a scale-dependent effective dimension of the entangled-state manifold. We propose that geometric observables along the renormalization flow may exhibit long-range dependence (LRD) characterized by a Hurst exponent H ∈ (1/2,1). A conjectured infrared attractor H* ≈ 0.65 is formulated as a falsifiable hypothesis. The framework preserves no-signaling and does not modify quantum mechanics. A direct link to the variance (RMS) of Eisenbud–Wigner–Smith time delay is proposed, providing operational accessibility of geometric LRD effects.
The foundational conflict between the probabilistic non-locality of quantum mechanics and the geometric determinism of general relativity remains the central challenge of modern physics. This paper addresses the tension by proposing a locally causal framework where Bell-inequality violations emerge as a direct consequence of the intrinsic curvature of a discretized state-space manifold. By violating the “Measurement Independence” assumption through a global geometric constraint, we eliminate the need for non-local “spooky action” while preserving the causal structure of spacetime. Our methodology utilizes a novel “Ontic Tensor” mapping that bridges Riemannian metrics with p-adic state-space discretization. The results demonstrate that the Ontic Tensor model reproduces sinusoidal Bell correlations with an R2>0.99 against standard quantum mechanical predictions. Furthermore, we identify a falsifiable “entanglement saturation” limit, predicting that entanglement fidelity must decay beyond m=log2(p) qubits due to the finite information capacity of the invariant set. The implications of this research suggest a return to the Einsteinian ideal of local realism, where randomness is viewed as an emergent mask for underlying geometric complexity. By resolving the measurement problem through state convergence on a fractal attractor, we provide a non-perturbative pathway toward the unification of quantum field theory and general relativity. This work addresses seven critical gaps in the literature, establishing Superdeterminism as a rigorous, testable, and parsimonious framework for the future of physics.