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A Riemannian-Geometric Approach to Superdeterministic Bell-Violations: Addressing the Tension between Intrinsic Curvature and Statistical Independence

Rowan Brad Quni-Gudzinas

Published Feb 9, 2026• 0 citations
Publisher

Abstract

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 $R^2 > 0.99$ against standard quantum mechanical predictions. Furthermore, we identify a falsifiable “entanglement saturation” limit, predicting that entanglement fidelity must decay beyond $m = \log_2(p)$ 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.

DOI
10.5281/zenodo.18545446

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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 ppp-adic state-space discretization. The results demonstrate that the Ontic Tensor model reproduces sinusoidal Bell correlations with an R2>0.99R^2 > 0.99R2>0.99 against standard quantum mechanical predictions. Furthermore, we identify a falsifiable “entanglement saturation” limit, predicting that entanglement fidelity must decay beyond m=log⁡2(p)m = \log_2(p)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.
Quantum entanglement is widely regarded as the most puzzling feature of quantum theory, apparently violating local realism through nonlocal correlations between spacelike-separated particles. Although violations of Bell inequalities are experimentally confirmed, their standard theoretical explanation relies on wavefunction collapse or nonlocal hidden variables. In this work, we present an alternative explanation based on Trembling Spacetime Relativity Theory (TSRT). In this framework, intrinsic metric fluctuations generate proper-time-synchronized geodesic ensembles whose deterministic trajectories give rise to statistical correlations across spacetime. Measurement outcomes are reinterpreted as geometric responses to these fluctuating backgrounds, without invoking quantum collapse or nonlocal influence. We show that the Clauser–Horne–Shimony–Holt (CHSH) inequality can be violated deterministically within a locally causal geometric structure. These violations emerge as macroscopic imprints of shared spacetime curvature, not quantum superposition. The resulting correlation function reproduces quantum predictions at short ranges but decays with separation—yielding testable deviations in long-baseline and gravitationally modulated experiments. TSRT thus offers a realist, Lorentz-invariant, and falsifiable account of entanglement grounded in the causal structure of spacetime.
A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry I U in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent. Consistent with the assumed primacy of I U , a non-Euclidean (and hence non-classical) metric g p is defined in cosmological state space. Here, p is a large but finite integer (whose inverse may reflect the weakness of gravity). Points that do not lie on I U are necessarily g p -distant from points that do. g p is related to the p-adic metric of number theory. Using number-theoretic properties of spherical triangles, the Clauser-Horne-Shimony-Holt (CHSH) inequality, whose violation would rule out local realism, is shown to be undefined in this framework. Moreover, the CHSH-like inequalities violated experimentally are shown to be g p -distant from the CHSH inequality. This result fails in the singular limit p = ∞ , at which g p is Euclidean and the corresponding model classical. Although Invariant Set Theory is deterministic and locally causal, it is not conspiratorial and does not compromise experimenter free will. The relationship between Invariant Set Theory, Bohmian Theory, The Cellular Automaton Interpretation of Quantum Theory and p-adic Quantum Theory is discussed.
ppp-adic Distance, Finite Precision and Emergent Superdeterminism: A Number-Theoretic Consistent-Histories Approach to Local Quantum Realism
Although the notion of superdeterminism can, in principle, account for the violation of the Bell inequalities, this potential explanation has been roundly rejected by the quantum foundations community. The arguments for rejection, one of the most substantive coming from Bell himself, are critically reviewed. In particular, analysis of Bell's argument reveals an implicit unwarranted assumption: that the Euclidean metric is the appropriate yardstick for measuring distances in state space. Bell's argument is largely negated if this yardstick is instead based on the alternative ppp-adic metric. Such a metric, common in number theory, arises naturally when describing chaotic systems which evolve precisely on self-similar invariant sets in their state space. A locally-causal realistic model of quantum entanglement is developed, based on the premise that the laws of physics ultimately derive from an invariant-set geometry in the state space of a deterministic quasi-cyclic mono-universe. Based on this, the notion of a complex Hilbert vector is reinterpreted in terms of an uncertain selection from a finite sample space of states, leading to a novel form of `consistent histories' based on number-theoretic properties of the transcendental cosine function. This leads to novel realistic interpretations of position/momentum non-commutativity, EPR, the Bell Theorem and the Tsirelson bound. In this inherently holistic theory - neither conspiratorial, retrocausal, fine tuned nor nonlocal - superdeterminism is not invoked by fiat but is emergent from these `consistent histories' number-theoretic constraints. Invariant set theory provides new perspectives on many of the contemporary problems at the interface of quantum and gravitational physics, and, if correct, may signal the end of particle physics beyond the Standard Model.
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.
Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics.
This paper presents a critical review of the geometric and linear assumptions underlying Bell's inequality, introducing an alternative theoretical framework based on the mechanism of particle genesis. We propose that the statistical correlations observed in quantum entanglement experiments can be comprehensively modeled through geometric tolerance probability rules, rather than non-local action. By establishing absolute variables governing the dynamic state changes during particle generation and propagation, this study addresses the apparent violations of local realism. Furthermore, we explore the implications of these geometric parameters within the framework of special relativity and wave-particle thought experiments, demonstrating that a reconsidered classical-geometric perspective can consistently account for quantum interference phenomena without relying on mystical or non-causal interpretations.