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.
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.
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.
There are two issues concerning hidden variables in quantum mechanics: 1.Whether the outcomes of quantum measurements are hidden variables has long been debated. Experiments violating Bell's inequalities have essentially refuted local hidden variable theories. 2.Quantum entanglement provides nonlocal effects that alter wave functions. However, these changes cannot transmit signals, making the exact time of such nonlocal effects a hidden variable. Theories about hidden variables are difficult to verify experimentally due to their unobservability. This paper connects these two hidden variable theories in quantum mechanics, proposing the spacetime relationship that nonlocal effects from entanglement must satisfy to prevent quantum measurement outcomes from being local hidden variables. It further outlines the spacetime relationship that any causal effects should adhere to. Based on this, the paper demonstrates the universal temporal order between relativistic spacelike events. On this foundation, it integrates the locally deterministic relativistic spacetime structure with the nonlocal phenomena of probabilistic quantum mechanics, thereby establishing the universal ordered spacetime structure.
The synthesis of quantum and gravitational physics is sought through a finite, realistic, locally causal theory where gravity plays a vital role not only during decoherent measurement but also during non-decoherent unitary evolution. Invariant set theory is built on geometric properties of a compact fractal-like subset
IU of cosmological state space on which the universe is assumed to evolve and from which the laws of physics are assumed to derive. Consistent with the primacy of
IU, a non-Euclidean (and hence non-classical) state-space metric
gp is defined, related to the
p-adic metric of number theory where
p is a large but finite Pythagorean prime. Uncertain states on
IU are described using complex Hilbert states, but only if their squared amplitudes are rational and corresponding complex phase angles are rational multiples of
2π. Such Hilbert states are necessarily
gp-distant from states with either irrational squared amplitudes or irrational phase angles. The gappy fractal nature of
IU accounts for quantum complementarity and is characterised numerically by a generic number-theoretic incommensurateness between rational angles and rational cosines of angles. The Bell inequality, whose violation would be inconsistent with local realism, is shown to be
gp-distant from all forms of the inequality that are violated in any finite-precision experiment. The delayed-choice paradox is resolved through the computational irreducibility of
IU. The Schrödinger and Dirac equations describe evolution on
IU in the singular limit at
p=∞. By contrast, an extension of the Einstein field equations on
IU is proposed which reduces smoothly to general relativity as
p→∞. Novel proposals for the dark universe and the elimination of classical space-time singularities are given and experimental implications outlined.
It is shown that when properly analyzed using principles consistent with the
use of a Hilbert space to describe microscopic properties, quantum mechanics is
a local theory: one system cannot influence another system with which it does
not interact. Claims to the contrary based on quantum violations of Bell
inequalities are shown to be incorrect. A specific example traces a violation
of the CHSH Bell inequality in the case of a spin-3/2 particle to the
noncommutation of certain quantum operators in a situation where (non)locality
is not an issue. A consistent histories analysis of what quantum measurements
measure, in terms of quantum properties, is used to identify the basic problem
with derivations of Bell inequalities: the use of classical concepts (hidden
variables) rather than a probabilistic structure appropriate to the quantum
domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument
for the incompleteness of quantum mechanics is the use of a counterfactual
argument which is not valid if one assumes that Hilbert-space quantum mechanics
is complete; locality is not an issue. The quantum correlations that violate
Bell inequalities can be understood using local quantum common causes.
Wavefunction collapse and Schr\odinger steering are calculational procedures,
not physical processes. A general Principle of Einstein Locality rules out
nonlocal influences between noninteracting quantum systems. Some suggestions
are made for changes in terminology that could clarify discussions of quantum
foundations and be less confusing to students.