This work introduces a theoretical framework for nonlocal hidden-variable models based on “complex jammers”, defined over a structured parameter space extending standard space–time. The framework is designed to explore whether hidden nonlocal mechanisms can modify quantum correlations while remaining consistent with relativistic causality and the no-signalling principle. A central result establishes that exact operational indistinguishability from quantum mechanics forces the effective dynamics to reduce to the identity channel. This implies that any hidden mechanism that is completely invisible at the level of observable statistics must be dynamically trivial. Prior to this regime, we show that admissible dynamics is already strongly constrained: it must preserve all local marginals and can only act on correlations. Beyond equilibrium, the framework predicts a restricted class of deviations from quantum mechanics. In particular, we derive a minimal geometric mechanism leading to anisotropic corrections of the form cos²(θ), arising from axial symmetry defined by the experimental configuration. These deviations induce measurable, orientation-dependent distortions in Bell-type correlations. An explicit two-qubit model is constructed, and angle-dependent CHSH bounds are obtained. The results define a concrete experimental program based on high-precision Bell tests, capable of probing structured deviations from standard quantum predictions. The work does not propose a complete dynamical hidden-variable theory, but rather a set of physically motivated constraints on possible nonlocal extensions of quantum mechanics, together with falsifiable signatures that can be tested with current experimental platforms.
This work introduces a theoretical framework for nonlocal hidden-variable models based on “complex jammers”, defined over a structured parameter space extending standard space–time. The framework is designed to explore whether hidden nonlocal mechanisms can modify quantum correlations while remaining consistent with relativistic causality and the no-signalling principle. A central result establishes that exact operational indistinguishability from quantum mechanics forces the effective dynamics to reduce to the identity channel. This implies that any hidden mechanism that is completely invisible at the level of observable statistics must be dynamically trivial. Prior to this regime, we show that admissible dynamics is already strongly constrained: it must preserve all local marginals and can only act on correlations. Beyond equilibrium, the framework predicts a restricted class of deviations from quantum mechanics. In particular, we derive a minimal geometric mechanism leading to anisotropic corrections of the form cos²(θ), arising from axial symmetry defined by the experimental configuration. These deviations induce measurable, orientation-dependent distortions in Bell-type correlations. An explicit two-qubit model is constructed, and angle-dependent CHSH bounds are obtained. The results define a concrete experimental program based on high-precision Bell tests, capable of probing structured deviations from standard quantum predictions. The work does not propose a complete dynamical hidden-variable theory, but rather a set of physically motivated constraints on possible nonlocal extensions of quantum mechanics, together with falsifiable signatures that can be tested with current experimental platforms.
We prove a no-go theorem for nonlocal jamming mechanisms under the spectral condition of relativistic quantum field theory. Modeling the action of a jammer as a modification of correlation functions subject to causal localization, we show that any such modification compatible with positive energy must vanish identically. The proof is based on Fourier-analytic arguments and the structure of distributions with spectral support in the forward light cone. In particular, the result follows from the incompatibility between causal support in spacetime and spectral support in momentum space, which forces triviality under mild regularity assumptions. This establishes that nonlocal jamming is impossible within any framework that preserves the spectral condition and causal localization. The result is independent of detailed analytic properties beyond those implied by positive energy. We also discuss a geometric interpretation of this obstruction in twistor space. In that setting, localized modifications correspond to cohomological data with restricted support, suggesting a form of global rigidity. This geometric formulation is presented as a conjectural extension and an open problem. The work connects foundational questions in quantum information (nonlocal correlations and jamming) with structural aspects of quantum field theory, highlighting the constraining role of spectral and analytic principles. This work is further developed in DOI: 10.5281/zenodo.19713348, where a classification of hidden-variable extensions is established.
This work develops a deterministic, field-based reformulation of quantum mechanics in which entanglement arises naturally from correlated hidden variables, directly realizing Einstein’s prediction. Fermions are modeled as coupled real fields whose internal oscillatory phases provide a physical ontology for spin, interference, and charge. The model yields the standard −cosθ correlation law in the uniform-phase limit, while predicting a small deterministic correction C( θ )=−cosθ+ε sin 2 θ with ε≈0.06 . This deviation is benchmarked against historic and modern Bell tests, showing it is not excluded but lies within the sensitivity of angle-resolved experiments. Thus, the work provides a realist, experimentally testable account of entanglement, aligning with Einstein’s vision of hidden variables. Experimental deviation between the quantum mechanics model to our real coupled-fields model is expected to be of order ε=0.06 . The model provides unique experimental predictions—a finite offset at symmetry points (e.g. Δ = 45˚) not explained by noise or reduced visibility. This work examines the violation of Bell’s inequality through the lens of the Coupled-Fields model. While standard quantum mechanics attributes these results to nonlocal entanglement, the Coupled-Fields framework reproduces the same correlations through deterministic, local interactions between the internal variables of the coupled strings. Each fermion pair shares an intrinsic phase relationship established at creation, which governs measurement outcomes without requiring instantaneous influence. Statistical violation of Bell’s inequality thus reflects the geometry of internal field orientations rather than true nonlocality. This analysis reconciles experimental data with physical realism, demonstrating that local hidden variables—when properly defined within the coupled-fields structure—can reproduce the full quantum correlation pattern. Our conclusion is that Einstein (EPR) [1] was right. Internal phase is the hidden variable.
We investigate the possibility of nonlocal “jamming” of quantum correlations under relativistic causality constraints, in the sense of Grunhaus–Popescu–Rohrlich (GPR). Within the framework of quantum field theory, we model jamming as a modification of correlation functions and introduce a class of causally localized jammers, defined by a spacetime support condition together with a spectral condition. Under these assumptions, we prove an analytic no-go theorem: any such modification compatible with the analytic structure of QFT must vanish identically. The proof relies on the interplay between spacetime support and spectral support of distributions, highlighting a rigidity phenomenon analogous to Paley–Wiener type results. While a fully rigorous proof of the underlying spectral-support incompatibility lemma is deferred, the framework identifies a clear mathematical mechanism obstructing localized modifications of correlations. We further propose a geometric interpretation in twistor space. The analytic rigidity suggests a corresponding constraint on cohomology classes with restricted support. This leads to a precise conjecture formulated in terms of sheaf cohomology and long exact sequences, and connected to partial vanishing problems in the sense of Andreotti–Grauert. The relation with the Penrose transform is discussed at a heuristic level. The result establishes a structural obstruction to a broad class of causally localized jamming mechanisms and identifies a well-posed open problem at the interface of quantum field theory, complex geometry, and twistor theory.This work motivates subsequent analytic and spectral results developed in DOI;10.5281/zenodo.19713348
Violations of Bell inequalities are commonly interpreted as evidence for nonlocal influences or as constraints on realist descriptions. We show that the failure of Bell-type factorizability arises naturally when observable outcomes are obtained through a non-injective mapping from an underlying configuration space. In this setting, the standard factorization assumption can be viewed as an implicit requirement that observable variables admit a jointly factorizable completion at the underlying level. We demonstrate that this requirement need not hold when the mapping from underlying configurations to observables is many-to-one. The resulting breakdown of probabilistic factorization does not rely on superluminal dynamics or hidden causal influences, but follows from information loss under projection. Observable outcomes correspond to equivalence classes of underlying configurations, preventing the assignment of independent local variables. We illustrate this mechanism with an explicit toy model producing Bell–CHSH violations while preserving operational no-signalling and statistical independence of measurement settings. The model is not intended to reproduce quantum correlations quantitatively, and may exceed the Tsirelson bound; its role is to isolate the structural origin of the violation. This analysis does not contradict Bell’s theorem, but identifies a class of effective descriptions for which its factorizability assumption does not apply. The framework preserves locality at the underlying level, introduces no additional hidden-variable dynamics, and does not modify quantum mechanics. It clarifies how classical factorization is recovered in regimes where the effective mapping becomes approximately injective. In the operator language of quantum theory, the same mechanism admits a natural reformulation in terms of reduction to an effective observable subalgebra by a noncommutative conditional expectation.
Relativistic causality in certain spacetime configurations permits jamming - superluminal causal influences that nevertheless do not enable superluminal signaling. We fully characterize the correlations compatible with relativistic causality (RC) by extending the operator framework of PRL 104, 140404. When the underlying state is required to be quantum, we prove that any nontrivial jamming - whether state-independent or state-dependent - necessarily leads to hidden superluminal signaling. Thus, the only consistent possibilities are standard quantum correlations without jamming or the full relativistically causal correlation set, with intermediate jamming extensions of quantum correlations leading to signaling. As an application of our characterization, we investigate the security of device-independent (DI) cryptographic primitives against adversaries constrained only by relativistic causality. We construct explicit RC attacks that break DI bit commitment and DI secret sharing in jamming geometries, even when these protocols remain secure against no-signaling adversaries. Our results show that security against relativistic adversaries requires behaviors to be specified together with the spacetime locations of their measurement events; input-output statistics alone are insufficient.
Bell inequalities have long served as the standard criterion to verify local hidden variable theories. Experimental violations of these inequalities are commonly interpreted as fundamental quantum nonlocality at the microscopic scale. This paper proves rigorously that Bell inequalities hold only under three prerequisites: countable discrete variables, countably additive probability measures, and classical absolute simultaneity. The state space of entangled quantum systems forms an uncountable infinite continuum. By the property of Vitali non-measurable sets in measure theory, the integral deduction of the CHSH inequality collapses naturally over continuous state spaces. Furthermore, special relativity excludes universal global time synchronization, so the absolute time embedded in Bell’s theory is an artificial assumption inconsistent with physical reality. Inspired by the framework dependence of probability revealed in Bertrand’s paradox, we demonstrate that the excess correlation observed in experiments is an apparent effect caused by the mismatch between classical measurement frameworks and the intrinsic continuum property of quantum systems, rather than evidence against local hidden variables. Statistical correlation between entangled particles originates from their shared evolutionary sequence defined at pair generation, with no superluminal interaction, fully complying with relativistic causality. This paper does not explore the ultimate origin of entanglement, but treats it as a given primitive physical law. Two falsifiable predictions are proposed to distinguish the continuum model from standard quantum mechanics. The conclusion is that hidden variable theories have never been falsified by experiments; they only need to be extended from discrete forms to continuum models compatible with relativity.