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Multimedia Research

Quantum Hidden Variables and Riemann Hypothesis

Doju K. Degefa

Published Jan 1, 2024• 0 citations
Publisher

Abstract

In this paper, I explore the intriguing connection between hidden variables in quantum mechanics and the nontrivial zeros of the Riemann zeta function.Despite the apparent randomness in quantum phenomena, I demonstrate that deterministic hidden variables can coexist without violating Bell's inequalities, particularly in scenarios involving small angles.Using MATLAB simulations and a simplified space-time model, I illustrate this relationship, shedding light on the fundamental nature of quantum systems.This research not only deepens our understanding of quantum mechanics but also opens new avenues for investigating the Riemann zeta function's implications, potentially transforming our approach to both fields.

DOI
10.46253/j.mr.v7i4.a2

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In this paper, I explore the intriguing connection between hidden variables in quantum mechanics and the nontrivial zeros of the Riemann zeta function.Despite the apparent randomness in quantum phenomena, I demonstrate that deterministic hidden variables can coexist without violating Bell's inequalities, particularly in scenarios involving small angles.Using MATLAB simulations and a simplified space-time model, I illustrate this relationship, shedding light on the fundamental nature of quantum systems.This research not only deepens our understanding of quantum mechanics but also opens new avenues for investigating the Riemann zeta function's implications, potentially transforming our approach to both fields.
Abstract. The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in contrast with variables characterizing the measured microscopic system, is shown to lead to a vi-olation of Bell’s inequalities and to agree with standard quantum mechanics. An explicit realization of this interpretation is explored (for details, see [1]) for a primitive model of cloud chamber inspired by Mott [2]. Being highly non local, this interpretation of quantum mechanics is argued to open the way to faster-than-light information transfer.
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.
This paper investigates the Riemann Hypothesis through the lens of quantum entanglement, proposing a novel theoretical model that posits the emergence of 'quantum branches' within the zeta function distribution. We explore a quantum-mechanical framework to simulate the evolution of the zeta function, incorporating entanglement as a fundamental process driving the formation of these branches. The goal is to provide a potential pathway for understanding the hypothesis and its connection to the nascent field of quantum computation. This work aims to initiate a discussion about the potential for a fundamentally new approach to the Riemann Hypothesis.
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure subject. Whereas to most physicists the possibility of a classical reinterpretation of quantum mechanics remains remote and perhaps irrelevant to current problems, a minority have kept the issue alive throughout this period. (See Freistadt [5] for a review of the problem and a comprehensive bibliography up to 1957.) As far as results are concerned there are on the one hand purported proofs of the non-existence of hidden variables, most notably von Neumann’s proof, and on the other, various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.