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Resolving Quantum Entanglement: A Deterministic Classical Framework from a Continuous Energy Field

Yousefi

Published Jul 15, 2026• 0 citations
Publisher

Abstract

Abstract: Quantum entanglement is one of the most remarkable phenomena in modern physics — a situation in which two particles, without any apparent physical connection, exhibit perfectly coordinated behaviour. This striking feature has led many to conclude that the universe must be fundamentally nonlocal. In this paper, we show that entanglement can be explained without any recourse to nonlocality, within a fully classical and deterministic framework. In this view, all physical phenomena arise from a single, continuous underlying substrate; what we call "entanglement" is simply a reflection of sharing this common foundation. The theory reproduces all known results of quantum experiments, including the violation of Bell inequalities, by relaxing the assumption of measurement independence — a step that is both physically motivated and locally consistent. A new testable prediction is also offered. The conclusion is that entanglement is not evidence of nonlocality, but rather a manifestation of the fundamental unity of nature

DOI
10.5281/zenodo.21373266

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Abstract: Quantum entanglement is one of the most remarkable phenomena in modern physics — a situation in which two particles, without any apparent physical connection, exhibit perfectly coordinated behaviour. This striking feature has led many to conclude that the universe must be fundamentally nonlocal. In this paper, we show that entanglement can be explained without any recourse to nonlocality, within a fully classical and deterministic framework. In this view, all physical phenomena arise from a single, continuous underlying substrate; what we call "entanglement" is simply a reflection of sharing this common foundation. The theory reproduces all known results of quantum experiments, including the violation of Bell inequalities, by relaxing the assumption of measurement independence — a step that is both physically motivated and locally consistent. A new testable prediction is also offered. The conclusion is that entanglement is not evidence of nonlocality, but rather a manifestation of the fundamental unity of nature
This work presents a conceptual and semi-formal analysis of quantum entanglement, locality, and determinism, motivated by a thought experiment involving double-slit measurements performed on entangled particles at spacelike separation. While quantum correlations appear instantaneous, the paper demonstrates that no superluminal information transfer or causal influence is required to explain observed outcomes.Building upon the Einstein–Podolsky–Rosen framework and Bell’s theorem, the study distinguishes between local dynamical processes and nonlocal informational correlations encoded in the global quantum state. It argues that measurement outcomes are locally realized yet globally constrained, leading to an effectively deterministic universal description while preserving epistemic uncertainty for observers.The paper reframes quantum nonlocality as a manifestation of global consistency rather than physical influence, offering insights into the relationship between realism, free will, and relativistic causality. The discussion is interpretational in nature and does not introduce new experimental claims, aiming instead to clarify foundational assumptions underlying quantum theory.This work is intended for researchers and students interested in quantum foundations, the philosophy of physics, and the conceptual structure of modern physical theories.
We propose a physical interpretation of quantum entanglement within the framework of the Superfluid Energy Field (SEF), in which the quantum vacuum is modeled as a coherent medium described by a complex scalar field. Within this approach, spacetime, matter, and interactions emerge as collective and topological properties of a single underlying field. We show that entanglement can be understood as a manifestation of long-range phase coherence in this medium. Spatially separated systems correspond to localized excitations embedded within a single, non-factorizable field configuration, and their correlations arise from the global structure of the phase rather than from dynamical nonlocal interactions. This interpretation provides a natural explanation for the violation of Bell inequalities while preserving relativistic causality. The no-signaling theorem is maintained through a clear distinction between global coherence and local dynamical evolution, while decoherence is reinterpreted as the loss of long-range phase coherence leading to the emergence of classical behavior. The framework is constructed to remain fully compatible with the empirical predictions of quantum mechanics at the effective level, while suggesting the possibility of small deviations associated with the finite coherence properties of the underlying field. These results support the view that quantum correlations may arise from the coherence of a continuous physical medium, thereby providing a unified hydrodynamic perspective on quantum phenomena.
Quantum entanglement represents one of the most profound and counterintuitive phenomena in modern physics, challenging our classical understanding of locality and causality. While the mathematical formalism of quantum mechanics accurately predicts entanglement correlations, the lack of a physically intuitive mechanism has led to numerous interpretational difficulties and philosophical debates. This article presents a comprehensive analysis of existing interpretations of quantum entanglement, from the Copenhagen interpretation to many-worlds and hidden variable theories, highlighting their limitations and motivating a novel vortex-based interpretation grounded in the hydrodynamic behavior of a superfluid vacuum, drawing upon the author’s published work on electron, quark, and gravitational force dynamics. This vortex model provides a physically intuitive and causally consistent explanation for nonlocal correlations without invoking superluminal signaling, offering a bridge between classical physics and quantum mechanics. The proposed interpretation suggests that entangled particles are surface manifestations of deeper, coherent vortex structures within a continuous vacuum medium, analogous to connected vortices in a fluid system. This framework not only resolves the conceptual difficulties associated with “spooky action at a distance” but also provides a foundation for understanding quantum phenomena through classical hydrodynamic principles.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.
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 look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Within this framework, theories are conceptual constructs applying to models generated in the phenomenal world within limited contexts.The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases of quantum mechanical states (entanglement). The quantum correlations are shared globally in the process of environment-induced decoherence whereby locally generated correlations are removed, the removal being especially manifest in the case of systems that appear as classical ones, in which case the process is almost instantaneous, being, in all likelihood, driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining its finest details, since Planck scale physics remains an obscure terrain. In other words, the present day quantum theory holds within a limited context set by the Planck scale.