The Unified Theorem of Correlation Determination: Mathematical and Physical Anatomy and Systematic Reconstruction of Bell's Theorem and CHSH Experiments
Year: 2026
Type: preprint
Abstract: "God does not play dice—he decrees the rules" “上帝不掷骰子——他制定规则” Peering through the veil of a century of history, this study provides a profound anatomy and comprehensive reconstruction of Bell’s theorem and the CHSH inequality from both mathematical and physical perspectives. Building upon this foundation, we establish the unified theorem of correlation determination (UTCD) for photon polarization. This framework comprehensively illuminates the underlying mechanism driving polarization correlation effects—including the long-mythologized phenomenon of quantum entanglement—thoroughly explains the physical phenomena and deep-seated paradoxes of CHSH experiments, and delivers four falsifiable experimental predictions with highly distinct boundaries, capable of immediate, direct, and unambiguous validation across contemporary optics laboratories while keeping existing standard configurations unchanged. The classical photon pairs defined by CH74 for local realism can perfectly yield the maximum violation of CHSH inequality under both parallel and orthogonal polarization correlations. This verification profoundly reveals the fundamental mechanism underlying the "correlation effect" of twin photons, while simultaneously elucidating why any peer-paired photons, regardless of whether they originate from homologous or non-homologous sources, can perfectly demonstrate this correlation. Leveraging rigorous mathematical and physical reasoning, the UTCD theorem provides an a priori constraint for determining the correlation between a pair of photons generated through an underlying stochastic mechanism. Its tautological expression is given below (in tribute to Bell): The intrinsic root cause behind the generation of the "correlation effect" between paired photons is that they possess parallel, antiparallel, or orthogonal polarization azimuth. As long as they satisfy Condition #1 before arriving at the PBS, their S value will be greater than 2. As long as they fail to satisfy Condition #1 before arriving at the PBS, their S value will not be greater than 2. Any instance with S > 2 necessarily satisfies Condition #1, while any instance with S <= 2 invariably stems from the non-fulfillment of Condition #1. The objective completeness of this theorem lies in its capability to comprehensively and exhaustively encompass all the probability dimensions of photon transmission event, thereby allowing for a complete and precise determination of the polarization correlation between the two paired photons. This “tautological” mathematical logic rule serves as the intrinsic explanation for “classical” photons breaking through Bell inequality, and moreover, provides the realistic explanation for all the entangled photons breaking through Bell inequality during CHSH experiments. Simultaneously, the extension of this theorem can likewise elucidate the experimental paradoxes in multi-setting Bell test and high-dimensional Bell tests once the -dimensional probability events encompassed by the UTCD theorem are fully incorporated, the so-called quantum entanglement effect will be demystified, entirely degenerating into the polarization correlation described herein and becoming mere subsets within the UTCD theorem. This work stands in tribute to Bell, and the pioneering minds of CHSH and CH74: it is precisely their relentless exploration of the quantum realm and their monumental achievements that laid the foundation for the successful formulation of the UTCD theorem. Enshrouded beneath the triple iron curtains of the Planck limit, the photon indivisibility principle, and the no-cloning theorem, this represents humanity’s sole triumph to date—relying strictly on profound conceptual insights and razor-sharp experimentation—in catching a glimpse of the world hidden within the quantum scale. For the first time in history, light quanta have pierced through these triple iron curtains to present humanity with a macroscopic manifestation of their intrinsic, microscopic properties. There can be no higher tribute paid to Dr. Bell, whose profound insights were first brought to light in 1964. The mathematical reconstruction presented in this study systematically closes the loop on the probability dimension previously lost in photon transmission events, while the physical reconstruction comprehensively encompasses a total understanding of the intrinsic properties of photons. The synergistic reconstruction of physics and mathematics fully demonstrates the inherent binding force of the UTCD theorem: the benchmark for determining the existence of correlation must be an objectively complete set of rules. Ultimately, the completeness of these objective rules provides the definitive closure to that historic dialogue of the century: “God does not play dice—he decrees the rules.” In the subsequent phases of this work, the author will unveil the physical nature of probabilistic events alongside the probabilistic expression of physical events, interpreting both the microscopic realization and macroscopic unfoldment of mathematical probability. As the relevant research indicates, this opens a brand-new horizon for humanity’s proper understanding of probabilistic physics: “The essence of interference and diffraction fringes in single-slit, double-slit, and all other wave-particle duality phenomena is merely the two-dimensional projection of probabilistic events onto the material world; if the dimension of time is added, we can furthermore witness the vibrant, breathtaking three-dimensional unfoldment of the probabilistic manifold!” Standing upon the firm bedrock of natural laws and causality, the organic fusion of classical and modern physics heralds a transformative new epoch in the advancement of physics.
Author: Xue, Zhicheng
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208738419
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