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On Bell's Theorem and Quantum-Mechanically Predicted Perfect Correlation

Guang-Liang Li

Published Aug 28, 2026• 0 citations
Publisher

Abstract

The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlation between two spatially separated photons. By interpreting the correlation non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view based on his separability principle and his ensemble interpretation of ψ-functions in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. This paper shows that Bell's theorem is incorrect and presents an explanation of the correlation based on Einstein's argument. The correlation is deterministic. A formal analysis supporting Einstein's explanation is also presented.

DOI
10.20944/preprints202608.2062.v1

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The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlation between two spatially separated photons. By interpreting the correlation non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view based on his separability principle and his ensemble interpretation of ψ-functions in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. This paper shows that Bell's theorem is incorrect and presents an explanation of the correlation based on Einstein's argument. The correlation is deterministic. A formal analysis supporting Einstein's explanation is also presented.
The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlation between two spatially separated photons. By interpreting the correlation non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view based on his separability principle and his ensemble interpretation of ψ-functions in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. This paper shows that Bell's theorem is incorrect and presents an explanation of the correlation based on Einstein's argument. The correlation is deterministic. A formal analysis supporting Einstein's explanation is also presented.
The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlations between two spatially separated photons. By interpreting the correlations non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. Einstein's argument is based on his separability principle and his ensemble interpretation of ψ-functions. This paper shows that Bell's theorem is incorrect, and an explanation of the correlations based on Einstein's argument is given. As shown by the explanation based on Einstein's argument, the correlations are deterministic. A formal analysis supporting Einstein's explanation is also presented.
In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete and disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding microscopic objects. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, the deterministic correlation between distant components of a separable system in Einstein's local-realist description of the world is mistaken for the so-called non-locality or "nonlocal-interaction" in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the formal axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.
In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete and disagreed with Born's probabilistic interpretation of wave-functions. Observers in the axioms of the theory also bothered Einstein. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, the deterministic correlation between distant components of a separable system in Einstein's local-realist description of the world is mistaken for non-locality in the world described by Bell's theorem, which interprets the experimental results of testing Bell inequalities incorrectly. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem, allowing quantum mechanics to be completed within the framework of local realism while keeping the definition of a general Hilbert space unchanged. Using disjunction (``or'') as the logical relation between superposed orthonormal vectors, the completed quantum theory provides the same probabilistic predictions of empirical results as those provided by the current version of the theory, precludes inexplicable collapses of wave-functions, eliminates observers from the axioms of quantum mechanics, and is intuitively comprehensible, thus alleviating much difficulty experienced by many people in understanding the theory in its present form. Among various world views, Einstein's local-realist world view is correct.
Three experimental groups succeeded recently to close, at the same time, locality and fair sampling loopholes and confirmed that realism understood as counterfactual definiteness may not be used to explain quantum phenomena. Since there is now a general consensus that Bell inequalities are violated it is important to understand what does it mean and how can we explain the existence of strong correlations between outcomes of distant measurements, predicted by quantum mechanics. Do we have to announce that: Einstein was wrong, Nature is not local and the correlations are produced due to the quantum magic and emerge, somehow, from outside space-time? We reject such conclusions and we show that violations of various inequalities can neither prove completeness of quantum mechanics nor that Nature is not local. We propose simpler contextual explanation of long range correlations predicted by quantum mechanics which reconciles in some sense Bohr with Einstein and we conclude that there is no evidence that Nature plays dice. We argue that to prove predictable completeness of quantum mechanics one has to search for fine structures in experimental data which might have been averaged out in standard statistical analysis and which were not predicted by the theory.
Since John Bell has established his famous inequality and several independent experiments have confirmed the distinct polarization correlation of entangled photons predicted by quantum mechanics it is evident that quantum mechanics cannot be explained by local realistic theories. Actually, the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of the two circularly polarized wave packets leaving the photon source simultaneously. The experimental results violate Bell's inequality although no non-local interactions have to be assumed. In consequence the principle of locality remains valid in the scope of quantum mechanics. However, the principle of realism has to be replaced by the less stringent principle of contextuality.