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Qeios

On Aspect’s Bell Inequality Experiment

Justo Pastor Lambare

Published Jul 28, 2026• 0 citations
Publisher

Abstract

In this short note, we explain the untenability of a recent claim in the technical literature purportedly proving that Aspect’s experiment testing the Bell inequality is based on a statistical flaw.
DOI
10.32388/qa9cto

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Bell inequalities are intended to formulate mathematically the argument of the thought-experiment proposed by Einstein, Podolsky and Rosen (EPR) in the Einstein-Bohr Debate. Devised to test Bell inequalities against quantum mechanics for resolving the Einstein-Bohr debate, Bell experiments are purportedly modern versions of the EPR experiment. However, there exists a fatal logical flaw in Bell experiments. Because of the logical flaw, Bell experiments differ essentially from the EPR experiment, and quantum correlation in the EPR experiment is not "quantum entanglement" in Bell experiments; the latter is not physically meaningful. In addition to the logical flaw in Bell experiments, a physical constraint imposed on measuring individual quantum objects is violated by all Bell inequalities, which makes Bell inequalities physically meaningless. Unlike Bell experiments, the EPR experiment will not violate any physical constraint, and the EPR argument has no logical flaw. Consequently, the experimental invalidation of Bell inequalities is not evidence for falsifying the two fundamental hypotheses for scientific research, i.e., locality and realism, underlying the EPR experiment, and by no means can Bell experiments resolve the Einstein-Bohr debate. Stemming from abandoning either locality or realism or both, the so-called new applications of quantum mechanics, including various quantum information technologies, are all ineligible and doomed to failure, for they attempt to exploit physically meaningless "quantum superposition" or "quantum entanglement", treating them as physical resources "out there" in the real world.
Bell’s correlation formula is based on a classical Kolmogorov probability theory. It is tested in experiment with an estimate correlation. The latter is the raw product moment (rpm) correlation that is classical Kolmogorov based as well. We note that the famous Bell inequalities are derived from Bell’s correlation formula. The problem is that the hypothesis: “is it possible that in experiment Bell’s correlation is equal to quantum”, can only found to be false. This is not because the data generating process does not produce the required data. Or that the inequalities sufficiently show that the data cannot violate the inequalities. It is because the statistics of the Bell experiment is flawed. The rpm correlation in experiment cannot be equal to the quantum value in principle. This is because it requires the classical Kolmogorov rpm correlation to be not Kolmogorov.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiments with the experimental results explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to represent quantum information. In the present paper, a new principle, the general principle of measurements, is introduced and proved as a mathematical theorem. Based on this principle, the experiments for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental results of testing Bell’s inequality, actually Einstein’s viewpoint is irrelevant to Bell’s theorem. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate. The experimental results of testing Bell’s inequality and the measurement outcomes of various experiments involving “qubit” are all erroneously explained. Without involving hidden variables, quantum mechanics can be completed based on the general principle of measurements by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space, and the mathematical setting can remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the real world. A very regrettable conclusion from the above findings is inevitable: Quantum information has no physical carriers, and all quantum information technologies are not physically realizable.