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Momentum Physics Education Journal

Completeness of quantum theory and entanglement: A simplified teaching framework

Mustafa Erol

Published Jun 22, 2026• 0 citations

Abstract

This work proposes a clear teaching framework for the completeness of quantum theory and the related phenomenon of quantum entanglement. The framework begins by summarizing and underlining the probabilistic structure of quantum theory. Next, the well-known Einstein–Podolsky and Rosen (EPR) paradox, which questions the probabilistic structure and completeness of the theory, is summarized. Afterward, Bell’s inequality and Clauser, Horne, Shimony, and Holt (CHSH) inequality approaches are enlightened by underlining their abilities to test completeness. The effort next explains how the completeness of quantum theory can be tested via quantum entanglement. Finally, the quantum entanglement of bipartite systems is generally illuminated, and the quantum entanglement of spins is fully resolved for undergraduate teaching purposes. The opinions of the students on the teaching proposal reveal that necessity, simplicity, and originality are high, and significance and importance are medium. The proposed teaching framework is reasonably simple and includes almost all the details that can be easily introduced for undergraduate quantum mechanics courses.

DOI: 10.21067/mpej.v10i1.11749

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This work proposes a clear teaching framework for the completeness of quantum theory and the related phenomenon of quantum entanglement. The framework begins by summarizing and underlining the probabilistic structure of quantum theory. Next, the well-known Einstein–Podolsky and Rosen (EPR) paradox, which questions the probabilistic structure and completeness of the theory, is summarized. Afterward, Bell’s inequality and Clauser, Horne, Shimony, and Holt (CHSH) inequality approaches are enlightened by underlining their abilities to test completeness. The effort next explains how the completeness of quantum theory can be tested via quantum entanglement. Finally, the quantum entanglement of bipartite systems is generally illuminated, and the quantum entanglement of spins is fully resolved for undergraduate teaching purposes. The opinions of the students on the teaching proposal reveal that necessity, simplicity, and originality are high, and significance and importance are medium. The proposed teaching framework is reasonably simple and includes almost all the details that can be easily introduced for undergraduate quantum mechanics courses.

The “spooky action at a distance” and consequently quantum entanglement of physical systems/particles has been debated ever since the famous paper of Einstein, Podolsky and Rosen-EPR Paradox (Einstein et al., 1935). In spite of being considered of highly controversial, there has been a considerable amount of work so far addressing the issue and many scientifically successful experiments were recently carried out proving that the entanglement is a physical reality (Horodecki et al., 2009). The influence of quantum mechanics and entanglement has been far from the imagination of most scientists, eventually reaching to the ultimate concept of consciousness/mind. The entanglement theory, its connection to the consciousness/mind and finally the entanglement theory of consciousness/mind therefore demands pure scientific interest. In order to maintain the requirements, the present work firstly summarizes the quantum entanglement theory together with its relations with Bell’s inequality and finally describes an “entanglement model of consciousness/mind”.

The Einstein–Podolsky–Rosen (EPR) argument was originally posed as a challenge to the completeness of quantum mechanics, rather than its empirical adequacy. While subsequent developments—most notably Bell’s theorem and experimental tests of nonlocal correlations— have constrained classes of hidden-variable theories, they have not resolved the underlying on- tological question raised by EPR: whether the quantum state exhausts physical reality. In this paper, we revisit the EPR criterion of completeness from the perspective of a temporally grounded physical framework, the Temporal Inertia Framework (TIF). We argue that the orig- inal EPR dilemma rests on an implicit assumption that physical reality must be specified on spacelike hypersurfaces, an assumption shared by both EPR and Bohr. By relaxing this assump- tion and allowing physical correlations to arise from shared temporal structure rather than local spatial variables or superluminal influence, one may satisfy the EPR realism criterion without violating relativistic causality or Bell-type constraints. Quantum mechanics is thus interpreted as operationally complete but ontologically incomplete, with quantum indeterminacy emerging from dynamical interactions with a proposed underlying temporal structure.

Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger

Quantum entanglement, a peculiar phenomenon where two or more particles become linked in such a way that they share the same fate, is a cornerstone of quantum mechanics. This paper explores the potential of leveraging this entanglement to revolutionize probability theory, proposing a formalization of probability based on quantum entanglement as a fundamental building block. We aim to develop a set of operators representing entanglement, enabling precise calculation of probabilities and correlations within quantum systems. The core claim is that this framework offers a deeper and more rigorous understanding of randomness and uncertainty inherent in quantum mechanics.

We emphasize the role of the precise correlations loophole in attempting to connect the CHSH type inequalities with the EPR-argument. The possibility to test theories with hidden variables experimentally by using such inequalities is questioned. The role of the original Bell inequality is highlighted. The interpretation of the CHSH inequality in the spirit of Bohr, as a new test of incompatibility, is presented. The positions of Bohr, Einstein, Podolsky, Rosen, Bell, Clauser, Horne, Shimony, Holt, De Broglie, Hertz, and Boltzmann on interrelation of theory and experiment are enlightened.