A Phase-Superposition Reinterpretation of Quantum Entanglement: Reproducing Bell Correlations within the Wavon Framework, with Falsifiable Consequences
Abstract. Bell's inequality established that no local hidden-variable theory can exceed a CHSH value of 2, andexperiment has repeatedly confirmed the quantum-mechanical prediction 2√2. Without modifying any measuredfact, this paper presents one structural picture of the origin of entanglement correlations — within a frameworkin which a particle is a bound triple of three wavons at mutual 120° phase: the two entangled systems do notcarry locally predetermined values, but share a single phase relation, and a measurement projects that sharedphase onto a direction angle. Within this picture the correlation function E(a,b) = ±cos 2(a−b) and CHSH = 2√2are reproduced, and no-signalling holds as a result rather than an assumption. For contrast, the value-sharinglocal translation is shown to fail, confined to CHSH ≤ 2, making explicit the criterion that separates the twopictures. At the present stage the picture is a restatement mathematically equivalent to the quantum formalism;no new prediction is claimed. Two forcing problems that must be proved before the restatement can be promotedto a derivation, and four points at which the picture is exposed to test and refutation, are stated explicitly.Keywords: Bell inequality · CHSH · quantum entanglement · no-signalling theorem · interpretation · phasesuperposition · wavon
Abstract. Bell's inequality established that no local hidden-variable theory can exceed a CHSH value of 2, andexperiment has repeatedly confirmed the quantum-mechanical prediction 2√2. Without modifying any measuredfact, this paper presents one structural picture of the origin of entanglement correlations — within a frameworkin which a particle is a bound triple of three wavons at mutual 120° phase: the two entangled systems do notcarry locally predetermined values, but share a single phase relation, and a measurement projects that sharedphase onto a direction angle. Within this picture the correlation function E(a,b) = ±cos 2(a−b) and CHSH = 2√2are reproduced, and no-signalling holds as a result rather than an assumption. For contrast, the value-sharinglocal translation is shown to fail, confined to CHSH ≤ 2, making explicit the criterion that separates the twopictures. At the present stage the picture is a restatement mathematically equivalent to the quantum formalism;no new prediction is claimed. Two forcing problems that must be proved before the restatement can be promotedto a derivation, and four points at which the picture is exposed to test and refutation, are stated explicitly.Keywords: Bell inequality · CHSH · quantum entanglement · no-signalling theorem · interpretation · phasesuperposition · wavon
In 1964, John Bell showed that any local hidden‑variable theory must satisfy a specific inequality on correlations between distant measurements. In its CHSH form (Clauser, Horne, Shimony, Holt 1969), the inequality reads |S| = |E(a,b) + E(a,b′) + E(a′,b) − E(a′,b′)| ≤ 2, where E(a,b) is the correlation between measurement outcomes at two separated parties using settings a and b. Any local realist theory respects this bound. Quantum mechanics violates it. Experiments confirm the violation. The standard quantum prediction for a maximally entangled state with optimal measurement angles is |S| = 2√2 ≈ 2.828. In 1980, Boris Tsirelson proved that 2√2 is not just one quantum prediction — it is the *maximum* value any quantum correlation can produce. No quantum state, no measurement scheme, no clever protocol can push |S| beyond 2√2. The bound is sharp, the value is exact, and it has been measured in laboratories around the world to experimental precision. The Tsirelson bound is one of the deepest empirical structures in physics. It tells us that quantum correlations exceed classical correlations by a specific, finite amount — there is room to violate Bell’s inequality, but only so much room. The number 2√2 has no obvious physical interpretation. It does not appear in the formulation of quantum mechanics. It emerges from the mathematics of the bipartite Hilbert space when the CHSH operator is constructed and bounded. The question is where it comes from. In standard QM, the answer is that it falls out of the Hilbert‑space structure plus Cauchy–Schwarz plus an operator‑norm bound on the CHSH operator. Technically correct, and Tsirelson’s 1980 proof remains the canonical derivation — but it leaves the deeper structure unanswered. The Hilbert space is postulated. The inner product that makes Cauchy–Schwarz available is postulated. The bipartite tensor‑product structure on H_A ⊗ H_B is postulated. The 2√2 value is what those postulates produce when run through the CHSH operator. This walkthrough shows how the Event Density framework derives the Tsirelson bound from a smaller set of structural commitments. The Hilbert‑space structure, the inner product, and the bipartite tensor‑product structure all emerge as forced consequences of the substrate ontology rather than being postulated. With those structures forced rather than assumed, Tsirelson’s 1980 argument applies directly, and the 2√2 value is no longer the output of a chain of postulates but the output of a chain of derived theorems. Like Heisenberg, Bell–Tsirelson is a place where the framework’s contribution is upstream. The bound itself is mathematical physics already in the literature; what changes is the foundational status of the structures the argument requires. ED does not produce a new derivation step beyond standard QM here — it removes the postulational status of the structures the standard derivation already uses. The 2√2 value is now a derived consequence of the substrate ontology, all the way down.
The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden variables exist) can take the maximum value of 2. Quantum mechanics violates this bound, allowing for a higher bound on the correlation, which can take the maximum value 22, known as the Tsirelson bound. Popescu and Rohrlich showed that the assumption of relativistic causality allows for an even higher bound on the CHSH correlation, this value being 4. Why is the bound coming from causality higher than the Tsirelson bound? Are there relativistic causal dynamical theories which violate the Tsirelson bound? In the present paper we answer this question in the affirmative. We show that the pre-quantum theory of trace dynamics, from which quantum theory is emergent as a thermodynamic approximation, permits the CHSH correlation to take values higher than 22. We interpret our findings to suggest that quantum theory is approximate, and emergent from the more general theory of trace dynamics.
Bell's theorem demonstrates that no local deterministic theory can reproduce the complete set of correlations predicted by standard quantum mechanics. The present work accepts Bell's theorem as mathematically correct but questions the physical interpretation of the quantum correlation function used in Bell analyses. It is argued that entangled particles inherit a complete common physical state at their creation and that subsequent measurements reveal selected observables of this state rather than generating new information or requiring superluminal communication. The paper further proposes that the standard quantum correlation function, (E(θ)=−cosθ), incorporates additional angular dependence beyond the information physically established at the source. Under this interpretation, the observed violation of Bell inequalities arises from the mathematical structure of the correlation function rather than from nonlocal information transfer between distant particles. An explicit local common-source model is presented, leading to a piecewise linear correlation function and motivating a decomposition of the standard quantum prediction into a local component and a supplementary angular term.
The Complete Disenchantment of Quantum Entanglement—Failure of Measurement Independence and a Field-Theoretic Explanation of Electron Internal Structure This paper provides a physical explanation of quantum entanglement—the most central puzzle in quantum mechanics—without relying on "nonlocality." The violation of Bell's inequality is widely interpreted by mainstream physics as "experimental falsification of local realism," from which the conclusion "the world is nonlocal" is drawn. This paper points out that this chain of reasoning depends on a premise that has never been independently tested: the measurement process does not change the hidden variable that determines the measurement outcome. This theory divides all matter in the universe into Nie-matter entities (massive, Staticity) and Ji-matter entities (massless, Dynamicity). The electron is not a point particle, but a Nie-matter entity composed of Zhonghua Micro-Particles, possessing an internal Ji-matter field configuration (the electron self-field). When a measurement device operates, it inevitably releases a Ji-matter field; this field undergoes local coupling with the electron self-field, changing the electron's effective configuration from the original configuration λ₀ at production to the coupled effective configuration λ_eff(a) = C[λ₀, F_device(a)]. The measurement outcome is a function of λ_eff(a), not a function of λ₀ alone—therefore, the measurement-independence premise of Bell's theorem does not hold physically. This paper further argues: the electron's having internal structure is precisely the physical origin of the angle-dependent correlations. If the electron were an unstructured point particle, measurements at different angles should give the same result—but experiments observe angle-dependent correlations, which in itself already proves that the electron is not a point particle. Bell-inequality experiments have never been a "victory of nonlocality"—they are ironclad evidence that the electron has internal structure. This paper gives four core arguments: P6-4C (failure of the premises of Bell's inequality derivation), P6-4D (change of electron state by the measurement device's Ji-matter field), P6-5 (how a point particle absorbs a photon—the electron must have internal structure to accommodate an absorbed photon), P6-4A (Bell's inequality—ironclad evidence that the electron has internal structure), and P6-4B (local mechanism of Bell experiments and experimental test paths for electron internal structure). These include an order-of-magnitude estimate of the electron internal structure correction to g-2 (~10⁻¹⁸), a comparison with current experimental precision (~10⁻¹²), and future test paths. The full text does not claim that Bell's inequality is "overturned"—it is a mathematically correct theorem. What this paper claims is: the measurement-independence premise on which Bell's inequality depends does not hold under the physical picture in which measurement is local field coupling. Violating Bell's inequality is precisely evidence that the electron has an internal Ji-matter field configuration, not evidence for nonlocality.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
Abstract This work presents an interpretation of the phenomenon of quantum entanglement within the framework of the Topological Model of Physics (MTF). It is proposed that correlations between particles can be described in terms of a shared global phase or structure, defined at the common origin of the particles in the system. This phase does not determine pre-existing values of observables, but rather acts as a common geometric or topological constraint that is preserved during separation, whose projection in each measurement depends on the experimental context. In this approach, such a phase does not require dynamical evolution during the separation of the particles, and therefore the observed correlations need not be interpreted in terms of action at a distance at the moment of measurement. This proposal is related to the original formulation of the EPR paradox, as well as to the restrictions imposed by Bell’s inequalities and their experimental verifications, particularly in the works of Alain Aspect and CHSH. In this framework, the notion of “spooky action at a distance” is considered unnecessary as an explanatory element, since correlations are interpreted as the manifestation of a structure shared from the origin. A form of state or structural realism is preserved, but not a classical realism of pre-existing values; furthermore, there is no signal transmission and the limit imposed by the speed of light is respected. In standard quantum theory, when a property of an entangled particle is measured, the collapse of the wave function common to both particles occurs. Therefore, the value of the property measured in one of them determines the value of that same property in the other. The theory is fully verified experimentally, but it does not explicitly state the physical mechanism underlying this result. The aim of this presentation is to offer a physical interpretation of an underlying mechanism.