Mechanism of Quantum Entanglement and Simultaneity Within the Framework of Relativistic Phase Velocity and Universal Quantum Energy

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ABSTRACT The emergence of correlations observed in quantum entanglement between spatially separated measurement regions has rendered the interpretation of the relationship between quantum mechanics and relativistic causality one of the fundamental problems in quantum foundations [Einstein et al., 1935; Bell, 1964]. In this study, two entangled particles are modeled not as two independent physical entities in Minkowski spacetime, but as a joint quantum state in configuration space. The relative space and time coordinates of the joint state are defined as: and the ideal spacetime correlation limit assumed in the model is expressed as: This limit is not a general definition of quantum entanglement, but an idealized geometric assumption representing the strong correlation in the relative coordinates of the joint state within the proposed model. In this approach, physical spacetime is treated as a geometric structure representing the projection of the joint quantum state onto observable spacetime coordinates. To render the projection Lorentz-covariant, the light-like interval is employed as the foundational geometric condition of the model. The dynamic scale parameter of the model is based on total relativistic quantum energy instead of rest mass, defining a dimensionless Planck-scaling factor as . Furthermore, modeling the proposed geometric effect as a dimensionless metric perturbation leads to the definition of an identification factor , sensitive to the spatiotemporal correlation widths () of the joint state, yielding the first-order geometric phase correction: Here, the factor prevents single-particle phase shifts independent of entanglement and directly couples the geometric phase contribution to the degree of entanglement. Under constant and finite , the convergence of the proposed correction to zero both in the low-energy regime relative to the Planck scale () and in the decorrelation limit () demonstrates that the geometric effect added to standard low-energy quantum mechanical results vanishes in accordance with the decoupling mechanism (decoupling limit). The study proposes a testable theoretical model aimed at explaining the spatiotemporal correlations of quantum entanglement within a Lorentz-covariant, correlation-sensitive, and phenomenological geometric framework.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.