Entanglement Energy in GMWT: An Exploratory Coupling Model and a Conditional Bell–CHSH Analysis

This paper develops a wave-based interpretation of entanglement within Gravitation–Matter Wave Theory (GMWT), centred on a proposed resonant coupling between particles of the same species. The link is established during their initial interaction and is hypothesized to persist after separation without continuing interparticle energy exchange; “entanglement force” denotesan interaction energy unless a mechanical force is explicitly derived. An exploratory construction relates the electronic wave charge to an instrumental spectral-energy scale and a reference numerical magnitude near 10−6, whose physical calibration remains open. The statistical analysis distinguishes this interaction amplitude from normalized photon correlations. AdoptingE(a,b) = cos[2(a − b)] and an explicit joint-probability law yields a Bell–CHSH parameter S =2√2 for consistent analyser settings, with normalized, nonnegative probabilities and no signalling marginals. Applied to the Micius satellite experiment, this construction exhibits a violation of the local bound and is compared with the reported value Sexp = 2.37 ± 0.09 for entangled photons near 810nm distributed between stations separated by 1203km. The ideal result establishes conditional compatibility with quantum Bell correlations, rather than a prediction of the measured central value. Because the common GMWT amplitude cancels under normalization, this comparison does not independently determine the coupling constant or entanglement-energy scale. The manuscript also explores spin-dependent wave-phase hypotheses for collective behaviour. Deriving the angular correlation law, measurement probabilities and decoherence dynamics from the proposed wave coupling remains the central step toward a quantitatively predictive model.