Causal action at a distance in a relativistic system of two bound charged spinless particles: Hydrogenlike models

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Abstract
We analyze the causal quantum behavior of two charged spinless particles having different masses interacting via an action-at-a-distance relativistic scalar Coulomb potential. Developing de Broglie’s idea of splitting the potential energy between the particles, we show that the predictivity constraints of relativistic predictive mechanics established by Droz-Vincent and Sudarshan are satisfied. In this way we develop a relativistic theory of hydrogenlike atoms in the framework of the causal interpretation of quantum mechanics.