Whence Nonlocality? Removing spooky action at a distance from the de Broglie Bohm pilot-wave theory using a time-symmetric version of de Broglie double solution

In this work, we review and extend a version of the old attempt made by Louis de broglie for interpreting quantum mechanics in realistic terms, namely the double solution. In this theory quantum particles are localized waves, i.e, solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave-particle duality and to explain the violations of Bell's inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Borglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action at a distance presents in the pilot-wave theory. In the double solution developed here there is fundamentally no action at a distance but the theory requires a form of superdeterminism driven by time-symmetry.