A natural cure for causality violations in Newton–Schrödinger equation

It is explicitly shown that a one-family parameter model reproducing the nonlinear Newton–Schrödinger equation as the parameter goes to infinity is free from any causality violation problem for any finite value of it. This circumstance arises from the intrinsic mechanism of spontaneous state reduction of the model, absent in the Newton–Schrödinger limit. A specific ideal EPR experiment involving a superposition of two distinct CM's position states of a massive lump is analyzed, showing recovered compatibility with quantum mechanics. Besides, the new framework suggests a soft version of the many worlds interpretation, in which the typical indiscriminate proliferation of Everett branches, together with the bizarre inter-branches communications made possible by nonlinearity, are strongly suppressed in the macroscopic world by the same mechanism of state reduction. (paper)