A natural cure for causality violations in Newton-Schr\"odinger equation

TL;DR

This paper introduces a parameterized model that avoids causality violations in the Newton-Schrödinger equation by incorporating spontaneous state reduction, aligning with quantum mechanics and proposing a soft Many Worlds interpretation.

Contribution

It presents a one-family parameter model that eliminates causality violations in the Newton-Schrödinger equation through spontaneous state reduction mechanisms.

Findings

Model reproduces nonlinear Newton-Schrödinger equation in a limit.

Resolves causality violations with finite parameter values.

Suggests a soft version of the Many Worlds Interpretation.

Abstract

It is explicitly shown that a one-family parameter model reproducing the nonlinear Newton-Schr\"odinger 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-Schr\"odinger 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 QM. 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.