A natural cure for causality violations in Newton–Schrödinger equation

Abstract

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 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.

Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds

“…The starting point is a general N-copy model, which is a fully consistent quantum theory without causality violation problems thanks to the validity of the nosignaling condition [255,256]. Furthermore, while superluminal communications are suppressed, new strange communications among Everett branches of the wave function [253] are shown to appear, in close agreement with previous findings by Polchinski [256]. Within NNG model the density matrix fully characterizes the state of a system.…”

“…A second topical issue, concerning causality violations in Newton-Schrödinger equation [235], has been fully addressed within the NNG model as well [252,253]. Here the single particle Newton-Schrödinger equation has been obtained as the meanfield approximation of an equation of N identical copies of the particle, interacting each other via gravitational interaction, when N goes to infinity [254].…”

Interaction between Everett worlds and fundamental decoherence in Non-unitary Newtonian Gravity

“…Here such correlations are induced by a fundamental decoherence mechanism of gravitational origin, which is built in the NNG model, and can be interpreted as a kind of communication between different branches of the wave function. 1 These conclusions are consistent with previous findings, pointing out the appearance of communications among Everett branches of the wave function as a consequence of the introduction of nonlinearities in some modified theories of quantum mechanics [47,46]. Furthermore our results are in agreement with existing treatments of intrinsic decoherence mechanisms [1,50].…”

“…Another interesting feature of De Filippo's model is its field-theoretical formulation, obtained by a Hubbard-Stratonovich transformation of the gravitational interaction [37], which allows to obtain the well known nonlinear Newton-Schrödinger equation [18,44] by gravitationally coupling N exact copies of the physical system and then taking the limit N → ∞ [45]. It has been also shown how, for any finite value of N , the same model is completely free from the usual causality violation problems that plagued Newton-Schrödinger model [46]; this happens thanks to the intrinsic mechanism of spontaneous state reduction of the model, absent in the Newton-Schrödinger limit. Furthermore, since within NNG density matrix plays a fundamental role, amounting to the most complete characterization of a physical system's state, the Everett Many World Interpretation appears to be the most natural conceptual framework of that theory.…”

Microscopic foundation of the second law of thermodynamics within nonunitary Newtonian gravity

“…The low-energy limit of this model, a brief account of which is given in the Appendix A, is known as Nonunitary Newtonian Gravity (NNG, from now on), and has been studied in detail, in particular the case N = 2, showing (entropic) dynamical self-localization for masses above the sharp threshold of 10 11 proton masses, with precise signatures susceptible to future experimental tests [13,14,15,16]. Recently it has been explicitly shown to be free from causality violation problems [17,18], at variance with semiclassical gravity, namely (in the Newtonian limit) Newton-Schroedinger model. Physically this is achieved by decohering linear superpositions of macroscopically distinct states, as a consequence of the dynamical mechanism of state reduction naturally embedded in the model.…”