A two-particle simulation of Nonunitary Newtonian Gravity

TL;DR

This paper presents a numerical simulation of two particles under Nonunitary Newtonian Gravity, demonstrating how fundamental gravity-induced entropy differs from subjective coarse-grained entropy, with implications for quantum gravity theories.

Contribution

It introduces a simulation framework for two particles interacting via Nonunitary Newtonian Gravity, highlighting entropy dynamics and the distinction from coarse-grained entropy.

Findings

Energy expectation remains constant during evolution.

A slow variation of von Neumann entropy is observed.

Gravity-induced entropy can be distinguished from subjective entropy.

Abstract

The result of a numerical simulation of two interacting particles in the framework of Nonunitary Newtonian Gravity is presented here. Particles are held close together by a 3-d harmonic trap and interact with each other via an `electrical' delta-like potential and via the ordinary Newtonian term, together with a fluctuational nonunitary counterpart of the latter. Fundamental nonunitarity can be seen as arising from the interaction of the physical degrees of freedom with (gravitational) hidden copies of them. Starting from an energy eigenstate within the ordinary setting, it is shown that, while energy expectation remains constant, a slow net variation of the von Neumann entropy for the system as a whole takes place, with a small modulation induced on the relative entanglement entropy of the two particles. Besides, the simulation shows explicitly how fundamental gravity-induced entropy can be clearly distinguished from the subjective notion of coarse-grained entropy, i.e. from the entropy of one particle with respect to the `environment' of the other.