Disfavoring the Schroedinger-Newton equation

TL;DR

This paper investigates the plausibility of the Schroedinger-Newton equation explaining classicality, finding it unlikely for electrons due to electromagnetic self-interaction constraints and highlighting the need to reach Planck scale for meaningful tests.

Contribution

It introduces an electric self-interaction term to the Schroedinger-Newton equation and analyzes its implications for hydrogen, providing new insights into testing the equation's validity.

Findings

Electromagnetic self-interaction for electrons is ruled out.

Testing the Schroedinger-Newton equation requires approaching the Planck scale.

Results disfavor the equation based on low-energy electromagnetic analogy.

Abstract

The main goal of this brief report is to provide some new insight into how promising the Schroedinger-Newton equation would be to explain the emergence of classicality. Based on the similarity of the Newton and Coulomb potentials, we add an electric self-interacting term to the Schroedinger-Newton equation for the hydrogen atom. Our results rule out the possibility that single electrons self-interact through their electromagnetic field. Next, we use the hydrogen atom to get insight into the intrinsic difficulty of testing the Schroedinger-Newton equation itself and conclude that the Planck scale must be approached before sound constraints are established. Although our results cannot be used to rule out the Schroedinger-Newton equation at all, they might be seen as disfavoring it if we underpin on the resemblance between the gravitational and electromagnetic interactions at low energies.