Disfavoring the Schroedinger-Newton equation
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.
Cite
@article{arxiv.2307.04914,
title = {Disfavoring the Schroedinger-Newton equation},
author = {Joao V. B. da Silva and Gabriel H. S. Aguiar and George E. A. Matsas},
journal= {arXiv preprint arXiv:2307.04914},
year = {2023}
}
Comments
6 pages, 3 figures, to appear in Phys. Rev. A