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.

arXiv comment6 pages, 3 figures, to appear in Phys. Rev. A

References in corpus (8)

• Testing the limits of quantum mechanical superpositions
• Levitodynamics: Levitation and control of microscopic objects in vacuum
• Gravitation and quantummechanical localization of macroobjects
• The Schrödinger-Newton equation and its foundations
• Problems with the Newton-Schrödinger Equations
• Optomechanical test of the Schrödinger-Newton equation
• Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems
• The hydrogen atom: consideration of the electron self-field

Cited by in corpus (2)

• A simple gravitational self-decoherence model
• Probing the Schroedinger-Newton equation in a Stern-Gerlach interferometer