Disfavoring the Schroedinger-Newton equation

• URL: http://arxiv.org/abs/2307.04914v1
• Date: Mon, 10 Jul 2023 21:38:35 GMT
• Title: Disfavoring the Schroedinger-Newton equation
• Authors: Joao V. B. da Silva, Gabriel H. S. Aguiar, and George E. A. Matsas
• Abstract summary: 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. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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