Hidden momentum of electrons, nuclei, atoms and molecules

TL;DR

This paper investigates hidden momentum in electrons, nuclei, atoms, and molecules within electromagnetic fields, revealing its presence and cancellation, and introduces the concept of 'hidden hidden momentum' in electron vortices.

Contribution

It demonstrates the existence of hidden momentum in particles and molecules and introduces the novel idea of 'hidden hidden momentum' in electron vortices.

Findings

Hidden momentum exists in electrons and nuclei within electromagnetic fields.

The hidden momentum is canceled by the electromagnetic field's momentum.

Electron vortices can harbor significant hidden momentum.

Abstract

We consider the positions and velocities of electrons and spinning nuclei and demonstrate that these particles harbour hidden momentum when located in an electromagnetic field. This hidden momentum is present in all atoms and molecules, however it is ultimately cancelled by the momentum of the electromagnetic field. We point out that an electron vortex in an electric field might harbour a comparatively large hidden momentum and recognise the phenomenon of 'hidden hidden momentum'.