A consequence of the repulsive Casimir-Lifshitz force on nano-scale and the related Wheeler propagator in the classical electrodynamics

TL;DR

This paper explores how the repulsive Casimir-Lifshitz force could induce charge disjunction phenomena at the nano-scale, leading to modified Maxwell equations with potential tachyonic solutions and implications for the Wheeler propagator.

Contribution

It introduces a new theoretical framework incorporating an additional term in Maxwell equations to model charge disjunction caused by Casimir-Lifshitz forces.

Findings

Derivation of modified Maxwell equations with a negative mass term

Formulation of a Wheeler propagator for the electric field

Calculation of electric field and charge density during disjunction

Abstract

Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other presently unknown interactions. The repulsive Casimir-Lifshitz force may be also a good candidate as a source of this kind of phenomenon. To cover this assumption mathematically an additional term should appear in the Maxwell equations. As a consequence of this term, similar Klein-Gordon equations with a negative mass term will be obtained for the electric and magnetic fields. These equations may have tachyonic solutions depending on the parameter of the charge disjunction process. Finally, the propagator is formulated, the electric field and the charge density are calculated during the charge disjunction.