Reconsidering the quantization of electrodynamics with boundary conditions and some measurable consequences

TL;DR

This paper explores two different boundary condition models for conductors in electrodynamics, revealing distinct classical and quantum physical effects, including measurable differences in Casimir-Polder forces.

Contribution

It introduces and compares 'thick' and 'thin' conductor boundary conditions, highlighting their different physical implications at classical and quantum levels.

Findings

'Thin' conductors allow for normal component interactions, unlike 'thick' conductors.

Casimir-Polder force is about 13% smaller for 'thin' conductors.

Different boundary conditions lead to observable quantum force differences.

Abstract

We show that the commonly known conductor boundary conditions $E_{||}=B_\perp=0$ can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component $E_\perp$ of the electric field whereas for a 'thin' conductor $E_\perp$ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction between the normal components of currents on both sides. On quantum level different forces between a conductor and a single electron or a neutral atom result. For instance, the Casimir-Polder force for a 'thin' conductor is by about 13% smaller than for a 'thick' one.