On the possibility of Casimir repulsion using Metamaterials

TL;DR

This paper investigates whether metamaterials with Pendry's magnetic permeability model can produce Casimir repulsion and concludes that such repulsion is not achievable with this model, despite theoretical possibilities.

Contribution

It demonstrates that Casimir repulsion cannot be realized using Pendry's magnetic permeability model for metamaterials, clarifying limitations of current models.

Findings

Casimir repulsion is not possible with Pendry's permeability model.

Theoretical conditions for repulsion are not met by this model.

Qualitative analysis explains why repulsion cannot be achieved.

Abstract

It is well known that the Casimir force between two half-spaces is dictated by their electromagnetic properties. In particular, when one of the half-spaces is mainly metallic or dielectric and the other is mainly magnetic, it is possible to show that the force is repulsive. This has attracted lots of interest towards the study of metamterials (MMs) in the context of Casimir effect, as their magnetic activity might help bring the idea of Casimir repulsion from the theoretical realm to experimental verification. In this paper we investigate the possibility of repulsion when the MM magnetic permeability is given not by a Drude-Lorentz behavior, but by a model put forward by Pendry et al. . After introducing the model and deriving the necessary formulas, we show that it is impossible to achieve repulsion with such a model and present a qualitative discussion of why this is so.