The paradox of the Casimir force in inhomogeneous transformation media

TL;DR

This paper investigates the Casimir force in inhomogeneous media and demonstrates that, under idealized metamaterials implementing virtual geometries, the force remains cutoff-independent and exactly calculable, resolving a paradox in the field.

Contribution

It shows that idealized metamaterials can produce cutoff-independent Casimir forces by effectively creating a homogeneous virtual space, reconciling inhomogeneous media results with recent theoretical advances.

Findings

Casimir force size is modified by inhomogeneous media

In idealized metamaterials, the force is cutoff-independent

The paradox dissolves with the concept of virtual geometries

Abstract

It has recently been argued that Casimir-Lifshitz forces depend in detail on the microphysics of a system; calculations of the Casimir force in inhomogeneous media yield results that are cutoff-dependent. This result has been shown to hold generally. But suppose we introduce an inhomogeneous metamaterial into a cavity that effectively implements a simple distortion of the coordinate system. Considered in its 'virtual space', the optical properties of such a material are homogeneous and consequently free from the cutoff-dependency associated with inhomogeneous media. This conclusion should be reconciled with recent advances in our understanding of Casimir-Lifshitz forces. We consider an example of such a system here and demonstrate that, whilst the size of the Casimir force is modified by the inhomogeneous medium, the force is cutoff-independent and can be stated exactly. The apparent paradox dissolves when we recognise that an idealised metamaterial that could implement a virtual geometry for all frequencies would be devoid of internal scattering, and would not give rise to a cutoff-dependency in the Casimir force for that reason.