Abstract
The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit. We argue that the Casimir self-stress cannot be regarded as due to pair-wise Casimir–Polder interactions, but rather due to reflections of virtual electromagnetic waves.
Highlights
Julian Schwinger et al, in a paper from 1977 [1], described the Casimir force as “one of the least intuitive consequences of quantum electrodynamics”
Inspired by the work [13] of Milton, DeRaad and Schwinger on the Casimir self force of a perfectly conducting shell, we solve the problem of calculating the Casimir stress in an arbitrary dielectric sphere embedded in an arbitrary dielectric background, both assumed to be isotropic and dispersionless (Fig. 1)
We found that the physical picture of Casimir forces as arising due to pair-wise van der Waals interactions is no longer justified in the dilute limit of the dielectric sphere
Summary
Julian Schwinger et al, in a paper from 1977 [1], described the Casimir force as “one of the least intuitive consequences of quantum electrodynamics”. We calculate the macroscopic contribution to the self stress as a function of the dielectric constant and give an estimation for the correction to the surface tension of the sphere that arises from it, which scales like a−3, a being the radius of the sphere We show that this method, different in essence, reproduces known results such as the stress in the limit of a perfectly conducting spherical shell and the case in which the speed of light is identical both inside and outside the sphere.
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