Proposal to repeat the Abraham force experiment using giant permittivity materials

In the more than 100 years-old Abraham-Minkowski problem in macroscopic electrodynamics, the issue of how to observe the so-called Abraham term ${\bf f}^{\rm Aterm} = [(\varepsilon\mu-1)/c^2] \partial/\partial t ({\bf E}\times {\bf H})$ has been a main point. Recent years have seen a number of beautiful experiments in radiation optics, but these experiments usually give no information about the Abraham term as this term simply fluctuates out. So one is left with somewhat indirect verifications of this force, as in the radiation pressure of Jones {et al.} in the 1950's, testing the radiation pressure on a mirror immersed in a dielectric liquid. Now, there is a different way to test the existence of ${\bf f}^{ \rm Aterm}$, namely to work with low (quasi-stationary) frequencies enabling one to observe the sinusoidal variation of the force directly. These kind of experiments were actually done by Walker {\it et al.} in 1he 1970's, using BaTiO$_3$ as a high-frequency dielectric (permittivity $\varepsilon \sim 3600$). Now, in recent years there have appeared dielectric materials with giant permittivities, of order $10^5$ or even higher. It is therefore natural to consider the idea of Walker {\it et al.} anew, in order to test if this demanding experiment can be facilitated and give better accuracy. That is the main topic of the present paper. The positive outcome of these kinds of experiments clearly supports the Abraham energy-momentum tensor at low frequencies. The Minkowski tensor is unable to predict a torque at all. The low-frequency and the high-frequency regimes are in this way highly contrasted, as it is obvious that in optical experiments the Minkowski tensor is by far the simplest and most convenient one to use. We end this note by commenting upon the use of the Einstein-Laub tensor (1908) in explaining this experiment, and discuss also the influence from air friction.