Forces and momenta caused by electromagnetic waves in magnetoelectric media

Abstract

We analyse the propagation of electromagnetic waves in magnetoelectric media. Recently, Feigel has predicted that such a medium may "extract momentum from vacuum" in the sense that the total momentum of the virtual waves (vacuum fluctuations of the electromagnetic field) is nontrivial. Our aim is to check the feasibility of this effect. The crucial point in our study is an assumption of the finite size of the magnetoelectric sample, which allows us to reduce the calculation of the momenta and forces of the electromagnetic waves acting on the sample to the vacuum region outside of the medium. In this framework, we demonstrate that, in contrast to Feigel, the total force caused by the virtual is zero, with an appropriate count of the modes that should be taken into account in this effect. Furthermore, we find that the two irreducible parts of the magnetoelectric matrix behave differently in the possible Feigel effect. Going beyond the original scheme of the virtual electromagnetic waves, we propose an experimental scheme which is suitable for the measurement of the magnetoelectric susceptibilities of the medium with the help of real electromagnetic waves.

Alternative derivation of the Feigel effect and call for its experimental verification

“…Further, a new expression for the vacuum stress on the fluid is derived, predicting a Poiseuille flow in a tube, with maximum speed U max ≈ 100µm/s (2000 times larger than Feigel's original estimate of 50nm/s). This prediction contrasts with that of Obukhov & Hehl (2008) that a magnetoelectric slab in the vacuum experiences no net force.…”

“…Turning now to the prediction of Obukhov & Hehl (2008), this implies that a vacuum radiometer, such as the four pane one shown in Fig. 1b, should not turn.…”

“…Note that an equivalent result for the vacuum stress could also have been obtained semi-classically by evaluating the contribution from counterpropagating modes to the electromagnetic stress tensor: Π zz k ∼ ǫE 2 0 (n 2 −kλ − n 2 kλ ). Indeed, it was by using such a semi-classical approach applied to a magnetoelectric slab of finite thickness in a vacuum that Obukhov & Hehl (2008) recently predicted that the net stress on the slab should be Π 0 = 0.…”

Anisotropic distribution of quantum‐vacuum momentum density in a moving electromagnetic medium

“…Apart from the vacuum effects in quantum field theory, quantum vacuum in electromagnetic materials can also exhibit some novel effects such as magnetoelectric vacuum birefringence [8], geometric phases at quantum vacuum level [9] and vacuum contribution to medium momentum [10,11] (as far as the vacuum contribution to medium momentum is concerned, Feigel suggested that there is an effect of momentum transfer between quantum vacuum and anisotropic media [10]. Whereas we should also point out that there are some researchers such as van Tiggelen, Rikken [12] and Obukhov, Hehl [13] who have contested the conclusion of Feigel). These vacuum effects are the phenomena taking place in the materials at rest, and, to the best of our knowledge, less attention was paid to the vacuum effects inside moving materials.…”

“…Since the quantum vacuum would have a nonzero momentum, one can conjecture that this would therefore lead to the effect of transfer of some dynamical physical quantities (such as momentum, energy, and even angular momentum) between the quantum vacuum and the moving material. In the reference [10], Feigel has considered the problem of quantum vacuum contribution to the medium momentum, where he suggested that the momentum transfer between a magnetoelectric medium and the quantum vacuum can possibly take place (though some researchers [12,13] have contested the conclusion of Feigel). As there is also a magnetoelectric coupling in the constitutive relation of the moving medium, we expect that such a quantum-vacuum mechanical effect would also emerge from the present system (the moving medium and the anisotropic vacuum).…”