There is a surprising number of papers seriously discussing the "feigel effect" This has been linked to the Abraham-Minkowski controversy also here. Although there are good discussions picking apart the feigel effect calculations, there does not appear to be a conclusive refutation of the effect under certain experimental circumstances. Much of this is linked to when the Poynting vector vanishes in the vacuum. Is there a legitimate possibility for seeing the Feigel effect? What would that mean about the nature of the poynting vector in physics?
Dear Humble, good questions. I can't answer all your questions, but:
First, the name of the author is Feigel, not Fiegel, and the paper is also a preprint here: http://arxiv.org/abs/physics/0304100
The controversies about the stress-energy tensor were inevitable. Only the total energy and momentum are conserved as a consequence of Noether's theorem, and how they're distributed in space may often be a matter of conventions. In particular, the Poynting vector may be defined in several different ways - and various automatically conserved pieces may be added, too. The integrals won't change. But for example, if there are crossing electric and magnetic fields in the vacuum, the usual Poynting vector $E\times B$ shows that the energy is flowing somewhere. This flow ends up "circular" if you look globally.
Feigel's paper seems to be just a generalization of the Casimir effect, with a slightly more complicated arrangement of things. Instead of the Casimir energy, he wants to play with the energy of the vacuum, and instead of the metallic boundaries, he plays with dielectric liquids.
None of these things changes that the total energy and the total momentum are exactly conserved, because of the symmetries. Whether the momentum is being extracted from the vacuum is a matter of interpretation. You may also say that it is extracted from a low-frequency electromagnetic wave that was emitted by another object.
Feigel suggests that there is a relevance of his setup for the Abraham-Minkowski arguments about the density of electromagnetic momentum in dielectric materials. But one must be careful. The energy carried by the Casimir effect is distributed nonlocally - it comes from modes that look like standing waves in between the metallic plates. So the Casimir energy is not "naturally" written as an integral of a density, I think. Please correct me if I am wrong.
I suspect this may be the case of any one-loop constructions of this sort, and Feigel's construction seems to be just a more complicated example. So I suspect the effect of the Feigel's phenomena are not just about changing some local densities either in the Abraham or in the Minkowski way.
Finally, I would say that in principle, Quantum Electrodynamics or the Standard Model have standardized prescriptions for the stress-energy tensor that should be calculable in any context, including dielectric liquids in crossed electric and magnetic fields.
All the best, LM