Energy conservation for the electromagnetic field requires a Poynting vector
S =
E×
H giving the electromagnetic energy flux density. For crossed (perpendicular) electric and magnetic fields, this is nonzero, and therefore we can say that electromagnetic energy is circulating even in the absence of electric charges, indeed even if the fields are unchanging and uniform. This shouldn't show up classically as a net force over bulk neutral matter, but both Feigel and van Tiggelen argue that an appropriate quantum-mechanical generalization can indeed be measurable.
The Feigel effect is wrapped up in the so-called Abraham–Minkowski controversy, which is a surprisingly contentious mountain made out of a tiny molehill. It is center-stage to Feigel's paper and covered in the introduction of van Tiggelen's. Elsewhere, van Tiggelen correctly says that Feigel doesn't actually address the controversy at all (despite Feigel's claims), but incorrectly implies that the controversy is a real problem to begin with. To summarize the issue, the dispute is over the electromagnetic momentum density in a medium. According to Minkowski (1908), it is
D×
B; according to Abraham (1910), it is
E×
H/c² = ε₀
E×μ₀
H; according to Nelson (1991), whose approach van Tiggelen largely parallels, it is ε₀
E×
H.
One can simply substitute the relations
D = ε₀
E+
P,
B = μ₀(
H+
M), where
P and
M are polarization and magnetization fields, from which it is easy to see that:
ε₀E×μ₀H = ε₀E×B + M×E/c² = D×B + B×P + M×E/c².
Fundamentally, Minkowski is right because momentum is the generator of spatial translations, which for the electromagnetic field matches Minkowski's
D×
B exactly. That's directly implied by Noether's theorem (1915/1918), so people who don't grok that Minkowski is correct are literally a century out of date. The
B×
P term is the momentum density of the bound charges. Since Nelson derived ε₀
E×
H by considering the Lorentz force coupling matter and radiation for both bound and free charges, it is not surprising that Nelson's momentum includes both, as ε₀
E×
H =
D×
B +
B×
P exactly. Finally, conceptually both Minkowski and Nelson are leagues ahead of Abraham because in the topological formulation of Maxwell's equations, both the electromagnetic and bound charge momentum densities directly correspond to differential forms that are definable without any constitutive equations or spacetime metric whatsoever, and are therefore more fundamental than the Abraham momentum density (which is quite unnatural).
Practically, though, it doesn't matter: it's just a dispute over book-keeping. It's fine to re-group various terms and perhaps give them special names such as 'canonical momentum' and 'kinetic momentum' and what-not. The only practical problem is that such a proliferation of different conventions can make it difficult to sort out who's done their book-keeping correctly and who hasn't. Van Tiggelen argues that Feigel hasn't done it correctly, but that a similar effect should be present nonetheless.
Quite appropriately, the same kind issues are related to the interpretation of the Feigel/van Tiggelen effects, should they prove real. The setup van Tiggelen is talking about involves a squeezed vacuum (à la Casimir) and an external magnetic field. The ground-state of this setup is a vacuum in the sense of having the lowest energy, so van Tiggelen is not wrong for interpreting his hypothetical effects in terms of virtual particles in a vacuum (or if he is, it's not for those reasons), but... and there's a big
but...
there's an external system responsible for those experimental conditions.
It's written plain as day in the paper: external magnetic field. So what's responsible for it? In real experiment, you can't just chunk your sources to infinity. It's an interpretational choice to say whether the momentum extraction is from the vacuum field or from an the experimental setup mediated by that field. Once again, it's simply a question of book-keeping conventions.