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## Main Question or Discussion Point

**"hidden momentum"**

There's an interesting thing in E&M which is referred to as "hidden momentum" in this paper:

Babson et al., Am. J. Phys. 77 (2009) 826

http://www.ate.uni-duisburg-essen.de/data/postgraduate_lecture/AJP_2009_Griffiths.pdf

The simplest example is a magnetic dipole immersed in an electric field, both of them at rest in a certain frame. The Poynting vector is the local density of momentum in the electromagnetic fields. The fields' total momentum doesn't vanish in general. But there's a theorem in SR that says that if a system's center of mass-energy is at rest, its total momentum must be zero. Babson resolves the problem by imagining the magnetic dipole as a current loop. Relativistic effects cause the flowing charged particles to have a total momentum (the "hidden momentum") that is not zero, and cancels the momentum of the fields. He does it for a couple of simple models of the charge carriers (balls rolling freely in a tube, and a perfect fluid).

This all seems fine, but in other examples, it's not clear to me how the hidden momentum can come about.

Suppose that the magnetic dipole is a fundamental particle such as a neutrino. How in the world does the hidden momentum come about? Does it have to be some kind of QFT effect, which we could imagine in terms of momentum of virtual particles?

Suppose I have access to some magnetic monopoles. I put uniform electric charges +q and -q on opposite sides of a cube, and on two other opposite sides I put equal and opposite monopole charges. Where is the hidden momentum now?