Discussion in comments on the two questions linked below leaves me confused about the following point.
We expect a magnetic or electric dipole to make a field that has some universal transformation properties, and we expect these properties to be purely classical, and independent of the other characteristics of the source. So what does this tell us about massless dipoles?
Suppose you make an electric dipole by gluing charges $\pm q$ to the ends of a popsicle stick of length $L$. Then under a boost $v$ parallel to the stick, we have $qL\rightarrow 0$ as $v\rightarrow c$. This suggests that a massless particle has zero electric dipole moment parallel to its motion.
On the other hand, field theorists seem to expect that massless magnetic dipoles are OK, and can have dipole moments aligned with their spins and parallel to their motion. I imagine that neutrinos would have been considered to be examples, back when we thought they were massless. Mike Stone says in a comment: "A massless charged chiral particle has a magnetic moment of exactly μ=±e/(2E)×k/|k| where the ± is the helicity and E the energy."
But this all seems odd to me. Shouldn't duality hold between electric and magnetic fields, so that whatever is true for electric dipole fields is also true for magnetic ones? If our universe had magnetic monopoles, then we could recap the popsicle stick argument and convince ourselves that massless magnetic dipoles could not have a dipole moment in the direction of motion.
Can anyone clarify what is going on here?
related:
No magnetic dipole moment for photon
Electric dipole moment of electron: about what point is the moment taken?
No comments:
Post a Comment