What I thought would be a boring post on EM boundary conditions a few days ago has turned into something interesting. Jonah Miller replied back to the post and made a comment that ultimately led to the Abraham-Minkowski controversy on how to interpret the momentum of a photon in a piece of material. Apparently this debate has progressed fora little bit over 100 y ears with the form of the momentum equation in a material proposed by Max Abraham
apparently conflicting with the one proposed by Hermann Minkowski of Minkowski metric fame
The controversy even led to people studying whether or not the discrepancy might be used as the basis for a reactionless drive with the Air Force and NASA purportedly getting in on the game according to Wikipedia.
It turns out that the answer in all likelihood is that everyone is correct, (OK, maybe everybody but NASA and the Air Force). A paper published by Stephen Barnett posits that the two indices of refraction have different meanings in the two different equations. The index of refraction in the Abraham version corresponds to the index of refraction associated with the group velocity of the light which corresponds to the experiments where the Abraham version has been experimentally verified, (momentum transfer). The index of refraction in the Minkowski version refers to the index of refraction associated with the phase velocity of light which corresponds to the experiments that have verified the Minkowski version, (diffraction and whatnot).
In a nice little twist, the references in Dr. Barnett's article led to the Aharonov-Bohm effect for neutral particles work mentioned in my quantum mecahnics II class a few night ago.
Wikipedia page on the controversy:
Controversy resolution paper:
Previous work on the same issue by Barnett free on arxiv:
A-B for neutral particles:
Picture of the Day: