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The Abraham-Minkowski Controversy

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


where n is the index of refraction for the material, h is Planck's constant, nu is the frequency of the light, and c is the speed of light.

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.

References:
Wikipedia page on the controversy:
http://en.wikipedia.org/wiki/Abraham-Minkowski_controversy

Controversy resolution paper:
http://prl.aps.org/abstract/PRL/v104/i7/e070401

Previous work on the same issue by Barnett free on arxiv:
http://arxiv.org/abs/0811.2771

Stephen Barnett:
http://phys.strath.ac.uk/information/acadstaff/stephen.barnett.php

A-B for neutral particles:
prl.aps.org/abstract/PRL/v53/i4/p319_1

Picture of the Day:
From 1/22/13

Comments

Erik Nelson said…
Light diffracting through a narrow aperture, into a medium of index of refraction n, appears to focus latterly. The width of the central maximum narrows by a factor of n. Since the width is proportional to dp_|_ / pz, it is argued that pz must increase by that factor. But the laterally propagating components of the light ought to be expected to REFRACT upon entering the new medium. Thus their angles, relative to normal, ought to decrease, according to Snell's Law:

n1 Sin a1 = n2 Sin a2
n1 a1 ~= n2 a2

in the limit of small angles. So an increase of n could be argued, to decrease dp_|_, rather than increase pz. If so, then that would pertain to one argument favoring Minkowski.

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