|Subject: RE: Question on a
statement on Snells Law Parity
Date: Thu, 9 Jan 2003 21:09:16 -0600
Here is a summary of Dr. Evans' answer, though he is quite ill at the moment.
Basically the problem resides in the kappa dot r part of the U(1) electromagnetic phase factor in Maxwell Heaviside theory. Under normal reflection, the received view incorrectly asserts that
kappa dot r goes to - kappa dot r
and that under reflection kappa goes to kappa and r goes to minus r, giving for example an interferogram in Michelson interferometry. However, reflection is equivalent to parity inversion, and under parity inversion
kappa goes to minus kappa and r goes to minus r
so under parity inversion kappa dot r is unchanged and there is no interferogram in Michelson interferometry, for example.
So the received view of reflection (based on Maxwell Heaviside theory and U(1) covariant derivatives) cannot give an interferogram in Michelson interferometry, in other words it cannot describe normal reflection (and also off normal reflection and Snell's Law).
In order to remedy this paradox we use round trips with O(3) covariant derivatives and an integral over the B(3) field in the electromagnetic phase factor of O(3) electrodynamics, specifically eqns. (42) and (43) of page 94 of vol. 119(2) of Advances in Chemical Physics. The round trips are constructed with Stokes' Theorem, surface and contour integrals of O(3) electrodynamics. More generally we need integrals of Sachs Einstein theory in order to construct the correct electromagnetic phase.
This procedure resolves the paradox and gives a correct explanation of reflection, refraction, diffraction and interferometry and so on, including Sagnac interferometry and phase effects such as the Tomita Chao effect which cannot be described in U(1) electrodynamics.
I have a question for you or Tom. I read a
very interesting website from the DOE Office of transportation
Technologies. Below is the link: