| Subject: RE: Question on a
statement on Snells Law Parity Date: Thu, 9 Jan 2003 21:09:16 -0600
Dear Frank,
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.
Best
wishes,
Tom
Bearden
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: |