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 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    Subject: Question on a statement on Snells Law Parity Tony,   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: http://www.ott.doe.gov/electromagnetic/history.shtml This site talks about the history of electromagnetics. the following is a statement on that site: The most drastic failure of Maxwell-Heaviside theory is its inability to describe Snell's Law without violating parity. I got quite a bit of interest in a discussion group with this statement, but I cannot explain it myself.  How does Maxwell-Heaviside violate parity describing Snell's law? Thanks, Frank