Superluminal and Subluminal Signals

In the appendix to Space TIme and Gravitation, V. Fock demostrated that singular solutions to Maxwell's Equations of electrodynamics satisfied the eikonal expression, a quadratic partial differential equation with signature {+++-}. Mappings which preserved the eikonal, taking a discontinuity in E field to a discontinuity, were of two and only two types. A linear type which Fock proved was the Lorentz group of transformations . This result is the foundation of special relativity.

The other mapping was a non-linear Mobius projective transformation. In the linear mapping, it can be argued that the propagation speed of the singular solutions must be a constant. (The ubiquitous c - the speed of light). For the non-linear mapping the propagation speed of the singularity can be anything - including infinity. !!!

In optically active media, the propagation speed of the discontinuities is faster or slower that the speed of light, depending on the whether or not the helicity (circular polarization) is aligned or anti-aligned with the optical axis.


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Last update 01/23/2009
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