| Modern Physics 3315 |
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Notes on Special Relativity
A perplexing problem about standard treatments of Special Relativity is that
there is no gut level explanation of what an electromagnetic signal is all
about. Einstein used a mathematical description (ds^2 = 0) but never connected
this idea, explicity, to electromagnetism. However, in an almost unknown (even
today) reference (an appendix in the book " Space Time and Gravitation") V. Fock
- in 1932 - cleared up the issue by defining an electromagnetic signal as a
propagating discontinuity in the amplitudes of the electromagnetic field
intensities (E and B).
Fock showed that the only linear transformation of coordinates that preserved a
discontinuity into a discontinuity was the Lorentz transformation, and the
propagation speed of the discontinuity was the constant we call c, the speed of
light. The value c was the same in all Lorentzian equivalent reference systems.
(One of the Einstein postulates)
Fock went further: He showed that, in addition to the linear Lorentz group, there was a NON-linear transformation group that ALSO preserved the propagating electromagnetic discontinuity. But surprise ! -- this group of transformations did not require the speed of discontinuity propagation to be constant. It could take on all values between zero and infinity, and was different between different observers.
This result has been ignored for almost 70 years, primarily for it apparently
refutes the Einstein postulate that c is a constant. IS there still something
to be learned and applied in a pratical sense? Is faster that the speed of the
light (meaning c) a possibility? Time will tell.
For more detail see
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