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Vladimir,
You wrote: " When objecting to the constancy of the speed of light I should always add that I believe there is a *maximum* speed of light c in a vacuum free of gravity and e/m fields, but that light slows down in denser media such as a gravitational field, air, water or glass etc."
The problem is different. See this:
Roger Barlow, Professor of Particle Physics: "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/(lambda) waves pass a fixed point. A moving point adds another vt/(lambda). So f'=(c+v)/(lambda)."
"In time t, ct/(lambda) waves pass a fixed point." That is, the speed of the waves relative to the fixed observer is c.
"A moving point adds another vt/(lambda)." That is, the speed of the waves relative to the moving observer becomes c'=c+v.
Is c'=c+v correct, Vladimir?
Pentcho Valev