THEOREM: The speed of light varies with the speed of the observer (c'=c+v) if and only if it varies with the gravitational potential (c'=c(1+gh/c^2)).

The top of a tower of height h shoots a bullet downwards with initial speed u. As the bullet reaches the ground, its speed (relative to the ground) is:

u' = u(1 + gh/u^2)

The top of a tower of height h emits a light pulse downwards with initial speed c. As the pulse reaches the ground, its speed (relative to the ground) is:

c' = c(1 + gh/c^2)

Einsteinians admit the validity of and sometimes even deduce the above result:

http://www.youtube.com/watch?v=ixhczNygcWo
"The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."

Integrating dc/dh=g/c gives:

c' = c(1 + gh/c^2)

Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed:

c' = c(1 + gh/c^2) = c + v

where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with the speed of the observer, in violation of special relativity.

Pentcho Valev