http://rockpile.phys.virginia.edu/mod04/mod34.pdf
Paul Fendley: "First consider light shined downward in a freely falling elevator of height h. (...) By the time the light hits the bottom of the elevator, it [the elevator] is accelerated to some velocity v. (...) We thus simply have v=gt=gh/c. (...) Now to the earth frame. When the light beam is emitted, the elevator is at rest, so earth and elevator agree the frequency is f. But when it hits the bottom, the elevator is moving at velocity v=gh/c with respect to the earth, so earth and elevator must measure different frequencies. In the elevator, we know that the frequency is still f, so on the ground the frequency f'=f(1+v/c)=f(1+gh/c^2). On the earth, we interpret this as meaning that not only does gravity bend light, but changes its frequency as well."

Substituting f=c/L (L is the wavelength) into Fendley's equations gives:

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

where c'=c+v=c(1+gh/c^2) is the speed of light relative to an observer on the ground or, equivalently, relative to an observer in gravitation-free space moving with speed v towards the emitter. Clearly the frequency shift is due to a shift in the speed of light - the speed of light varies with both the gravitational potential and the speed of the observer, as predicted by Newton's emission theory of light and in violation of Einstein's relativity.

Pentcho Valev