http://www.einstein-online.info/spotlights/redshift_white_dwarfs Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."
That is, Newton's emission theory of light predicts that, in a gravitational field, the speed of light varies in accordance with the equation c'=c(1+gh/c^2), and this prediction is consistent with the frequency shift f'=f(1+gh/c^2) measured by Pound and Rebka.
Einstein's general relativity predicts that, in a gravitational field, the speed of light varies in accordance with the equation................., and this prediction is also consistent with the frequency shift f'=f(1+gh/c^2) measured by Pound and Rebka.
Clever Einsteinians would not complete the above sentence. The consistency between c'=c(1+gh/c^2) and f'=f(1+gh/c^2) is so straightforward that any prediction about the speed of light different from c'=c(1+gh/c^2) would be almost obviously inconsistent with f'=f(1+gh/c^2). General relativity would be put in great danger:
http://ebooks.adelaide.edu.au/o/orwell/george/o79n/chapter2.9.html Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."