http://www.einstein-online.info/spot...t_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..."

The following arguments are both valid:

Argument 1 (consistent with Newton's emission theory of light)

Premise 1: If the top of a tower of height h emits light with frequency f (as measured by the emitter), an observer on the ground will measure the frequency to be f'=f(1+gh/c^2).

Premise 2: There is no gravitational time dilation.

Premise 3: The wavelength remains unchanged as the light falls.

Conclusion: The acceleration of the falling light is g, like the acceleration of ordinary falling objects. The observer on the ground will measure the speed of the light to be c'=c(1+gh/c^2).

Argument 2 (consistent with Einstein's relativity):

Premise 1: If the top of a tower of height h emits light with frequency f (as measured by the emitter), an observer on the ground will measure the frequency to be f'=f(1+gh/c^2).

Premise 2: There is gravitational time dilation.

Premise 3: The wavelength decreases as the light falls - if it is λ at the top of the tower, it will be λ'=λ/(1+gh/c^2) at the bottom..

Conclusion: The acceleration of the falling light is negative, -2g (that is, the speed of the light decreases as it falls). Yet the observer on the ground will measure the speed of the light to be c (unchanged).

References showing that, according to Einstein's relativity, the speed of falling light decreases (the acceleration is -2g), but the observer on the ground will nevertheless measure the speed of the light to be c:

http://www.youtube.com/watch?v=FJ2SVPahBzg
"Relativity 3 - gravity and light"

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. (...) ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+phi/c^2) where phi is the gravitational potential relative to the point where the speed of light co is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm
"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+phi. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2phi, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

http://math.ucr.edu/home/baez/physic..._of_light.html
Updated 2014 by Don Koks. Original by Steve Carlip (1997) and Philip Gibbs 1996: "So consider the question: "Can we say that light confined to the vicinity of the ceiling of this room is travelling faster than light confined to the vicinity of the floor?". For simplicity, let's take Earth as not rotating, because that complicates the question! The answer is then that (1) an observer stationed on the ceiling measures the light on the ceiling to be travelling with speed c, (2) an observer stationed on the floor measures the light on the floor to be travelling at c..."

http://www.amazon.com/Why-Does-mc2-S.../dp/0306817586
Brian Cox, Jeff Forshaw, p. 236: "If the light falls in strict accord with the principle of equivalence, then, as it falls, its energy should increase by exactly the same fraction that it increases for any other thing we could imagine dropping. We need to know what happens to the light as it gains energy. In other words, what can Pound and Rebka expect to see at the bottom of their laboratory when the dropped light arrives? There is only one way for the light to increase its energy. We know that it cannot speed up, because it is already traveling at the universal speed limit, but it can increase its frequency."

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