What were the findings of the Pound-Rebka Experiment? I am currently learning very basic astrophysics, more specifically, the principles of Einstein's General Relativity. 
In my notes, one of the paradoxes is the Pound-Rebka Experiment. The paradox is that when the light from the laser was emitted, it was expected that the frequency of the emitted ray equaled the frequency of the detected ray.
However, the frequency detected was less than the emitted frequency. My professor showed us that if space was flat, that the frequencies would be equal. Initially, I thought that the wavelength of the light emitted from the laser was redshifted and that's why the frequency decreased, although I don't know how this can be related to disproving that "space is flat."
 A: There was no paradox in the Pound Rebka (PR) experiment. It was designed and proposed to determine if indeed there is a frequency shift when light travels in a gravitational field that is different when emitted than when received. 
GR, general relativity, predicted that when light travels in a gravitational field that changes, the frequency will change, or equivalently time will be slower in one end than the other. In the PR experiment the light was emitted at the top of a tower, and would have been received at the bottom as BLUESHIFTED. They had the receiver go up at some speed to cause an opposite redshift due to Doppler, and the two cancelled. It was done in 1959, and was a test of GR. Initially it was to 10% accuracy, later gotten to 1%. Experiments with masers later got the results, by others than PR, to 0.01%. Not sure if that's been improved. 
No controversy. The gravitational field causes a red or blue shift - depending on whether you go to a stronger or weaker gravitational filed. For the tower, if was going towards the earth, a stronger field, and it would have been a blueshift. The Doppler effect from the motion of the receiver caused a redshift, and they cancelled when the velocity was adjusted just right. 
The red and blue shifts were very small, it was over vertical distance of about 20 meters, and the shift was about 1 part in $10^{15}$, and the speed they used for the receiver motion was also very small. They used a 14 kEV gamma ray from an atom. See the description at https://en.m.wikipedia.org/wiki/Pound–Rebka_experiment
A: The Pound-Rebka experiment demonstrated that the velocity difference (acceleration) of photons is "identical to that which a material object would acquire in free fall", as predicted by Newton's emission theory of light and in violation of Einstein's relativity: 
R. V. Pound and J. L. Snider, Effect of Gravity on Gamma Radiation (pdf): "It is not our purpose here to enter into the many-sided discussion of the relationship between the effect under study and general relativity or energy conservation. It is to be noted that no strictly relativistic concepts are involved and the description of the effect as an "apparent weight" of photons is suggestive. The velocity difference predicted is identical to that which a material object would acquire in free fall for a time equal to the time of flight." 
That the speed of falling light varies like the speed of ordinary falling bodies is so obvious that many scientists confirm the fact and so inadvertently disprove Einstein's relativity: 
University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."
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..." 
