Does the speed of light change in a gravitational field? We know that even light follows a parabolic path in uniform gravitational field. In that case does it change its speed ? Or does it move with constant speed unlike regular objects?
 A: In Europe this year the precision between two atomic clocks was measured. The scientist who was responsible for this experiment tells that the experiment was so successful that they could explain the differences between the clocks by the high difference of 24 meters between the places where the clocks are installed. She says that this can be used in the future for very precise measurements of high differences on earth due to time slow down / speed up from different gravitational potential.
A Google translation from the German source:

Krauter : And you were actually in this first attempt already show that virtually the minimum frequency shift that occurred then , exactly correlated with the height difference of the two laboratories in Braunschweig and Paris .
  Grosche : Exactly , so we have a difference of about two times ten minus fifteen observed here in this case, with an accuracy of five times ten to minus seventeen . This corresponds to an altitude uncertainty of half a meter , there were about 22.5 feet of vertical drop , you can now determine exactly level over such a long distance with these optical clocks.

Source: http://www.deutschlandfunk.de/optische-atomuhren-erstmals-ueber-grosse-distanz-verbunden.676.de.html?dram:article_id=363771
