Time is Relative

This theory (special relativity) and the more general form (which takes gravitional affects into accounts) of it makes several other important predictions which have withstood empirical observations. But one of the prediction of general relativity is time should appear to run slower near a massive body like the earth. This is because the energy of light is proportional its frequency (waves/second). As light travels upward in earth's gravitional field, it loses energy, and therefore its frequency goes down. (The length of time between one wave crest and the next goes up.) To someone high up, it would appear that that everything down below was taking longer to happen. Apparently, this prediction can be tested by using a pair of very accurate clocks, one at the bottom nearer to the earth, and the other at the top. This was done in 1962, and the clock at the bottom was found to run slower, in exact agreement with general relativity! This is of practical importance, if you wish to trust navigational signals from satellites. If you ignore relativistic effects, you could be off by several miles!

Now, my question is, what is the basis for this phenomenon? Why should the clocks have different times? Why should it be related to light and its frequency? This is saying that time slows down when it is exposed to intense gravity. Why is this the case?