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Can someone help me giving a qualitative answer to this problem in General Relativity:

Imagine you are on earth with two perfectly synchronized clock's. If you hold one clock in your hand and throw the other one in the air and catch it back after a certain time interval, would the clock's still give the same time? Explain.

Thank you!

APORIL
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    This probably belongs on physics stackexchange. However, recall: https://en.wikipedia.org/wiki/Gravitational_time_dilation – Alex R. Jan 20 '17 at 23:37
  • As Alex R. commented, physicists are usually better in explaining qualitatively problems like this! –  Jan 20 '17 at 23:49
  • The answer is no, because there are different forces acting on the two clocks. The clock you hold in your hand is affected by the force preventing it from dropping, whereas the clock thrown in the air is accelerated in the beginning and free fallling afterwards. –  Jan 21 '17 at 00:12
  • Ok thank you mr. Klirk! But do you know why the thrown clock will run faster? – APORIL Jan 21 '17 at 11:58
  • @Itachi This copy of your question was migrated to [physics.se] from [math.se] creating a duplicate because you also asked it on our site (the better place, to be sure). For future reference, the etiquette and expectation of Stack Exchange site is that you don't cross-post questions and instead rely on the migration mechanism to move them to the better sight if you have initially placed them less than optimally. In any case, welcome to Physics Stack Exchange. – dmckee --- ex-moderator kitten Jan 21 '17 at 20:04

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Assuming your are standing still with one clock in your hands while the airborne clock is in motion, time passes slower in the accelerated frame with respect to the stationary frame (often called the "laboratory frame or reference").

Thus, if you could measure the difference, the clock that did not leave your hands would lead the clock that was accelerated in the gravitational field. Note that the rate at which time passes does not change within a given frame, it changes with respect to a comparative frame.

As observed from the moving frame, during the acceleration time in the stationary frame seems to elapse faster and when observed from the stationary frame, time seems to elapse slower in the moving frame.

Imagine I am standing next to a black hole, you are on Earth and we can observe each other's movement. In my frame where the acceleration from gravity is much stronger than in your frame on Earth, I would still see time on my watch pass at a "normal" rate and I would see you moving extremely fast. On Earth, time on your own watch would also pass at a "normal" rate as you would observe it in your frame, and you would see me moving extremely slow.

If you need a helpful ressource for physics check out http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#hph

Hope this helps.

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