Time is slower deep down in a potential well

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1) If you lift a clock to a greater height, you have to do work on it - the work done appears as gravitational energy stored in the clock; This shows up in the guise of extra tick-tock energy, as a result of which the clock ticks a bit faster.
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2) Time is slower deep down in a potential well. Potential measures the work that it would take to haul something back out.
Tie a rope to it and lower it down a hole and it will run slower.
What matters is how much work it would take to haul it up and out.
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Do you agree w/#1 and or #2 above?

Both of these points, which are not mine, make it seem that it is the act of moving the clock which changes its time to run either faster or slower, and not 'where' it is located.
So, a clock made on the top of a mountain, or made at the bottom of a mine shaft should run exactly like a clock located at the earth's surface!?
 
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Sunfist

No, not number 1. The change in the speed of the clock is due to gravitational force, not kenetic energy.
 
9
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#1 is from Paul Davies book:
ABOUT TIME
Einstein's Unfinished Revolution
 
9
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#1 & #2 make it appear that its the act of moving the clock that causes its time to run either faster of slower and not the gravity in that location.

If that is the case wouldn't the extra 'tick-tock' energy wear off after awhile with the clock now being stationary?

And how does the clock know how much energy it would take to haul it out, so it can slow down by that exact amout?
 

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