| [paraphrasing] Acceleration is a kind of speed. The more you're accelerating in a given direction, the faster you're going - even if there's something stopping you. Gravity makes you accelerate - even if there's ground stopping you from moving "down". So the higher the gravity, the higher the acceleration, so the higher your (instantaneous) speed, so time goes slower for you relative to other things not moving/accelerating as much. If you're really close to a black hole, with LOTS of gravity, time will pass really slowly for you relative to most everything else - even if something is preventing you from actually falling in. At the top of a mountain, gravity is lower. You're farther away from most of the Earth. Less gravity (however minute) means less acceleration means less (instantaneous) speed means time traveling relatively faster (or, well, not as slow as further downhill). In space, far far away from everything, and so long as you're kinda averaging a speed of 0 relative to everything else, time ticks by the fastest (relative to most everything else). So if you build two clocks that are practically perfectly in sync, and you move one to the bottom of a mountain, and one to the top, and then bring them back together, you can measure the tiny difference between them caused by one (the one from the top of the mountain) experiencing time faster than the other (from the bottom). |
Though if you are constantly a accelerating, with the earth stopping you, what is your instantaneous speed? The faster you go, the more time dilation.