I understand that the faster you move through space the slower you move through time, but how does gravity play a role in that?
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1Does this help? https://physics.stackexchange.com/a/276524/123208 – PM 2Ring Sep 15 '21 at 21:29
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1You don't move slower through time in the sense that you would notice any difference. Time dilation has to do with how two observers moving relative to each other would measure the time interval between two events. – Not_Einstein Sep 15 '21 at 22:14
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2Does this answer your question? Does gravitational time dilation happen due to height or difference in the strength of the field? – Paul T. Sep 15 '21 at 23:05
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1This may help - Why can't I do this to get infinite energy? – mmesser314 Sep 16 '21 at 03:05
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Gravitation is an effect due to the curvature of spacetime. Both space and time are curved by the presence of matter (and other energy). One manifestation of the curvature is time dilation: time passes more slowly for someone close to a heavy mass than for someone far away. This isn't just a theoretical effect, it's easily observed by modern atomic clocks. For example, if you place two identical atomic clocks on different floors of a building, the higher one will gain time relative to the lower one. The difference is a matter of nanoseconds per week (or less) but it is measurable.
The time dilation due to gravity is related to the time dilation due to different speeds by an interesting formula: a clock that is "stationary" in a gravity well (e.g. on the surface of the Earth) runs slow relative to a distant stationary observer by the same amount that a clock moving at escape velocity would. The deeper you are in a gravity well, the higher the escape velocity from that point, and hence the greater the time dilation.
Eric Smith
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FWIW, with a height difference of 10 m, the time difference over a week is ~0.66 nanoseconds. That's using 6371 km for the radius of the Earth (assuming the lower clock's at that distance from the centre of the Earth), and 8.870056 mm for the Earth's Schwarzschild radius – PM 2Ring Sep 16 '21 at 01:58