Let's say there are 2 people, A and B. They both are at the sea level. A gets higher than B. Does time moves faster to A then B? (Does height -in other words gravity- causes Time Dilation?)
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2$\begingroup$ Gravitation is described by General Relativity, not Special. If by "above water level" you mean height then say so (and if this is the case then the answer is "yes"). I would recommend editing your question! $\endgroup$– m4r35n357Commented Aug 16, 2021 at 12:24
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$\begingroup$ @m4r35n357 Thanks. I edited it 👍. $\endgroup$– Kamil FurkanCommented Aug 16, 2021 at 12:44
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3 Answers
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As already said in the comments, yes. However, gravitational time dilation is described by general relativity. One will find that clocks closer to a massive object (such as the earth) will tick slower compared to clocks farther away. In other word, time "flows"1 slower closer to the surface of the earth.
There are two things however that I'd like to further elaborate on.
First, you cannot tell that time has "slowed down" for you in your own frame of reference. For you, time will always appear to pass at the same "rate".
Second, I'm not sure about whether you can say that height or gravity causes time dilation. In general relativity, gravity is the curvature of spacetime (thus doesn't cause it). However, this is more a question of language – I just wanted to clarify.
1 I put this in quotes because time cannot actually flow – see What is time, does it flow, and if so what defines its direction?. Though it should be clear what is meant by that.
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The title to your question "Does Gravity Cause Time Dilation" and the body of your question "Does height -in other words gravity- causes Time Dilation?" are slightly different and the difference is important.
It is generally considered that a massive object (like a planet) causes the warping of spacetime. In other words, the planet causes time dilation. And then the closer you are to the centre of the planet, the greater time dilation you will face. So you at sea level will indeed face slower relative time than your friend a the top of a mountain.
But this is where you need to understand the slight difference in interpretation. Many scientists believe that it is the gradient in time dilation that causes gravity. (And not the other way around that gravity causes time dilation) There is a saying: "The reason your bum is stuck to your seat is because time runs faster at your head than your feet." Things fall because of the gradient in time dilation. Things like to be where time runs slowest. So time dilation comes first and gravity comes second - but of course they are simultaneous.
answered Aug 16, 2021 at 17:44
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$\begingroup$ I don't think it's accurate to say that the gradient in time dilation "causes" gravity. Rather both time dilation and gravity are due to the curvature of spacetime. At least that's the case in the best theory of gravity we currently have (general relativity). $\endgroup$ Commented Aug 17, 2021 at 1:50
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$\begingroup$ @EricSmith I'll defer to Nobel Lauriet Kip Thorne who said "Things like to live where they age the most slowly. And so as an application, the Earth's mass warps time according to Einstein. It slows time near the surface of the Earth. And this time warp is what produces gravity.” $\endgroup$ Commented Aug 17, 2021 at 15:16
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$\begingroup$ Even Nobel prize winners simplify things in their popular science explanations. If you really want to understand relativity, I suggest reading Prof. Thorne's textbooks rather than his pop-sci articles. $\endgroup$ Commented Aug 17, 2021 at 18:53
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$\begingroup$ @EricSmith This was from a lecture he gave at Cornell University so I'll take it as accurate. Until someone (other than myself) comes up with a reasonable explanation of exactly how the warping of spacetime causes something to fall, this seems like a pretty good explanation to me. The bowling ball in a trampoline just doesn't cut it. $\endgroup$ Commented Aug 17, 2021 at 19:10
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$\begingroup$ The bowling ball on a trampoline is a horrible example, agreed (it only shows curvature of space). Both space and time are curved together. As for why things fall, they follow geodesics in spacetime. Approximating "geodesic" as "path that maximizes proper time" is reasonable for a pop-sci explanation, but the full definition of "geodesic" is more complicated. I recommend Misner, Thorne, and Wheeler's book Gravitation for the full story, and it includes the details of how and why things fall. $\endgroup$ Commented Aug 17, 2021 at 22:21
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Or you might consider that other solutions exist. For instance, that Time is NOT going to ever "dilate", for any reason, its a concept, so it not able to be affected by any Physical forces.
So Time as a concept, does not change with changes in gravitational force, but CLOCKS, (any type of physical process) can and must change under differing physical conditions.
Clocks can get out of sync with changing gravity, but TIME can not. Even the physical process in an Atomic Clock is affected by Gravity.
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3$\begingroup$ There is no universal concept of "time", any more than there's a universal concept of "height". A sitting person might say the ceiling is two meters above them; someone standing up might say that it's only one meter above them; someone else on the other side of the planet might say that the person is "below" the ceiling. Just like height, time is relative. $\endgroup$ Commented Aug 17, 2021 at 1:49
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$\begingroup$ I never said that there is a "universal concept" of Time. Humans use such things as Cesium clocks to allow some form of standardization for time keeping according to their pre defined CONCEPTS. In that framework, these clocks can and do get out of sync, but this CONCEPT will continue on unaffected nonetheless. That's why we have a Global Network of Atomic Clocks, so that the concept of stability of the concept of time can remain intact, despite some of these Master Clocks getting out of sync occasionally. "Time" can not be affected by Motion but Physical clocks are due to Physical changes. $\endgroup$ Commented Aug 17, 2021 at 2:35