Since on the top of a mountain you're going faster, due to the rotation of the Earth. At sea level, you have to move for a distance of approximately $2\pi R$, while on the top of a mountain you have to move for a distance of $2\pi(R+h)$, where $h$ is the height of the mountain. Hence, you go faster on a mountain. How does that affect time dilation?
According to SR, would you see time go slower when you look at the top of a mountain from sea level?
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