Why does time flow more slowly on the ground than on a mountain? [duplicate]

Question

I'm reading the book The Order of Time by 'Carlo Rovelli', which says that time flows more slowly on the ground than on a mountain. It also says that the presence of matter changes how time flows, and specifically that it flows more slowly near the surface of the earth. Why is this?

Answer 1

The language we often use to describe time (like "time flowing") gives a misleading picture -- it makes it seem as though "time" is a thing that is moving. The modern view in physics is that time is more like a direction in 4 dimensional spacetime.

You've probably heard that gravity is due to the curvature of spacetime. This curvature also means that the direction of time is different in different places. For a rough analogy, consider the direction "up" at the North Pole and near the equator: something moving "up" near the equator hardly moves "up" at all relative to the North Pole. Similarly, the time direction is different near the Earth's surface (where spacetime is curved more by the Earth's mass) than it is high above the Earth's surface (where spacetime is curved less). The exact details are a little more complicated in the case of spacetime than of space, because the geometry of spacetime is different from that of space alone, but the upshot is that a clock on the surface seems slow when compared to a clock on the mountain. The difference is tiny though and it takes very sensitive atomic clocks to detect it.

Answer 2

So this is a question related to a thing called 'Time Dilation', predicted by Albert Einstein in the theory of Special Relativity. It basically says that if I was on earth and you were in space, for example, and you and me had a clock each (atomic clock) which were both showing the same time initially, and if you were to go close to the speed of light for a while, once you stop and when we both check our clocks, we would see that your clock would show a time that already elapsed on my clock. This means that your clock ticked slower and my clock ticked relatively faster. But, from your perspective, your clock ticked normally for you, and from my perspective, my clock ticked normally for me. But when we compare them, because you travelled faster than me relatively, your clock ticked slower.

Now, coming to your question specifically, time does tick slower on the ground than on a mountain. This is because of the difference in gravity acting on an object on ground (more gravity) and on an object on a mountain (less gravity). The rate at which time ticks also depends on gravity. If the gravity is more, time ticks slower and vice versa. That's why time ticks slower on ground (higher gravitational acceleration) than on a mountain (lower gravitational acceleration). But, the time dilation effect in such a case would be very very tiny, yet, it would still exist.