Gravitational Time Dilation on Mountaintops: New Member Questions

[jeepdriver74]

New member here; just a physics hobbyist. There is probably a simple answer to this question but I could not find it. We know time flows faster on mountaintops relative to sea level due to gravitational time dilation. Over millions of years, wouldn't there be a cumulative effect making the mountaintop several seconds to minutes ahead in time compared to sea level? The Earth would be in a future location and rotational position causing some strange effects, which obviously does not happen.

 

[Orodruin]

The Earth would be in a future location

No, it would not. The top would just be a bit different in age.

 

[Ibix]

Over millions of years, wouldn't there be a cumulative effect making the mountaintop several seconds to minutes ahead in time compared to sea level?

Well, clocks on the mountaintop would be ahead if they weren't corrected.

The Earth would be in a future location and rotational position

No. If clocks on the mountaintop see the sun at its zenith, so do clocks at sea level. They can exchange messages to confirm this. They won't agree on the elapsed time between successive noons by about one part in $10^{13}$ (assuming a 1km high mountain) but that's all.

 

[jeepdriver74]

No, it would not. The top would just be a bit different in age.

Oh right. That's where I went wrong. Thank you.

 

[DanAil]

The top would just be a bit different in age.

Does this imply that what runs slower in stronger gravitational field is not Time, but Aging? These two are very different things.

 

[DaveC426913]

Does this imply that what runs slower in stronger gravitational field is not Time, but Aging? These two are very different things.

Setting aside whether or not time and aging "are" very different things, can you point to any observable phenomenon that be diagnostic of a difference?

 

[DaveC426913]

I post this every few years because it's just so cool.

http://leapsecond.com/great2005/
"In September 2005 the kids and I took several very accurate cesium atomic clocks from home and parked 5400 feet up Mt Rainier (the volcano near Seattle) for a full two days. The goal was to see if the clocks actually gained time, even if billionths of a second, as predicted by Einstein's general theory of relativity. Does gravity really alter time and can this weird phenomenon be detected with a family road trip experiment?"

Spoiler

Yes.

 

[jeepdriver74]

I post this every few years because it's just so cool.

Very cool!

 

[DanAil]

Setting aside whether or not time and aging "are" very different things, can you point to any observable phenomenon that might manifest such a difference?

Well, for one, many celebrities are aging much slower than me, although we are supposedly living in the same time :).

Joke aside, aging of matter is related to space movements in time and as such can be slowed down or sped up.

 

[PeterDonis]

aging of matter is related to space movements in time

This is too simplistic. For some special situations, such as an idealized isolated massive body like a planet and objects moving in the space surrounding it, it works, but it does not generalize.

The general rule is that "aging of matter" (or more precisely differences in aging of matter) only has meaning in the first place if two pieces of matter separate, and then come back together again later. In that case, the piece of matter whose worldline through spacetime from the separation event to the coming back together event has a longer length will age more. In other words, "aging" is driven by "length of worldline through spacetime".

 

[David Lewis]

It's estimated that the Earth's core is about 2.5 years younger than the surface.

 

[Ibix]

Joke aside, aging of matter is related to space movements in time and as such can be slowed down or sped up.

Not really. Aging, or elapsed time, is a measure of the "length" of a path through spacetime since some chosen event. In flat spacetime you can only get different lengths between events A and B if at least one of the paths isn't inertial, so what you say is sort of true there although not well phrased. But in curved spacetime there is a much wider range of options for ways to achieve differences, including just hovering at different altitudes.