general relativity - Does one age quicker at higher altitudes?

See title: Does one age quicker at higher altitudes?

A few years ago I heard that you would age slightly faster (or slower) at higher altitudes.

Is this true? What is the theory or evidence for this?

Or to put it a little differently:

Does time move faster or slower at higher altitudes?

Answer

The term you are looking for is Gravitational Time Dilation.

Gravity has effects on the surrounding space-time, directly dependent on the mass of the bodies. This effect is not noticeable to us on Earth unless considering a large timescale, since the Earth is nowhere near massive enough for it, as opposed to extremely massive celestial objects (e.g: black holes and neutron stars).

To give an idea to how little it matters on Earth (same Wikipedia article as first link):

Clocks that are far from massive bodies (or at higher gravitational > potentials) run more quickly, and clocks close to massive bodies (or at lower gravitational potentials) run more slowly. For example, considered over the total time-span of Earth (4.6 billion years), a clock set at the peak of Mount Everest would be about 39 hours ahead of a clock set at sea level. This is because gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects.[4]

[Emphasis mine]

Using those numbers as reference, we can calculate that if an observer at sea level stayed there for 100 years, someone who would have stayed on the Everest would be older by roughly 0.003 seconds.

Technically yes, relative to an observer on Earth, a person at higher altitudes will age faster.