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Before reading any further, I want to warn everyone that I have absolutely no formal (nor much informal) exposure to physics outside of the small amount I got during a calculus course I took in college. Please forgive me if the question I ask is posed incorrectly or makes any underlying assumptions that aren’t true. I’ve tried to look into the question on google, but I can’t seem to find a good answer based on what I’ve searched.

That being said, here it is:

If there are two observers, one being in an inertial frame with a very low gravitational potential, and the other being in an inertial frame with a very high gravitational potential, will both observers observe the other’s time as moving slower than their own? I know one of the interesting components of the twin’s paradox and special relativity is that each observer will perceive the other’s time as moving slower while being in different inertial frames. Does this same concept apply with regards to gravity and general relativity?

Again, sorry if this question is off topic or makes some readers want to pull hair out. Any response is appreciated.

brandonstolz
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If there are two observers, one being in an inertial frame with a very low gravitational potential, and the other being in an inertial frame with a very high gravitational potential, will both observers observe the other’s time as moving slower than their own?

No. As Wikipedia explains,

Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference.

For weak gravitational fields, the gravitational time dilation depends on the Newtonian gravitational potential.

G. Smith
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  • This is very interesting. So in the case of an observer near a strong gravity source, would events occurring outside of their inertial frame appear to be happening at a much faster rate? – brandonstolz Jan 04 '21 at 23:17
  • Faster. Whether it’s “much” faster depends on how deep the gravitational well is. In Insterstellar I think 51 years elapsed on Earth while they were near the black hole. Since famous GR expert Kip Thorne was their science advisor, this is probably realistic. – G. Smith Jan 04 '21 at 23:23