Undergrad Age Slower or Faster in Center of Earth? Time Dilation Explored

[diseasedrat]

theoretically if you were in the center of the earth, would you age slower or faster from time dilation?

this question is asked here as well:

https://www.quora.com/Can-someone-c...km-deep-cave-How-much-longer-would-my-life-be

It would actually be shorter. While the net gravitational force initially increases as you go deeper, eventually it starts to decrease. At your chosen depth you are at about .2 Earth radii from the center and the gravitational force is less than half of its value at the surface. In addition, your velocity would be quite a bit less further speeding up time.

this is a wrong answer right?

although you would gravitationally "feel" less pull on yourself in the center of the Earth - however, technically, since you're closer to more mass, what you call space-time would be more warped in the center of the Earth than on the surface of the earth, so you should age slower in the center of the Earth right?

has time dilation ever been tested deeper in the Earth before?

https://en.wikipedia.org/wiki/Preliminary_reference_Earth_model - just a link for reference, etc

thanks 4 answers

 

[rootone]

Deep inside the Earth or any other large gravity well,
you would appear to age more slowly if you could be observed by somebody outside if it.
Time would seem to be passing as usual to you though according to whatever clocks you have available.
However the gravity well of Earth is not enough to cause impressive time dilation.
You need to be inside a neutron star for things to start looking significantly time distorted.
That is not an experiment to be recommended.

 

[Nugatory]

theoretically if you were in the center of the earth, would you age slower or faster from time dilation?

Slower than what, or faster than what?

 

[pervect]

A clock that was stationary at the center of the Earth would tick more slowly than a clock that was stationary on the surface of the Earth.

 

[PeterDonis]

this is a wrong answer right?

Yes, it certainly is. In fact almost everything said in that quora thread is actually irrelevant to the question; what they are calling "gravitational potential" there is actually the "acceleration due to gravity", which is the gradient (slope) of the potential. But time dilation depends on the potential itself, which continues to get lower from the surface of the Earth all the way down to the center. So pervect's answer is correct.