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The time dilation seem to slow time in stronger gravitational fields.

Lets say we put a person with a clock in the center of the earth. It will feel no gravity since it's pulling from every direction effectively reducing itself to zero.

Is the effect of time slow will still be observable? In that case one can "theoretically" build a time slowing machine.

Corneliu Maftuleac
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At the center of the Earth there would be no net gravitational force. This does not mean the same as no gravity. The center is affected equally by all of Earth's mass so it is pulled equally in all directions. So there would still be gravitational time dilation even though there is no net force to pull it more in one direction than another.

Adrian Howard
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  • Rough, non-rigorous calculation that tries to blend Newton & Schwarzschild: set the gravitational potential $u$ to be $0$ at infinity, so at $r=R$ we have time dilation factor $\sqrt{1+2u}$ with $u=-\frac{GM}{Rc^{2}}$. At $r=0$, you can show $u=-\frac{3GM}{2Rc^{2}}$, so $\sqrt{1+2u}=\sqrt{1-\frac{3GM}{Rc^{2}}}$. – J.G. Aug 05 '21 at 08:55
  • The differential time rate is ~3.48E-10, so over a century a clock at the centre of the Earth would be slow by ~1.1 seconds compared to a clock on the surface. – PM 2Ring Aug 05 '21 at 15:32