Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Would time stand still at center of earth?

  1. Jan 14, 2010 #1
    would time stand still at center of earth?...or at least be really slow
     
  2. jcsd
  3. Jan 14, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    Re: time

    Not at all.

    Time is not a function of distance from Earth's center, so that distance will not affect time.

    However, a pet theory of mine is that you will not feel Gravity at the center of Earth.
     
  4. Jan 14, 2010 #3

    Nabeshin

    User Avatar
    Science Advisor

    Re: time

    Time will indeed run slower at the center of the Earth than at the surface. This effect is due to the fact that large gravitational potential wells lead to a slowing of time with respect to other observers. For an object like the earth, however, one cannot expect the effect to be detectable by humans, but would be measurable by sensitive instruments.

    Caveat: Presumably those on the surface of the earth are rotating with it, and this rotational velocity also leads to a slowing of time (Our bloke at the center is probably not moving). The two effects compete, then.
     
  5. Jan 14, 2010 #4
    Re: time

    For a non rotating Earth, a clock at the centre will run slightly slower than a clock at the surface because the gravitational potential is lower at the centre of the Earth (and gravitational potential is a function of radius.) You can calculate how much slower by using the interior Schwarzschild solution. For a rotating Earth, the velocity of the clock at the surface will be slowed down by an additional factor due velocity time dilation. It would be interesting to work out which effect wins out, but that would require making some assumptions about the density distributon of matter within the Earth.

    For a non rotating massive body of even mass density, time does not stand still at the centre until the radius of the body is 9/8 of its Schwarzschild radius. (ie almost a black hole.)
     
  6. Jan 14, 2010 #5

    Char. Limit

    User Avatar
    Gold Member

    Re: time

    Oh.

    Never mind then.
     
  7. Jan 14, 2010 #6
    Re: time

    At the centre of Earth the gravitational effect is null.
    The field is maximum at surface.
    google images for 'gravitational potential earth center'
     
  8. Jan 14, 2010 #7

    Nabeshin

    User Avatar
    Science Advisor

  9. Jan 14, 2010 #8

    Char. Limit

    User Avatar
    Gold Member

    Re: time

    Nabeshin, I'm curious to know why that is.

    Is that the point where M/r^2 in the gravitational equation is maximized, or where you have the maximum amount of mass per unit radius squared?
     
  10. Jan 14, 2010 #9

    Dale

    Staff: Mentor

    Re: time

    It has to do with the fact that the earth is not uniform density. If the earth were a sphere with uniform density then what heldervelez said would be correct, however the earth bulges slightly and is much more dense at the core than at the surface. When you take that into consideration g increases below ground for some distance.
     
  11. Jan 14, 2010 #10

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: time

    I made an idealized GR calculation of this in

    https://www.physicsforums.com/showthread.php?p=1543402#post1543402.
     
  12. Jan 14, 2010 #11
    Re: time

    quoting from that post
    "If an observer on the Earth's surface uses a telescope to look down a tunnel to a clock at the Earth's centre, he will see his clock running faster than the clock at the Earth's centre."

    quoting from http://en.wikipedia.org/wiki/Gravitational_time_dilation" [Broken]
    "The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground."

    As seen above to be at the center of the Earth is equivalent to be at an infinite distance of the Earth.

    Do I see a contradiction?
     
    Last edited by a moderator: May 4, 2017
  13. Jan 14, 2010 #12

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: time

    There isn't a contradiction. These two situations aren't that similar, and stuff like this has to be calculated on a case-by-case basis. See

    http://en.wikipedia.org/wiki/Hafele-Keating_experiment

    for a more detailed analysis of the experiment done with clocks and planes. The Pound-Rebka experiment

    http://en.wikipedia.org/wiki/Pound-Rebka_experiment

    is closer to the situation that I described in my post.

    In each case, general relativity makes a prediction that is verified by experiment.
     
    Last edited by a moderator: May 4, 2017
  14. Jan 14, 2010 #13

    Dale

    Staff: Mentor

    Re: time

    There is a difference between gravitational acceleration and gravitational potential. The time dilation (in a stationary spacetime) depends on the gravitational potential, not the gravitational acceleration. So the fact that the gravitational acceleration is zero at the center and at infinity is not relevant.
     
  15. Jan 14, 2010 #14
    Re: time

    That WP statement is not entirely true. See http://hyperphysics.phy-astr.gsu.edu/HBASE/Relativ/airtim.html


    Predicted: Time difference in ns Eastward
    Gravitational__ 144 +/- 14
    Kinematic_____ -184 +/- 18
    Net effect____ -40 +/- 23
    Observed:____ -59 +/- 10

    Predicted: Time difference in ns Westward
    Gravitational __ 179 +/- 18
    Kinematic _____ 96 +/- 10
    Net effect ____ 275 +/- 21
    Observed: ____ 273 +/- 21

    The clocks going Westward were slightly faster, but the clocks going Eastward were slightly slower. Clocks flying in either direction speeded up due to being higher up in the gravitational field, but the slowing down of the clocks due to velocity time dilation exceeded the gravitational speed up for the Eastward clocks.

    As mentioned earlier, the clock at the centre of the Earth would look slower if the Earth was not rotating. You have to take both gravitational and velocity effects into account.

    It is not too difficult to work out the interior solution for a monotonically increasing density towards the centre, which might yield a better aproximation.
     
    Last edited by a moderator: May 4, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook