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Gravitational Time Dilation - Is my head older than my feet?

  1. Jul 25, 2011 #1
    According to general relativity, objects in a strong uniform gravitational field experience time slower that objects in a weak uniform gravitational field.

    Does this mean that my feet, being closer to the earth that my head, are younger than my head when I die?

    If this is correct could someone oblige me in showing me the maths involved should it not be to complicated. Or at least link a source to be where I can learn these calculations for myself.

    Kindest Regards,
     
    Last edited: Jul 25, 2011
  2. jcsd
  3. Jul 25, 2011 #2
    Yes, that's right. They experience stronger acceleration, and so are more time-dilated.
     
  4. Jul 25, 2011 #3
    Is the maths involved complicated to a lay person? i would like to be able to demonstrate this to others.
     
  5. Jul 25, 2011 #4
    You could try this: http://en.wikipedia.org/wiki/Gravitational_time_dilation" [Broken]. The maths isn't too complicated.
     
    Last edited by a moderator: May 5, 2017
  6. Jul 25, 2011 #5
    That's very useful. One more question if you don't mind.

    Once I have a value for Td how do I put this in context?

    For example after my feet are 1 second old my head is y seconds old?
     
  7. Jul 25, 2011 #6
    Yes you are correct. But remember, Earth's gravity is very weak (and gravity is already the weakest of the 4 forces) compared to most cosmic bodies. So its not like your head is years older than your feet, but by a very tiny amount of time. Great observation though.
     
  8. Jul 25, 2011 #7
    This equation gives the ratio of the two times.
     
    Last edited by a moderator: Jul 25, 2011
  9. Jul 25, 2011 #8
    Fantastic. Thanks for your help.

    So I tried to calculate this. I took my height and approximate age (of my feet) in seconds to the nearest day.
    And i used the linear "weak field" approximation Td = 1 + gh / c2 of the equation.

    I calcualted that my head is 180ns older than my feet, assuming of course i have been standing upright since birth :smile:
     
    Last edited: Jul 25, 2011
  10. Jul 25, 2011 #9

    bcrowell

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    Looks fine, but don't you feel silly copying down 8 sig figs at intermediate steps in a 2-sig-fig calculation?
     
  11. Jul 25, 2011 #10

    atyy

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    How do you justify the asusmption that your head and feet die at the "same time"?

    Couldn't you equally argue that your head would die first, since time runs faster for it?

    ;)
     
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