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Twin Paradox in outgoing frame

  1. Apr 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that as calculated in the rest frame comoving with the twin on the outgoing trip, the ratio of the two ages of the twins is the same: i.e. the twin on earth has age gamme times the other twin


    2. Relevant equations
    Lorentz Transforms


    3. The attempt at a solution
    We are supposed to do this from the frame of the outgoing twin: but staying in the departing reference frame, and watching the twin that returns to earth speed away from us.

    So the age of a twin on earth as seen from our frame is 2*L'/v with L' = L * gamma

    The age of the twin which left is the time while the twin is moving with our frame + the time it takes to return to the earth.

    This is where I run into trouble. I can't verify that the twin that left earth has t = 2*L/(gamma^2)

    I assume t(1/2) which is the time the twin which left is still in our frame is L'/v.

    Then t(return) = 2*L'/v(ret) with v ret the relativistic added velocity 2*v/(1+(v/c)^2).

    This doesn't work, however, I can't get the sum to be what it should be.

    Any ideas?
     
  2. jcsd
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