# Twin Paradox in outgoing frame

1. Apr 7, 2009

### bndnchrs

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?