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bndnchrs
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Homework Statement
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
Homework Equations
Lorentz Transforms
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?