How Does Special Relativity Explain the Age Difference Between Twins?

[godtripp]

Homework Statement

Two twins start their clocks at the same time, one of them travels for 7 years at a speed of 4/5c, reverses direction and returns at half the speed. The other twin remains stationary, what is the difference in their age?

Homework Equations

t = t_p γ

The Attempt at a Solution

I'm hung up on the thought... when he reverses direction he travels at half speed. Intuitively I think that it takes him 14 years to return at half speed... but is this necessarily the case? How can I prove that it is necessarily 14 years for him to return (considering Lorentz contraction) or find the actual time it would take him to return?

 

[vela]

14 years as measured by whom? Same question for the initial 7 years.

 

[godtripp]

The 7 years is as measured by the traveling twin's frame. So my intuition wants to say that his return is 14 years in his frame. However I think that this may be flawed due to lorentz contraction of the distance being traveled.

 

[vela]

Yes, you're right. It'll be longer than 14 years in that case. Not only is he going half the speed, he's having to travel a longer distance.