# Twin Paradox

1. Dec 1, 2011

### the_kid

1. The problem statement, all variables and given/known data
Twins are separated at birth on earth. Twin B travels in a straight line back and forth at a velocity, V. According to twin A, who stays on earth, twin B travels away for 10 years, and then back toward earth for ten years.

They send light signals to each other at every birthday each one celebrates. When do they receive another's signals and does each count agree with their ages upon return?
2. Relevant equations

3. The attempt at a solution
Event 1: A emits a pulse
Event 2: Y receives the pulse

Event 1, in earth-frame: (t$_{1}$, 0)
Event 1, in moving frame of B: (t$^{'}_{1}$, -Vt$_{1}$)

Event 2, in earth-frame: (t$_{2}$, Vt$_{2}$)
Event 2, in moving frame of B: (t$^{'}_{2}$, 0)

This gives me both events in each coordinate system. They can be related by the expression c=$\frac{x_{2}}{t_{2}-t_{1}}$. After substituting x$_{2}$=Vt$_{2}$ and simplifying, we have t$_{2}$=$\frac{ct$_{1}$}{c-V}$. This gives the relationship in the earth-frame.

Now how do I get the relationship in the moving frame?

2. Dec 2, 2011

### Simon Bridge

You can get an understanding of what is happening by constructing the space-time diagram. Try this description.

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