The Twin Paradox Brenda goes off at 4/5 c to a distant star and then returns. Her twin brother Ali stays on Earth. When she gets back she is no longer the same age as Ali. The first part looks like this. During this half, Ali sees Brenda’s clock run slowly and Brenda sees Ali’s clock run slowly. Ali t Brenda t’ x’ x The second part looks like this. During the second half they each see the other person’s time run slower. Ali t Brenda t’ x’ x Suppose Ali ages 10 years during the trip. How much did Brenda age? What is v? v is 4/5 c. t What is g? 10 g is 5/3. What is the time in the middle of the trip? 5 t’ x’ 3 Brenda has only aged 6 years. x If Brenda always sees Ali’s time ticking more slowly and Ali always sees Brenda’s time ticking more slowly. Why don’t they age by the same amount? t t’ x’ Brenda turns around. Her frame is not inertial andx therefore not equivalent. If Brenda always sees Ali’s time ticking more slowly and Ali always sees Brenda’s time ticking more slowly. When does Ali pick up the extra 4 years? t t’ x’ x During the turnaround. t t’ x’ x This is Brenda’s time at the start of the turn… t t’ x’ x ... in the middle … t t’ x’ x … and at the end. t t’ x’ x Almost no time passed for Brenda during the turnaround, while a lot passed for Ali. t t’ x’ x Reality Check #4: GPS satellites are constantly turning around. This makes their time run slower than ours by 8.99 x 10-11s every second. If the GPS failed to adjust for the different times, then they would be out by 2.5 km after one day!