Question

Twins A and B are both 19.0 years old when twin B decides to embark on a space voyage. Twin B blasts off from Earth and travels at a speed of 0.97c. Twin A remains on Earth, and after waiting 35.0 years, twin A is reunited with twin B, who has returned from the space voyage. Twin A is now 54.0 years old. How old is twin B?

Answer 1

ΔT = ΔT0 / (1 - v^2/c^2)^1/2

ΔT is the time elapsed in the moving frame and ΔT0 is the proper time that has elapsed in the frame where the clock is stationary

ΔT = 35 years which is the elapsed time in frame A - age of twin in that frame

ΔT0 = 35 * (1 - .97^2) = 2.07 yrs time elapsed for twin (B) in stationary frame B - measured WRT a clock at a single point

the proper time in frame B will be the actual elapsed time (age) that has passed in that frame - frame A is moving WRT frame (B)