There are two twins, A and B. While twin A stays home, twin B travels with a speed (12/13)c to a far planet. Once twin B arrives at the planet, they turn around and travel back home at the same speed. When twin B arrives home, they find that they are 32 years younger than twin A.  Quantitatively prove that twin A cannot be younger than than twin B when they get back together.

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.