Twin Paradox

On their twenty-first birthday, Peter leaves his twin brother, Paul, behind on Earth and goes off in a straight line for 7 years on his own wristwatch time (2.2 × 10⁸ seconds) at 0.96 c with respect to an inertial reference frame at rest with respect to Earth, then reverses direction, and in another 7 years of his time returns at the same constant speed. Paul sees Peter’s wristwatch running slower, so Peter ages  as much, or 1.96 years for each direction. But Peter looks back to see Paul’s clock running slower than his own wristwatch, so Paul should be aging slower by 0.28 as much that is, 1.96 years for each direction. On his return, Peter is surprised: “I know that I aged 14 years, but Paul should have aged only 3.92 years. Why is Paul an old man with gray hair?”

Answer

Peter experiences actual accelerations during his spaceship journey that will result in less aging than for his twin brother, who has remained at home on Earth. Even if the acceleration was simply an immediate turnaround at the farthest distance, the spaceship velocity vector reversed direction from +V to –V, a change of 2V, in a time interval T. Peter felt the acceleration. Therefore, all observers will agree that Peter was the traveler and that his clocks ran slow, so he ages less than his stay-at-home twin.