The twin paradox in relativity revisited

“Everything should be as simple as it is, but not simpler”, Albert Einstein
Posted on April 26, 2012 


The twin paradox in relativity has a history almost as long as the theory of relativity itself. It was originally proposed by Einstein as a gedanken experiment to highlight the fact that an observer sees a moving clock going at a slower rate than a clock at rest. Because this is an entirely symmetric effect (in that each clock sees the other clock ticking slower), the paradox arises when two identical synchronized clocks are temporarily separated into different Lorentz frames and then brought back together.
Applied to twins, the paradox starts with identical twins on Earth. One of the twins then accelerates away on a rocket, moves away from Earth at a constant velocity u for a time T/2, fires rockets to accelerate again so that his velocity changes to −u, moves at the constant velocity u towards the Earth for a time T/2, and decelerates to a stop on reaching the Earth again. The acceleration times are assumed to be negligible compared to T . The paradox arises because both twins observe the other to be aging slower during the period of uniform relative motion. Are they the same age when they meet again or is one of them younger, and if so, which one and by how much?
Over the years, the paradox has been discussed extensively in many books and articles. The American Journal of Physics has carried a large number of articles on the paradox, highlighting the difficulty in conveying this concept to first-time students of relativity. It still remains one of the most puzzling aspects of the theory of relativity.
In the standard resolution, as presented in many textbooks on relativity, both twins conclude that the traveling twin (who accelerated) is younger. The argument proceeds as follows. The Earth-bound twin always remains in an inertial frame and therefore his observation that the other twin is aging slower is correct. On the other hand, the rocket-bound twin sees his brother age slowly during the time when the relative velocity is constant, but sees a sudden jump in his brother’s age during the short acceleration phase when he is not in an inertial frame. Thus, the change of inertial frames results in a jump in age….

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