A twin paradox for 'clever' students

Abstract

We discuss the twin paradox or the clock paradox under the small velocity approximation of special relativity. In this paper the traveller twin of the standard twin parable sets out with a non-relativistic speed for the trip leaving behind the stay-at-home one on earth and continues up to a distance and finally returns home with the same speed when the siblings can compare their ages or their initially synchronized wrist watches. The common knowledge that at small velocities the length contraction and time dilation effects of special relativity can be ignored so that the world becomes essentially classical, tends to lead to a paradox in connection with the twin problem, which a "clever" student eventually discovers. After discussing and resolving the issue, some more related paradoxes have been presented. The resolution of all these problems provides some additional insight into the century old paradox.