Solving the Twin’s Paradox with Special Relativity

Abstract

In this paper, we examine one of the most well known of special relativity’s apparent paradoxes: the twin’s paradox. It is regularly claimed that because this paradox contains accelerating frames that it does not belong in the domain of special relativity but must be solved via general relativity. We will demonstrate that this is not the case by considering to solutions to the paradox which only involve flat Minkowski spacetime. The first is the Doppler shift analysis which considers what each observer actually sees according to the relativistic Doppler equation which finds that both observers agree the travelling twin is younger. Then we solve it analytically by considering Rindler coordinates which quantify accelerating frames in special relativity. This will give us a numeric result which shows that the Earthbound twin ages the required amount during the turnaround according to the accelerated frame. Thus, by considering the appropriate framework, we demonstrate there is no paradox involved at all.