The clock paradox

Abstract

Let us suppose that two clocks of identical construction are found to run in perfect synchronism while they are side by side, and that this synchronism is maintained even if one of the clocks, while remaining very near the other, is subjected to accelerations, however great. The clocks are then widely separated from one another with a relative velocity comparable with the velocity of light, and subsequently reunited. Are their readings necessarily identical? This question has caused controversy at intervals during the last fifty years. The controversy has been renewed recently when the apparently imminent advent of space travel has brought to the attention of a wider audience some of the striking predictions of the theory of relativity, concerning the possibility of “asymmetric ageing”. In this article the correctness of the result deduced by Einstein in 1905, that the two clocks will in general not agree, is defended from a number of points of view, including the experimental evidence. The effect of a permanent gravitational field on the clocks is also discussed, and questions concerning the rate of a clock in an Earth satellite and the ageing of space travellers in a gravitational field are shown to have unexpected and amusing answers.