Paper 4, Section II, B

Dynamics and Relativity | Part IA, 2016

(a) Alice travels at constant speed vv to Alpha Centauri, which is at distance dd from Earth. She then turns around (taking very little time to do so), and returns at speed vv. Bob stays at home. By how much has Bob aged during the journey? By how much has Alice aged? [No justification is required.]

Briefly explain what is meant by the twin paradox in this context. Why is it not a paradox?

(b) Suppose instead that Alice's world line is given by

c2t2+x2=c2t02,-c^{2} t^{2}+x^{2}=c^{2} t_{0}^{2},

where t0t_{0} is a positive constant. Bob stays at home, at x=αct0x=\alpha c t_{0}, where α>1\alpha>1. Alice and Bob compare their ages on both occasions when they meet. By how much does Bob age? Show that Alice ages by 2t0cosh1α2 t_{0} \cosh ^{-1} \alpha.

Typos? Please submit corrections to this page on GitHub.