A traveller leaves Earth at and flies at a steady to a station at rest relative to Earth
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics
Relativity and Gravitation, Ch Time dilation, length contraction and simultaneity
Problem
A traveller leaves Earth at t=0 and flies at a steady v=0.600c to a station at rest relative to Earth, a distance D=6.00 light-years away as measured in the Earth frame S. On reaching the station she turns round in a negligible time and returns at the same speed. Treat the Earth frame S, the outbound frame Sout (moving at +v along the x axis from Earth to the station) and the inbound frame Sin (moving at −v) as inertial, each in standard configuration with S and each with clocks synchronised in its own frame. Ignore gravitation.
((a)) Find the elapsed time of the round trip on Earth clocks, and the elapsed time on the traveller's own clock.
((b)) Name the event "the traveller reaches the station" by its coordinates (t,x) in S. Find the reading of the Earth clock at the Earth event that Sout judges simultaneous with it, and the reading at the Earth event that Sin judges simultaneous with it.
((c)) Using your two readings from (b) and the time dilation of the Earth clock on each leg as judged by the traveller, account for the whole of the Earth elapsed time found in (a), and say in one sentence what breaks the symmetry between the two twins.