Introduction to Electrodynamics · Problem 12.8
Electrodynamics and Relativity — David J. Griffiths
Physics · special-relativity-time-dilation
Problem
A rocket ship leaves earth at a speed of . When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth. (a) According to earth clocks, when was the signal sent? (b) According to earth clocks, how long after the rocket left did the signal arrive back on earth? (c) According to the rocket observer, how long after the rocket left did the signal arrive back on earth?Intuitive explanation
This problem combines time dilation with light travel time—you need to separate what different observers measure. The rocket clock runs slow relative to Earth (that's time dilation), so when the rocket clock reads 1 hour, Earth clocks have measured a longer time. Then you must account for the light signal's journey back, which takes real time to traverse the distance the rocket has traveled. Keep track of which frame (Earth or rocket) is doing the measuring at each step.
Intuitive explanation
This problem combines time dilation with light travel time—you need to separate what different observers measure. The rocket clock runs slow relative to Earth (that's time dilation), so when the rocket clock reads 1 hour, Earth clocks have measured a longer time. Then you must account for the light signal's journey back, which takes real time to traverse the distance the rocket has traveled. Keep track of which frame (Earth or rocket) is doing the measuring at each step.