A light clock (two parallel mirrors with a light pulse bouncing between them
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics
Relativity and Gravitation, Ch The postulates and the Lorentz transformation
Problem
A light clock (two parallel mirrors with a light pulse bouncing between them, the intervening air ignored) is carried aboard an airliner cruising in level flight at a steady 250ms−1 relative to the ground. Treat both the ground and the aircraft cabin as inertial frames and ignore gravitation. The flight lasts 8.0 hours as measured by ground clocks.
((a)) Estimate γ−1 for the aircraft, using the first-order approximation γ≈1+v2/2c2 valid when v≪c. Give one or two significant figures.
((b)) Estimate the accumulated difference, in seconds, between the elapsed time on the ground clocks and the elapsed time recorded by the light clock on the aircraft. Which reads less?