Physics Notes - Herong's Tutorial Notes - v3.25, by Herong Yang
Demonstration of Time Dilation - Amy on the Train
This section provides a thought experiment to demonstrate time dilation by starting with Amy synchronizing a clock with a bouncing light pulse on a moving train.
The most common way to demonstrate time dilation is to follow a thought experiment using a clock on a train moving relative the ground.
Part 1 - Amy on the Train: The first part of the thought experiment is to synchronize the moving clock and a laser light pulse bouncing perpendicular to the moving direction of the clock. This part consists of the following:
Based on Amy's observations in her frame, we can derive a formula to express time T in terms of distance L:
2*L = c*T (T.1) - Amy's observation # Light pulse speed, time and distance relation T = 2*L/c (T.2) - moving variables around # Time on the moving clock in Amy's frame
Notice that T also represents the elapsed time observed by Amy between two events: event A when the light pulse is leaving the meter, and event B when the same light pulse is returning to the meter reflected back from the mirror.
With Amy's clock synchronized with the bouncing light pulse, we can say that the bouncing light pulse itself is also a moving clock. It moves T seconds per click.
Now we are ready to measure the speed of time on the moving frame from a stationary frame by observing the elapsed time of between two clicks of the bouncing light pulse clock. Continue with the second part of the thought experiment in the next section.
Table of Contents
Introduction of Frame of Reference
Introduction of Special Relativity
►Time Dilation in Special Relativity
Time Dilation - Moving Clock Is Slower
►Demonstration of Time Dilation - Amy on the Train
Demonstration of Time Dilation - Bob on the Ground
Demonstration of Time Dilation - Formula
Elapsed Time between Distant Events
Length Contraction in Special Relativity
The Relativity of Simultaneity
Minkowski Spacetime and Diagrams
Introduction of Generalized Coordinates