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.

Time Dilation Demonstration - Amy on Train
Time Dilation Demonstration - Amy on Train

Table of Contents

 About This Book

 Introduction of Space

 Introduction of Frame of Reference

 Introduction of Time

 Introduction of Speed

 Newton's Laws of Motion

 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

 What Is Lorentz Factor

 Reciprocity of Time Dilation

 Elapsed Time between Distant Events

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

 Minkowski Spacetime and Diagrams

 Introduction of Hamiltonian

 Introduction of Lagrangian

 Introduction of Generalized Coordinates

 Phase Space and Phase Portrait


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