**Herong's Notes on Physics** - Version 3.21, by Dr. Herong Yang

Time Dilation in Minkowski Diagram

This section provides a demonstration of the time dilation phenomenon using a Minkowski diagram.

Minkowski diagram can also be used to demonstrate the time dilation phenomenon. Let's follow another simple thought experiment described below:

- Amy stays in frame moving at a speed of v=0.6*c relative to Bob's frame.
- Amy holds a clock in her frame at (0,0) as event O.
- Amy waits for 4 seconds at arrives at event E, (X',cT')=(0,4).
- The elapsed time of E in Amy's frame is cT'=4 seconds.

Now in Bob's frame:

- The event E would be observed at (X,cT)=(3,5) in Bob's frame based on the Minkowski diagram given below.
- The elapsed time of E in Bob's frame is cT=5 seconds.

So the elapsed time in Amy's moving frame is dilated by cT/cT' = 5/4 = 1.25, which matches Lorentz factor of the time dilation formula presented earlier in the book.

*Last update: 2014.*

Table of Contents

Introducion of Frame of Reference

Introduction of Special Relativity

Time Dilation in Special Relativity

Length Contraction in Special Relativity

The Relativity of Simultaneity

►Minkowski Spacetime and Diagrams

What Is Lorentz Transformation?

Constancy of Speed of Light in Minkowski Diagram

►Time Dilation in Minkowski Diagram

Length Contraction in Minkowski Diagram

Relativity of Simultaneity in Minkowski Diagram

Invariant Spacetime Interval in Minkowski Diagram