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

Length Contraction in Minkowski Diagram

This section provides a demonstration of the length contraction phenomenon using a Minkowski diagram.

Minkowski diagram can also be used to demonstrate the length contraction 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 measuring rod of 4 (light seconds) long in her frame with one end at (0,0) as event O.
- Amy checks the other end of the rod at event E, (X',cT')=(4,0).
- The length of the rod in Amy's frame is X'=4 light seconds.

Now in Bob's frame:

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

So the length of the rod is contracted by X/X' = 5/4 = 1.25. which matches Lorentz factor of the length contraction 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