**Physics Notes - Herong's Tutorial Notes** - v3.22, 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.

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