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
About This Book
Introduction of Space
Introducion of Frame of Reference
Introducion of Time
Introduction of Speed
Newton's Laws of Motion
Introduction of Special Relativity
Time Dilation in Special Relativity
Length Contraction in Special Relativity
The Relativity of Simultaneity
Introduction of Spacetime
►Minkowski Spacetime and Diagrams
What Is Minkowski Spacetime?
Events Interval and Relations
What Is Lorentz Transformation?
What Is Minkowski Diagram?
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
Multiple Reference Frames in Minkowski Diagram
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