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

Reciprocity of Length Contraction

This section introduces the reciprocity of length contraction. Length of a moving object is shorter when measured by a stationary observer; and length of a stationary object is shorter when measured by a moving observer.

Length contraction is reciprocal because moving between two observers is reciprocal. So the following two statements are both true:

- Length of a moving object is contracted (shorter) when measured by a stationary observer in the moving direction.
- Length of a stationary object is contracted (shorter) when measured by a moving observer in the moving direction.

The first statement was demonstrated by the thought experiment presented in previous sections. The second statement can be demonstrated by modify that experiment slightly as below:

- Put the carriage on the ground and let Bob performs the experiment on the ground.
- Now considering Amy on the moving train, she will see the carriage and the ground is moving in the opposite direction.
- If we follow the same thought process used in previous sections, we will arrive the same conclusion in the opposite way. That is L = (1/gamma)*L', where L is the length observed by Amy and L' is the length observed by Bob.

Reciprocity of length contraction can lead us to some interesting phenomena. For example, we have two trains, a red train and a green train, running side by side in opposite directions. Passengers will experience the following when they are watching the other train passing by:

- Red train passenger experiences with his fingertips a contracted green train car.
- Green train passenger experiences with his fingertips a contracted red train car.

*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

Length Contraction - Moving Object Is Shorter

Demonstration of Length Contraction

Length Contraction Formula and Lorentz Factor

►Reciprocity of Length Contraction

The Relativity of Simultaneity