Home / Topics / Relativity
Length contraction
Intermediate
Moving objects shorten along the direction of motion.
L = L₀/γLengths along the direction of motion shorten: L = L₀/γ, where L₀ is the proper length in the object's rest frame. Perpendicular lengths are unchanged.
A 100 m ship at 0.8c measures 60 m.
Appears only in the frame where the object moves.
In more detail
Objects moving at high speed appear shorter along their direction of motion, L = L0/γ. The effect is only significant at speeds approaching the speed of light.
Real-world uses
- Particle physicists account for length contraction in accelerator design.
- Cosmic-ray muons reach the ground because of length contraction in their frame.
- Particle physicists note that fast-moving particles appear shorter along their direction of motion to an observer in the lab.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Is length contraction real?
It is real in the sense that measurements agree, though the object is not physically squashed.
When does it matter?
Only at speeds that are a significant fraction of the speed of light.
Does length contraction really happen?
Yes, it is a consequence of the Lorentz transformations, though it is only noticeable near the speed of light.
Related topics in Relativity
Postulates of special relativity · Relativity of simultaneity · Time dilation · Lorentz factor · Lorentz transformations · Velocity addition