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Muon decay evidence
Intermediate
Muons reach the ground due to time dilation.
Cosmic-ray muons (T½ 2.2 μs at rest) are created ~15 km up and reach sea level because at 0.998c, γ ≈ 16 extends their lifetime to 35 μs.
From the muon's frame the distance contracts instead.
Both pictures agree.
In more detail
Muons created high in the atmosphere reach the ground in greater numbers than their short lifetime allows. Time dilation explains this, as the muons live longer in Earth's frame.
Real-world uses
- Muon experiments are used to test special relativity.
- Cosmic ray physics relies on this effect.
- Physics teachers use muon decay to show time dilation, since muons created high in the sky survive long enough to reach the ground.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is a muon's lifetime at rest?
About 2.2 microseconds.
How do muons prove relativity?
Their survival at ground level matches the time-dilated lifetime predicted by relativity.
Why is the muon result convincing?
The number of muons reaching the ground matches the predictions of special relativity, not the classical expectation.
Related topics in Relativity
Lorentz factor · Lorentz transformations · Velocity addition · Twin paradox · Spacetime diagrams · Spacetime interval