1. A Strange Phenomenon
There is a type of unstable particles called Muon.
They are produced in the upper atmosphere 14 km above Earth’s surface and travel towards Earth at 99.9% the speed of light.
A person standing on Earth would observe that stationary muons have an average lifetime of 2.2 microseconds before disintegrating into other forms.
Given that the speed of light is 3.00 x 108 m/s, what is the average distance you expect the muons to travel before they disintegrate?

2. If muons have an average lifetime of 2.2 microseconds…
The average distance which muons can travel should be around 660 m before they disintegrate.
Hence most muons should NOT be able to reach Earth’s surface.
Muon is created at an altitude of 14km above Earth’s surface.
0.66 km
14 km

3. However in reality…
An observer on Earth’s surface is able to detect muons that reach Earth’s surface.
This means that the muons must be able to reach Earth’s surface before they disintegrate.
Hence, the average lifetime of muons must be much longer than 2.2 microseconds when they are moving at very high speed.
Muon is created at an altitude of 14km above Earth’s surface.
14 km

4. A stationary observer would observe that
Average lifetime of stationary muons: 2.2 microseconds
Average lifetime of muons moving at very high speed: more than 2.2 microseconds
How can the duration for the disintegration be different for stationary and fast-moving muons?!

5. In the early 20th century, scientists found out through experiment that the speed of light is always the same to all observers regardless of their motion. Strangely enough, this can explain why the average lifetime of muons is different when they are stationary compared to moving at high speed.

6. Your challenge for the day!
Using the fact that the speed of light is always the same to all observers, explain the discrepancy between the average lifetime of stationary muons and that of fast-moving muons.