Real example of time dilation:
As we have already discussed the concept of time dilation. Let us discuss its example:
Decay of µ- mesons:
µ- mesons are the particles formed in the earth atmosphere. The half life time of µ- mesons is 3.1 microseconds.
They travel with the speed of 0.9c.
where c is the speed of the light.
So they must covered the distance d = vt
d = 3.1 x 10-6 x 0.9c = 840m
It means there population should become half after this distance. But this does not happen. Population remains much higher than the half value.
Why this happened? This is because the time here should be dilated time and 3.1 microseconds should be the proper time. This is because the µ- mesons are travelling with speed comparable to the speed of the light.
So t = t’/(1 – v2/c2)
Here t’ = 3.1 microseconds
After solving, we get
t = 7.2 microseconds
thus distance traveled by µ- mesons will be
d = vt
or d = 7.2 x 10-6 x 0.9c
or d = 1920 m
Now when the population is measured after this distance it was approximately half.
It proves that the time dilation is a real effect.