Time Dilation

We consider here a rail car (i.e., a moving frame) moving with velocity ‘v’. A mirror is fixed to its roof inside the car and an observer is at rest inside the car. He starts a light pulse at an instant vertically towards the mirror and the light signal reflects immediately back to the observer with a velocity ‘c’.

The time interval is measured as,

∆T =2h /c

Here, ‘h’ is the vertical height of the mirror from the floor of the rail car as shown in Figure. 8.4. Also an observer on the ground outside the rail car (i.e., a stationary frame) observes

that both the mirror and the light source are moving with a velocity ‘v ‘ which is now at the point C.

If’ ∆t’ is the time taken for the light pulse to reach at C from A, then from Figure. 8.4 we have

Hence ,                        ∆t  =∆t √ 1- v2 /c2

So, time measured in the moving frame becomes lengthened or dilated. Hence, from the point of view of the observer at the stationary frame the events will be found happening at a slower rate in the moving frame. This is known as Time Dilation effect. The effect has been experimentally verified by the decay of Muons in 1941 and also in 1971 in a jet plane travel.