TIME DILATION – TIME DILATION
IN RELATIVITY
The word dilate means
“Enlarge beyond normal size”. Time is also not absolute but relative. It is
found that a moving clock in the space craft appear to tick at a slower rate
than the stationary one on the ground as seen by an observer on ground.
Thus if a clock moves with
very high speed v relative to an observer then it appears to be slowed down or
time to time interval is increased by a factor 
.
Let us consider two frame
of reference s and s’. s’ is moving with velocity v relative to s which is at
rest along +x direction. A clock is at point x in the frames. Let the clock
give out signal at two instant t1 and t2 then the interval between signal is
given by 
.
.
If
the signal interval is observed in frame of reference s’ then interval
is
given by
From Lorentz transformation
equation for time
Hence for a moving observer, the time interval appear to be dilated (increased).This phenomenon is known as Time Dilation.
