Q. What do you mean by Time Dilation?

To an observer a moving clock always appears to run slower. The time interval between two events occurring at a given point in space in a frame of reference, moving with respect to the observer, appears to be greater as noted on clock at rest with respect to him than an identical clock in the moving frame of reference itself. This effect is called as time dilation meaning apparent lengthening of time. Let us consider two inertial frames of references S and S' where the axes, x and x', y and y' and z and z' are parallel and the origin O' of frames S' is moving with a uniform velocity v with respect to frames S as shown in fig. Let a clock is placed at the point x' in the moving frame S'. An observer O' in frame S' records that the clock gives two ticks at time t1' and at time t2' the time interval between these two ticks that occurs at the same place (means events are co local) in an observers frame of reference S' is called the proper time interval for events and then frame will be called proper frame. If these two ticks are observed in another frame i.e. laboratory frame of reference in which clock is moving in x direction with a uniform velocity v, they will be observed at different times. Suppose these two events occur at the instants t1 & t2 in the frame S moving in the x direction with a velocity - v relative to the frame S'. the time interval as observed in frame Sis observed time.