LENGTH CONTRACTION IN RELATIVITY
Let us consider two inertial frame s and s’. s’ is moving with velocity v relative to s along +x direction. Frame s is at rest. Let a rod AB is laying along the x axis in frame s. If x1 and x2 be coordinate of ends A and B respectively then the length L0 of the rod in frame s is given by
Let an observer in s’ measure the length of the same rod and its x1’ and x2’ are the coordinate of end A and B of the rod at the same time then the length of the rod L will be given by
According to Inverse Lorentz Transformation we have
Hence the length of rod moving with velocity v relative to the observer is contracted by a factor in the direction of motion. This phenomenon is also called Lorentz-Fitzgerald Contraction.