Suppose two inertial reference frames S and S’ are moving with velocity v with respect to each other. Also suppose that an observer at reference frame S measures an event as and another observer at frame S’ measures the same event as . Now if we want to relate the measurements of S frame with S’ frame we have to use transformation equations.
If we take Newtonian mechanics granted then we use the Galilean transformation. Galilean or Classical transformation equations are:
Notice that the time co-ordinates are measured the same by both observer—that is .
But if we take Special Relativity instead of Newtonian Mechanics than we use Lorentz transformation. Lorentz transformation equations are:
The fraction is also called relativistic gamma .