Lorentz Transformations

A peculiar effect of Einstein's postulates is the transformation that connects space-time in two inertial frames. Such transformations are called Lorentz transformations.

The standard Lorentz transformation in the x direction is (for reference also the classical Galilei transformation is included):

Lorentz transformation (special relativity)	Galilei transformation (classical Newtonian mechanics)

where is the Lorentz factor. Note that the spatial coordinates (y and z) perpendicular to the direction of motion (x) are unchanged. In the classical limit , which means that , special relativity is equivalent with classical Newtonian mechanics. Furthermore, note that , i.e. time is relative in special relativity.

Directly from Lorentz transformations, one obtains the concepts of length contraction, time dilation, relativistic Doppler effect, and relativistic addition of velocities.