universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime. Rather than considering universal Lorentz covariance to be a derived principle, this article considers it to be the fundamental postulate of special relativity. The traditional two-postulate approach to special relativity is presented in innumerable college textbooks and popular presentations. Textbooks starting with the single postulate of Minkowski spacetime include those by Taylor and Wheeler and by Callahan. This is also the approach followed by the Wikipedia articles Spacetime and Minkowski diagram. Lorentz transformation and its inverse Define an event to have spacetime coordinates in system S and in a reference frame moving at a velocity v with respect to that frame, S. Then the Lorentz transformation specifies that these coordinates are related in the following way: where is the Lorentz factor and c is the speed of light in vacuum, and the velocity v of S, relative to S, is parallel to the x-axis. For simplicity, the y and z coordinates are unaffected; only the x and t coordinates are transformed. These Lorentz transformations form a one-parameter group of linear mappings, that parameter being called rapidity. Solving the four transformation equations above for the unprimed coordinates yields the inverse Lorentz transformation: Enforcing this inverse Lorentz transformation to coincide with the Lorentz transformation from the primed to the unprimed system, shows the unprimed frame as moving with the velocity , as measured in the primed frame. There is nothing special about the x-axis. The transformation can apply to the y- or z-axis, or indeed in any direction parallel to the motion (which are warped by the γ factor) and perpendicular; see the article Lorentz transformation for details. A quantity invariant under Lorentz transformations is known as a Lorentz scalar. Writing the Lorentz transformation and its inverse in terms of coordinate differences, where one event has coordinates and , another event has coordinates and , and the differences are defined as we get If we take differentials instead of taking differences, we get Graphical representation of the Lorentz transformation Spacetime diagrams (Minkowski diagrams) are an extremely useful aid to visualizing how coordinates transform between different reference frames. Although it is not as easy to perform exact computations using them as directly invoking the Lorentz transformations, their main power is their ability to provide an intuitive grasp of the results of a relativistic scenario. To draw a spacetime diagram, begin by