Minkowski diagram

The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity. It allows a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.

The term Minkowski diagram is used in both a generic and particular sense. In general, a Minkowski diagram is a graphic depiction of a portion of Minkowski space, often where space has been curtailed to a single dimension. These two-dimensional diagrams portray worldlines as curves in a plane that correspond to motion along the spatial axis. The vertical axis is usually temporal, and the units of measurement are taken such that the light cone at an event consists of the lines of slope plus or minus one through that event.

A particular Minkowski diagram illustrates the result of a Lorentz transformation. The horizontal corresponds to the usual notion of simultaneous events, for a stationary observer at the origin. The Lorentz transformation relates two inertial frames of reference, where an observer makes a change of velocity at the event (0, 0). The new time axis of the observer forms an angle α with the previous time axis, with α < π/4. After the Lorentz transformation the new simultaneous events lie on a line inclined by α to the previous line of simultaneity. Whatever the magnitude of α, the line t = x forms the universal bisector.