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 graphical depiction of a portion of Minkowski space, usually 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. The horizontal lines correspond to the usual notion of simultaneous events for a stationary observer at the origin.

A particular Minkowski diagram illustrates the result of a Lorentz transformation. The Lorentz transformation relates two inertial frames of reference, where an observer stationary at the event (0, 0) makes a change of velocity along the x-axis. The new time axis of the observer forms an angle α with the previous time axis, with α < π/4 (see the first figure on the right). In the new frame of reference the simultaneous events lie parallel to a line inclined by α to the previous lines of simultaneity. This is the new x-axis. Both the original set of axes and the primed set of axes have the property that they are orthogonal with respect to the Minkowski inner product or relativistic dot product.

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