page_title: Minkowski diagram
section_title: Spacetime diagrams in Newtonian physics
hierarchical_section_title: Minkowski diagram / Spacetime diagrams in Newtonian physics
context_page_description: 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.
  Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.
  In this way, each object, like an observer or a vehicle, traces a certain line in the diagram, which is called its world line. Also, each point in the diagram represents a certain position in space and time, and is called an event, regardless of whether anything relevant happens there and then.
context_section_description: The black axes labelled x and ct on the adjoining diagram are the coordinate system of an observer, referred to as 'at rest', and who is positioned at x = 0. This observer's world line is identical with the ct time axis. Each parallel line to this axis would correspond also to an object at rest but at another position. The blue line describes an object moving with constant speed v to the right, such as a moving observer.
  This blue line labelled ct′ may be interpreted as the time axis for the second observer. Together with the x axis, which is identical for both observers, it represents their coordinate system. Since the reference frames are in standard configuration, both observers agree on the location of the origin of their coordinate systems. The axes for the moving observer are not perpendicular to each other and the scale on their time axis is stretched. To determine the coordinates of a certain event, two lines, each parallel to one of the two axes, must be constructed passing through the event, and their intersections with the axes read off.
  Determining position and time of the event A as an example in the diagram leads to the same time for both observers, as expected. Only for the position different values result, because the moving observer has approached the position of the event A since t =  0. Generally stated, all events on a line parallel to the x axis happen simultaneously for both observers. There is only one universal time t = t′, modelling the existence of one common position axis. On the other hand, due to two different time axes the observers usually measure different coordinates for the same event. This graphical translation from x and t to x′ and t′ and vice versa is described mathematically by the so-called Galilean transformation.
caption: In Newtonian physics for both observers the event at A is assigned to the same point in time.