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A Minkowski diagram is a two-dimensional graphical depiction of a portion of Minkowski space, usually where space has been curtailed to a single dimension. The units of measurement in these diagrams are taken such that the light cone at an event consists of the lines of slope plus or minus one through that event. [ 3 ]
Hyperbolic motion can be visualized on a Minkowski diagram, where the motion of the accelerating particle is along the -axis.Each hyperbola is defined by = / and = / (with =, =) in equation ().
Minkowski's principal tool is the Minkowski diagram, and he uses it to define concepts and demonstrate properties of Lorentz transformations (e.g., proper time and length contraction) and to provide geometrical interpretation to the generalization of Newtonian mechanics to relativistic mechanics.
Commonly a Minkowski diagram is used to illustrate this property of Lorentz transformations. Elsewhere, an integral part of light cones is the region of spacetime outside the light cone at a given event (a point in spacetime). Events that are elsewhere from each other are mutually unobservable, and cannot be causally connected.
The Minkowski diagram is drawn in a spacetime plane where the spatial aspect has been restricted to a single dimension. The units of distance and time on such a plane are units of 30 centimetres length and nanoseconds, or; astronomical units and intervals of 8 minutes and 20 seconds, or; light years and years.
For easy visualizations of four dimensions, two space coordinates are often suppressed. An event is then represented by a point in a Minkowski diagram, which is a plane usually plotted with the time coordinate, say , vertically, and the space coordinate, say , horizontally. As expressed by F.R. Harvey
To explain Minkowski diagrams: In Newtonian physics for both observers the event at A is assigned to the same point in time. Date: 12 September 2011, 11:53 (UTC) Source: Minkowski_diagram_-_Newtonian_physics.png; Author: Minkowski_diagram_-_Newtonian_physics.png: Wolfgangbeyer; derivative work: Duschi (talk)
The Penrose diagram for Minkowski spacetime. Radial position is on the horizontal axis and time is on the vertical axis. Null infinity is the diagonal boundary of the diagram, designated with script 'I'. The metric for a flat Minkowski spacetime in spherical coordinates is = + +.