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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 ]
Minkowski diagram: Sending a message with superluminal speed from O via A to B in the own past. Both observer consider the temporal order of the pairs of events O and A as well as A and B different. Date: 12 September 2011, 11:25 (UTC) Source: Minkowski_diagram_-_time_travel.png; Author: Minkowski_diagram_-_time_travel.png: Wolfgangbeyer
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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 x = ± c 2 / α {\displaystyle x=\pm c^{2}/\alpha } and η = α τ / c {\displaystyle \eta =\alpha \tau /c} (with c = 1 , α = 1 {\displaystyle c=1,\alpha =1} ) in equation ( 2 ).
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.
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)
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To explain Minkowski diagrams: Choosing ct instead of t on the time axis the world line of a photon becomes a straight line with a slope of 45°. Date: 12 September 2011, 09:53 (UTC) Source: Minkowski_diagram_-_photon.png; Author: Minkowski_diagram_-_photon.png: Wolfgangbeyer; derivative work: Duschi (talk)