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User:Mpatel/sandbox/Light cone

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A worldline through a light cone in 2D space plus a time dimension.

In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. This can be visualized in 3-space if the two horizontal axes are chosen to be spatial dimensions, while the vertical axis is time.

The light cone is constructed as follows. Taking as event a flash of light (light pulse) at time , all events that can be reached by this pulse from form the future light cone of , whilst those events that can send a light pulse to form the past light cone of .

Given an event , the light cone classifies all events in spacetime into 5 distinct categories:

  • Events on the future light cone of .
  • Events on the past light cone of .
  • Events inside the future light cone of are those which are affected by a material particle emitted at .
  • Events inside the past light cone of are those which can emit a material particle and affect what is happening at .
  • Events in the absolute elsewhere of are those that can never be affected by .

If space is measured in light-seconds and time is measured in seconds, the cone will obviously have a slope of 45°, because light travels a distance of one light-second in a vacuum during one second. Since special relativity requires the speed of light to be equal in every inertial frame, all observers must arrive at the same angle of 45° for their light cones. This is ensured by the Lorentz transformation.

In general relativity, the future light cone is the boundary of the causal future of a point and the past light cone is the boundary of its causal past.

See also

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Category:Astrophysics Category:Relativity