User:Mpatel/sandbox/Light cone

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 $p$ a flash of light (light pulse) at time $t_{0}$, all events that can be reached by this pulse from $p$ form the future light cone of $p$, whilst those events that can send a light pulse to $p$ form the past light cone of $p$.

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

• Events on the future light cone of $E$.

• Events on the past light cone of $E$.

• Events inside the future light cone of $E$ are those which are affected by a material particle emitted at $E$.

• Events inside the past light cone of $E$ are those which can emit a material particle and affect what is happening at $E$.

• Events in the absolute elsewhere of $E$ are those that can never be affected by $E$.

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

• Minkowski diagram

External link

• The Einstein-Minkowski Spacetime: Introducing the Light Cone
• The Paradox of Special Relativity

Category:Astrophysics Category:Relativity