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 axis 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 $E$ .

All other events are in the (absolute) elsewhere of $E$ and are those that will never affect and can never be affected by $E$ .

If space is measured in light-seconds and time is measured in seconds, the cone will have a slope of 45°, because light travels a distance of one light-second in 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.

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.

[edit] Light-cones in general relativity

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.

In a curved spacetime, the light-cones cannot all be tilted so that they are 'parallel'; this reflects the fact that the spacetime is curved and is essentially different from Minkowski space. In vacuum regions (those points of spacetime free of matter), this inability to tilt all the light-cones so that they are all parallel is reflected in the non-vanishing of the Weyl tensor.