Light cone

In relativistic physics, the light cone of an event is the set of all events that affect the speed of light to or may be affected by the speed of light.

The light cone is a double cone in four-dimensional Minkowski space. It consists of

• The backward light cone, which consists of events that occurred before ( past ) and may have caused the speed of light, and
• The forward light cone, which are events that take place later than ( future ) and may have been caused by the speed of light.

Definition

Be the spatial and temporal coordinates of   the coordinates of, and   the components of the differential vector

If the difference vector is light-like:

Then lies in the special relativity theory on the light cone of precisely the events on the reverse or address the past light cone are currently visible to an observer, who is in ( without taking into account the expansion of the universe ).

If the difference vector is time-like:

So lies in the interior of the reverse or forward light cone of, depending on whether it has occurred before or after. Then it may be, in the cause or the effect of the slower effect than light. Events within the reverse or address the past light cone were once visible to an observer, who was at the same point in space as ( without taking into account the expansion of the universe).

If the difference vector space-like:

So is out of reverse or forward light cone. The events may not have to be cause and effect, because then would have a cause with superluminal velocity impact. Events outside of the reverse or address the past light cone and above are for an observer who is staying in, not (yet) visible ( event horizon, without taking into account the expansion of the universe ).

Follow for the solution of differential equations of relativistic

The solution of the inhomogeneous Klein-Gordon equation, valid for bosons depends, for the event only on the previous initial conditions as well as the inhomogeneity on the backward light cone of, and in its interior.

The solution of the homogeneous Klein-Gordon equation ( vanishing mass, corresponds to the wave equation ) depends only on the initial conditions and of the inhomogeneity on the backward light cone of, but not more of the inhomogeneity in its interior. Initial conditions and inhomogeneity will, in this case, only the speed of light.

The consequences for the solution of other fundamental relativistic equations (eg, the Dirac equation, valid for fermions ) are accordingly.