Causality and the Light Cone

An inertial observer sits at the origin of his rest frame. The points in 4D Minkowski space that have an (invariant) 4D spacetime interval of zero, \bgroup\color{black}$ s^2=0$\egroup from the observer form a 4D cone. \bgroup\color{black}$ s^2=0$\egroup is a lightlike separation, that is, the cone consists of the points in the future that can be reached by light emitted by the observer plus the points in the past from which light could be reaching the observer. (The 4D cone is basically a spatial 3D sphere for every time. The size of the sphere grows with the time difference from the present.) This is referred to as the light cone. Often this light cone is pictured in the time dimension plus two space dimensions to make it understandable.

The cone divides space into the causally connected future, the causally connected past, and elsewhere. Events that are elsewhere, cannot affect the observer in the present, nor can the observer affect those events because he cannot move or signal faster than the speed of light. It is however possible that some past event from elsewhere can reach the observer in the future.

Jim Branson 2012-10-21