Light-cone

The light-cone of an event E is the locus of all spacetime events that can be connected to E by a light signal. In 1+1 dimensions it appears in a spacetime diagram as a pair of lines through E at slopes ±c (45° in units c = 1); in 1+3 dimensions it is a 4D double cone with apex at E. The light-cone partitions spacetime into three causally distinct regions. The future light-cone contains all events E can causally affect — points lying on or inside the upper cone, reachable by sub-c or null signals from E. The past light-cone contains all events that can causally affect E. The elsewhere region — outside both cones — contains events spacelike-separated from E, with no possible causal contact.

The light-cone is the fundamental structure encoding relativistic causality. Lorentz transformations preserve it: every inertial observer agrees on which events lie inside, on, or outside the light-cone of any given event. A massive particle's world-line at any instant lies strictly inside its instantaneous future light-cone (timelike everywhere), a photon's world-line lies on the cone (null everywhere), and tachyonic world-lines would lie outside (spacelike everywhere) — which is one of the structural reasons no consistent theory of subluminal-to-superluminal transitions has been found. In general relativity the light-cone tilts with curvature; black hole event horizons are exactly the surfaces where the future light-cone tips over so that all timelike futures point inward toward the singularity.