Spacetime & four-vectors

light cone

Picture a single flash of light going off at one event and spreading outward in all directions. In a spacetime diagram, that expanding sphere of light traces a cone opening upward into the future. There is a matching cone opening downward into the past — the set of all light rays that could have converged on this event. Together these two cones form the light cone of the event.

The light cone is more than a pretty shape: it sorts the rest of spacetime into three sharply separate regions. Everything inside the upper cone is the event's absolute future — places and times it could possibly influence, since you could reach them without exceeding light speed. Everything inside the lower cone is its absolute past, the events that could have influenced it. Everything outside both cones is the 'elsewhere': too far away in space, in too little time, to be reached by anything — causally cut off.

What makes this structure profound is that everyone agrees on it. Two observers moving differently will tilt their time and space axes and disagree about durations, but they never disagree about whether an event lies inside or outside a given light cone. The light cone is the same for all of them because the speed of light is the same for all of them, and that shared agreement is what keeps cause and effect in a fixed order for the whole universe.

future cone: c t > sqrt(x^2 + y^2 + z^2), t > 0

The future light cone holds every place reachable from the event without exceeding light speed.

Events in the 'elsewhere' (outside both cones) cannot be ranked in time in any absolute way — different observers can disagree about which came first. Only events inside someone's light cone have a fixed before-and-after that everyone shares.

Also called
null cone光锥结构