at the time zero form a cone called the light-cone with its apex at
. Straight lines passing through
and contained within the light-cone are possible world-lines, or time directions; those passing through
but lying outside the cone constitute possible space directions for appropriate observers, or again possible loci of simultaneous events. Of course each point-event taken as point of departure gives rise to a light-cone, so that in a general way we may say that all lines parallel to lines contained within any given light-cone and passing through its summit constitute possible world-lines or time directions. It is thus apparent that any light-cone defines limiting directions in space-time. All lines whose slant is less than that of the generators of the cone are possible time directions, while all those whose slant is greater are possible space directions. We thus realise the importance of the light-cone in defining the particularities of structure of space-time. In the case of four-dimensional space-time the cone becomes a three-dimensional surface, which it is not easy to visualise, but this, of course, need not trouble us when we reason analytically.
And here a further point must be mentioned. Since no disturbance can reach us with a speed greater than that of light, the world-line of the disturbance can never lie outside the light-cone at whose apex we momentarily stand. In other words, the events of which we may become conscious (otherwise than visually) at a given instant will always be represented by point-events situated within the cone below us, in the direction of the past. Events which we perceive visually at an instant will always lie on the cone’s surface.
