Spacetime entails a new concept of distance. Whereas distances in Euclidean spaces are entirely spatial and always positive, in special relativity, the concept of distance is quantified in terms of the space-time interval between two events, which occur in two locations at two times:
(spacetime interval),
where:
c is the speed of light,
Δt and Δr denote differences of the time and space coordinates, respectively, between the events.
(Note that the choice of signs for s2 above follows the Landau-Lifshitz spacelike convention. Other treatments reverse the sign of s2.)
Space-time intervals may be classified into three distinct types based on whether the temporal separation (c2Δt2) or the spatial separation (Δr2) of the two events is greater.
Certain types of worldlines (called geodesics of the spacetime) are the shortest paths between any two events, with distance being defined in terms of spacetime intervals. The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences.