Spacetime
The 4-dimensional pseudo-Euclidean manifold of events introduced by Hermann Minkowski in 1908, in which the three spatial coordinates and time enter on equal footing. The geometric arena of special relativity; the substrate on which world-lines, light-cones, and the invariant interval are defined.
Definition
Spacetime is the four-dimensional pseudo-Euclidean manifold introduced by Hermann Minkowski in 1908 as the geometric arena of special relativity. Each point in spacetime is an event — a location in space at a definite time — and the three spatial coordinates (x, y, z) enter on equal footing with the time coordinate (ct). Lorentz transformations are pseudo-orthogonal rotations of this 4D manifold preserving the indefinite-signature metric ds² = c²dt² − dx² − dy² − dz²; observers in different inertial frames disagree on which slice constitutes "now," but all agree on the spacetime distance between any two events. Spacetime is a stage on which physical history unfolds, not a substance: it has no aether, no mechanical properties, no rest frame.
Minkowski announced the reformulation in his Cologne lecture of 21 September 1908, opening with the now-famous declaration that "henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." Einstein, his former student at the ETH Zürich, had initially regarded the geometric reformulation as superfluous mathematical decoration; by 1912, working on what would become general relativity, he had come to depend on it completely. The Minkowski metric is the flat-space limit of the metric tensor of general relativity; the entire structure of relativistic physics — kinematics, dynamics, electromagnetism, the Standard Model — is built on top of spacetime as its base manifold.