Spacetime is the union of space and time into a four-dimensional whole. More precisely, the inseparable four-dimensional manifold, or combination, which space and time are considered to form in the special and general theories of relativity. In the absence of a gravitational field, spacetime reduces to Minkowski space.


A point in spacetime is known as an event. Each event has four coordinates (x, y, z, t). Just as the x, y, z coordinates of a point depend on the axes being used, so distances and time intervals, which are invariant in Newtonian physics, may depend, in relativistic physics, on the reference frame of an observer; this can lead to bizarre effects such as length contraction and time dilation. A spacetime interval between two events is the invariant quantity analogous to distance in Euclidean space. The spacetime interval s along a curve is defined by the quantity


    ds2 = dx2 + dy2 + dz2 - c2dt2


where c is the speed of light. A basic assumption of relativity theory is that coordinate transformations leave intervals invariant. However, note that whereas distances are always positive, intervals may be positive, zero, or negative. Events with a spacetime interval of zero are separated by the propagation of a light signal. Events with a positive spacetime interval are in each other's future or past, and the value of the interval defines the proper time measured by an observer traveling between them.


On ultramicroscopic scales, the quantum nature of spacetime would become apparent and require a quantum theory of gravity to describe it.