Spacetime

In special and general relativity, space and time are treated together as a single 4-D manifold called space-time. The idea is that, just as the x and y coordinates of a point depend on the axes one is using, so distances and time intervals may depend on the reference frame of an observer. Each point in space-time has four coordinates (t, x, y, z), and the space-time interval along a curve is defined by

ds² = dt² - dx² - dy² - dz²

in flat space, where units have been taken so that c = 1. Coordinate transformations have to leave intervals invariant, and they form a pseudo-metric very similar to distance in Euclidean space. However, note that whereas distances are always positive, intervals may be positive, zero, or negative.

See also:

• Manifold

• Metric space