Spacetime geometry

In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum. Since 300 BCE, the spacetime of our universe has historically been interpreted from a Euclidean space perspective, which regards space as consisting of three dimensions, and time as consisting of one dimension, the "fourth dimension". By combining space and time into a single manifold called Minkowski space in 1908, physicists significantly simplified a large number of physical theories, as well as describing in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

In non-relativistic classical mechanics, the use of Euclidean space instead of spacetime is appropriate, because time is treated as universal with a constant rate of passage that is independent of the state of motion of an observer. In relativistic contexts, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of gravitational fields, which can slow the passage of time for an object as seen by an observer outside the field.

In physical cosmology, the concept of spacetime combines space and time to a single abstract universe. Mathematically it is a manifold whose points correspond to physical events. In a local coordinate system whose domain is an open set of the spacetime manifold, three spacelike coordinates and one timelike coordinate typically emerge. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space". For example, on the globe the latitude and longitude are two independent coordinates which together uniquely determine a location. In spacetime, a coordinate grid that spans the 3+1 dimensions locates events (rather than just points in space), i.e., time is added as another dimension to the coordinate grid. This way the coordinates specify where and when events occur. However, the unified nature of spacetime and the freedom of coordinate choice it allows, imply that to express the temporal coordinate in one coordinate system requires both temporal and spatial coordinates in another coordinate system. Unlike in normal spatial coordinates, there are still restrictions for how measurements can be made spatially and temporally (see Spacetime intervals). These restrictions correspond roughly to a particular mathematical model which differs from Euclidean space in its manifest symmetry.

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