spacelike

Spacelike is a term used in relativity to describe a type of separation between two events or, more generally, a type of vector or curve whose spacelike character is determined by the spacetime metric. Intuitively, two events are spacelike separated if the spatial distance between them is greater than the distance light could travel in the time interval separating the events. In such a case no signal or causal influence traveling at or below the speed of light can connect the events.

In mathematical terms, spacetime intervals can be classified as spacelike, timelike, or null (lightlike). Depending on the common metric convention, a spacelike interval is described by a positive or negative squared interval (for example, Δs^2 > 0 in one convention and Δs^2 < 0 in another). The important point is that the sign of the interval is invariant under Lorentz transformations, so all observers agree on the causal character of the separation. A spacelike separation lies outside the light cone of either event; timelike separations lie inside the light cone, and null separations lie on the light cone.

Spacelike can also describe vectors or curves. A spacelike vector has a positive norm in Minkowski spacetime, and a spacelike curve has a tangent vector that remains spacelike along its length. Spacelike surfaces, or hypersurfaces, are used in physics to represent “instantaneous” slices of space in a given frame, though the notion of simultaneity is frame-dependent in general relativity.

In summary, spacelike denotes separations or directions that cannot transmit causal influence at or below light speed, and its classification is a fundamental, frame-invariant aspect of spacetime structure.