Space-like
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In the context of special relativity, space-like separated points (or events) in spacetime have a spacetime interval less than 0 (see sign convention). This means that the events cannot be causally connected (i.e. one cannot be a cause or effect of the other) because light from one event cannot reach the other. Observers in different reference frames may therefore see the events as occurring in either order or simultaneously.
A space-like surface is a submanifold of spacetime whose dimensions correspond to spatial dimensions of spacetime (e.g. x,y,z).