Space-like separated events are events that, in a well-chosen reference frame, can take place at the same time but never happen at the same location.
On the other hand for time-like events, one can chose a reference frame such that they happen at the same place but never simultaneously.
I can't help thinking that the labels are therefore very ill-chosen… Is there another motivation for these names?
Best Answer
Suppose you draw a spacetime diagram and measure the angle of your trajectory to the spatial and time axes. You'll find time like trajectories are more nearly parallel to the time axis - i.e. the angle the trajectory makes to the time axis is smaller than the angle it makes to the spatial axis. Conversely space like trajectories are more nearly parallel to the spatial axis. This seems to me a plausible origin for the terms.