Any two points in a Euclidean space determine a unique line, but I wasn't sure if this result generalized to Minkowski spacetime given that the latter is not a Euclidean 4-space, but is, instead, a Euclidean 3-space plus a fourth temporal dimension.
Points in Minkowski spacetime are events and you can draw a straight line through any two events which are time-like or light-light separated to get the worldline of an inertial particle which is present at both events.
If the events are space-like separated, a single particle cannot be at both (its motion would be tachyonic) but you can define an inertial frame in which the events are simultaneous. In that frame, the two points define a line in the usual way but at a single epoch.
RGT: If you mean by "line" a generic world line, the answer is no, ...
Why not? Remember the question is relation to Minkowski spacetime only.
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