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Spacelines and Timelines

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A spacetime is the set of all points of a space in all its moments of time, and it is depicted by the whole two-dimensional surface of a graph. A spaceline (space dimension) is the set of all points of a spacetime that coexist in a specific moment of time, i.e. all points that have the same time coordinate (isochronal line). The timeline of a spacepoint is the set of all points of a spacetime that have the same space coordinate as the spacepoint. This is also the timeline of a stationary object. Obviously, we can also define in a similar manner spacesurfaces and spacevolumes, and timesurfaces and timevolumes.

Thus a spacepoint (a space coordinate) defines a timeline (or a timesurface in a 2+1 spacetime, or a timevolume in a 3+1 spacetime), and a timepoint (a time coordinate) defines a spaceline (or a spacesurface in a 2+1 spacetime, or a spacevolume in a 3+1 spacetime). Finally, we can define the timeline of a moving object as the set of all points that satisfy the motion equation of the object.