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Proper length is a relativity concept. It is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous. (Unlike classical mechanics, simultaneity is relative in relativity. See relativity of simultaneity for more information.) In special relativity, the proper length L between spacelike events is , where Along an arbitrary spacelike path P in either special relativity or general relativity, the proper length is given in tensor syntax by the line integral , where Proper length is analogous to proper time. The difference is that proper length is the invariant interval of a spacelike path while proper time is the invariant interval of a timelike path. For more information on the path integral above and examples of its use, see the proper time article.
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