In
relativistic physics,
proper length is an
invariant measure of the
distance between two
spacelike-separated
events, or of the length of a spacelike
path within a
spacetime.
The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of simultaneity is dependant on the observer. Proper lengths provide an invariant measure, whose value is the same for all observers.
Proper length is analogous to proper time. The difference is that proper length is the invariant interval of a spacelike path or pair of spacelike-separated events, while proper time is the invariant interval of a timelike path or pair of timelike-separated events.
In special relativity, the proper length between two spacelike-separated events is the distance between the two events, as measured in an inertial frame of reference in which the events are simultaneous. So if the two events occur at opposite ends of an object, the proper length of the object is the length of the object as measured by an observer which is at rest relative to the object.