How to obtain the Lorentz space contraction formula for a moving rod from knowledge of the positions of its ends at different times

Abstract

The Lorentz length contraction for a rod in uniform motion is derived performing two measurements at arbitrary times. Provided that the velocity of the rod is known, this derivation does not require the simultaneous measurement of two events. It thus avoids uncomfortable superluminal relationships. Furthermore, since the observer's simultaneous measurement is not needed in order to observe spatial contraction, this procedure is more akin to the Lorentzian relativity approach and is better suited for more general schemes such as deformed spacetime versions of special relativity. An example of a space contraction measurement from the same rest position in the observer's frame illustrates the procedure.