A Critical Examination on the Lorentz Contraction of a Rod

Abstract

When studying special relativity, we usually find Lorentz contraction as one of the most clear and
straightforward consequences of the Lorentz Transformation. The derivation of Lorentz contraction
from Lorentz Transformation is apparently so simple that we usually overlook an important ideal
assumption. A body which is Lorentz contracted is assumed to exist in infinite time in its rest frame
of reference. In this paper we will derive Lorentz contraction without that assumption. We will
derive Lorentz contraction (using spacetime diagram) of a rod with finite lifetime in its rest frame of
reference. The result is such that the famous Lorentz contraction formula is only valid in certain
condition concerning the lifetime of the rod.