Lorentz Contraction and its Derivation

Observe moving objects near the light speed from a static system. Then, the object looks shorter than the original length (the length when the object stopped). This phenomenon is called Lorentz contraction.

Let \(L_0\) be the length of the bar when the object is stopped and \(L\) the length of the moving bar observed from the static system. Then, the following relationship holds between the two. However, it is assumed that the system S’ is moving at a speed V in the x direction with respect to the system S and the bar is moving with the system S’.

\begin{eqnarray} L&=&L_0\sqrt{1-\frac{V^2}{c^2}}\\&=&L_0\sqrt{1-β^2} \end{eqnarray}


Lorentz Transformation


Most relativity theory book starts with Lorentz transformation. Lorentz transformation is to connect time and space of two systems that have different motion.

Unlike the classical mechanics and electromagnetism we have learned so far, the theory of relativity is incredible at first sight. For example, according to the theory of relativity, an object with mass can not catch up with the speed of light. In addition, if you are moving at a speed close to light, the time progresses slowly for you. Let’s consider the meaning of Lorentz transformation carefully by reading this article.