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}