Direct computation using the Lorentz transformations shows that \begin{eqnarray} x'^2 - \csq t'^2 &=& \gamma^2 \, (x-vt)^2 - \gamma^2 \,\left( \cc t - \vc x\right)^2 \nonumber\\ &=& x^2 - \csq t^2 \end{eqnarray} so that the quantity $x^2 - \csq t^2$, known as the interval, does not depend on the observer who computes it. We will explore this further in later chapters.