The Real Meaning of the Spacetime-Interval

The spacetime interval is measured in light-meters. One light-meter means the time it takes the light to go one meter, i.e. $3\cdot 10^{-9}$seconds. One can rewrite the spacetime interval as: $\Delta s^{2}=c^{2}(\Delta t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}]$. There are three possibilities: a)$\Delta s^{2}=$0 which means that the Euclidean distance $L_{1}L_{2}$ between locations $L_{1}$ and $L_{2}$ is travelled by light in exactly the elapsed time $\Delta t$. The events of coordinates (x, y, z, t) in this case form the so-called light cone. b)$\Delta s^{2}>0$ which means that light travels an Euclidean distance greater than $L_{1}L_{2}$ in the elapsed time $\Delta t$. The below quantity in meters: $\Delta s=\sqrt {c^{2}(\Delta t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}} ]$ means that light travels further than $L_{2}$ in the prolongation of the straight line $L_{1}L_{2}$ within the elapsed time $\Delta t$. The events in this second case form the time-like region. c)$\Delta s^{2}<0$ which means that light travels less on the straight line $L_{1}L_{2}$. The below quantity, in meters: -$\Delta s=\sqrt {-c^{2}(\Delta t)^{2}+[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}} ]$ means how much Euclidean distance is missing to the travelling light on straight line $L_{1}L_{2},$ starting from $L_{1}$ in order to reach $L_{2}$. The events in this third case form the space-like region. We consider a diagram with the location represented by a horizontal axis $(L)$ on \textit{[0, }$\infty ),$ the time represented by a vertical axis $(t)$ on \textit{[0, }$\infty ),$ perpendicular on $(L),$ and the spacetime distance represented by an axis ($\Delta s)$ perpendicular on the plane of the previous two axes. Axis ($\Delta s)$ from \textit{[0, }$\infty )$ is extended down as $(-\Delta s)$ on \textit{[0, }$\infty ).$