Spacetime

\[s^2 = (ct)^2 - x^2 - y^2 - z^2\]

\[ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2\]

(My mess here:)

And as ds approaches zero, gives us

\[0 = c^2dt^2 - dx^2 - dy^2 - dz^2\]

or

\[dx^2 + dy^2 + dz^2 - c^2dt^2 = 0\]