It is very long time ago that I took a physics lesson, so I want to refresh my memory. I think I learned that there is only one inertial frame in Minkowski spacetime (or special relativity time) that $ct$ and $x$ are orthogonal. (inertial frames are assumed as Lorentz-invariant, and we assume one space axis, $x$.) So, why is it?
($ct$ is in vertical axis, $x$ is in horizontal axis.)
To avoid confusion: I think I found a question on my old textbook :)
Edit: orthogonality in Euclidean term is assumed.
Show that the $S'$ axes, $x'$ and $ct'$, are nonorthogonal in a spacetime diagram. Assume that the $S'$ frame moves at the speed of $v$ relative to the $S$ frame ($S'$ is moving away from $S$ to the side of $+x$) and that $t = t' = 0$ when $x = x' = 0$. (The $S$ axes, $x$ axis and $ct$ axis, are defined orthogonal in a spacetime diagram.)