In relativity, why does spacetime diagram have position on $x$-axis and time on $y$-axis? In regular Newtonian physics, we use $ x(t) - t$ graph to under position of a particle but why is it that in special relativity that we switch up the axis notation? I was seeing the lecture by Leonard Susskind and, after one hour, I came under the impression that it is just a relabelling of an the axes because, I think it'd be possible to write every derivation said in the $t-x$ in the $x-t$ plane. Or is there something more deep about it which I am missing?
 A: It is merely a convention. It has no particular importance or significance.
A: I believe the reason for this is because in the first spacetime diagrams Minkowski was using a pseudo-euclidean metric with a complex time
$$
ds^2 = (icdt)^2 + dx^2 
$$
But the convention is that complex quantities are plotted on the y-axis. And so Minkowski chose to also draw the the (complex) time on the y-axis and the (real) position on the x-axis.
Later the pseudo-euclidean metric fell out of fashion, but the habit of drawing the time on the y-axis in spacetime diagrams stayed.
I believe that from a pedagogical point of view this is a bad convention and the physics community should stop using it. It simply does not make a lot of sense to plot $t(x)$ instead of $x(t)$. For example, the slope of a $x(t)$ curve is the velocity. But the slope of a $t(x)$ curve is the inverse of velocity, a quantity which just helps to confuse students.
A: It makes past and future clearer, with past being down and future up, rather than having to remember which is right and left.
A: It doesn't matter. You can switch things: put position in the vertical axis and time in the horizontal axis. This time around though, the worldline for clocks at fixed position will be horizontal lines instead of vertical
