Spacetime diagram

A spacetime diagram is a way of plotting some events in space and time, in a static image.

The two axes are space (usually $x$) and time, with the units set such that light moves at $45\degree$. Lines represent motion and straight lines represent inertial motion.

We can draw several sets of axes in the same spacetime diagram to represent several reference frames. Following from the Lorentz transform, a moving reference frame will have its $x$ and $t$ directions be a combination of $x$ and $t$ of a stationary frame.

Looking at this diagram, it’s clear that two events that are simultaneous in one frame are not necessarily simultaneous in another.