It is more than you want, but in the
The following paper Alexandrov shows that if chronological order on $\mathbb R^n$ is defined by cone (i.e. event i.e., $x$ x\in \mathbb R^n$ chronologically precedes $y$ if y\in \mathbb R^n$ iff $y − x$ belongs to some fixed cone) then any map bijection which preserve the chronological order is has to be linear.(I think this statement was later reproved independently 5 times or so.)
This statement is much stronger than you need. After Alexandrov, it was reproved independently 5 times or so.