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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.

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It is more than you want, but in the following paper Alexandrov shows that if chronological order is defined by cone (i.e. event $x$ chronologically precedes $y$ if $y − x$ belongs to some fixed cone) then any map which preserve the chronological order is linear. (I think this statement was later reproved independently 5 times or so.)

Alexandrov A.D. Contribution to chronogeometry Canad. J. Math. - 1967.- V.19, N.6. - P.1119-1128.

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