Exercise 1.03

Three events, $A$, $B$, $C$, are seen by observer $\mathcal{O}$ to occur in the order $ABC$. Another observer, $\tilde{\mathcal{O}}$, sees the events to occur in the order $CBA$. Is it possible that a third observer sees the events in the order $ACB$? Support your conclusion by drawing a spacetime diagram.

In two or more dimensions, it is possible to see the same three events in any order. In the following diagram, the circles represent the light cones of the events at different instants. The observers are static in this reference frame. $\mathcal{O}'$ is the observer seeing the events in the $ACB$ order.