# Temporal order of events seen by different Lorentz observers

1. Apr 25, 2016

### spaghetti3451

1. The problem statement, all variables and given/known data

Three events, $A$, $B$, $C$, are seen by observer $\mathcal{O}$ to occur in the order $ABC$. Another observer, $\mathcal{\bar{O}}$, 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.

2. Relevant equations

3. The attempt at a solution

Here's a particular placement of the events $A$, $B$, $C$ in the order $ABC$ as seen by observer $\mathcal{O}$ ($t$-$x$ coordinate system) and in the order $CBA$ as seen by observer $\mathcal{\bar{O}}$ ($t'$-$x'$ coordinate system):

I find that not all placements of the events $A$, $B$, $C$ on the spacetime diagram simultaneously produce the orders $ABC$ and $CBA$ as seen by two different observers $\mathcal{O}$ and $\mathcal{\bar{O}}$.

How I proceed with demonstrating whether or not a third observer sees the events in the order $ACB$?

2. Apr 25, 2016