PX155 - G4 - relativity of simultaneity

3 observers, all at rest in frame $S^{'}$ . $B$ sends light pulses to $A$ and $C$ at the same time. $E_{A}$ , and $E_{B}$ represent events of the light pulses reaching $A$ , and $B$ respectively
space-time diagram in $S^{'}$
- light covers a distance, $Δ x^{'} = c t^{'}$ , after time, $t$ , so, world line of light pulses is at $\pm 45 °$ from the x-axis. $A$ , $B$ , and $C$ have constant $x$
- events $E_{A}$ , and $E_{B}$ are simultaneous
now consider some process in $S$
- $A$ , $B$ , and $C$ are moving, so, world lines are at an angle
- light still has world lines at $\pm 45 °$ , as per RP2
- times of $E_{A}$ , and $E_{B}$ are different $⟹ t = t^{'}$ is no longer true