I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario.
Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event $e_1$) and front of the train (Event $e_2$). Train is moving from left to right at a relativistic velocity $v$.
For an observer on the station, the light pulse travelling towards the rear has to travel a much lesser distance since the train is moving towards it. Let this distance be $0.5-vt$.
Obviously, station observer, who has a moving reference frame, sees the $e_1$ first.
Let us place another man at the back of the train, since he is at rest with the train, light has to travel $0.5$ (exactly half the length of the train) to reach him.
But according to the station observer for whom light has to travel only $0.5-vt$, the light reaches the man before it actually reaches him, in his own reference frame. How is the moving observer able to see an event before it even happened in the rest frame?