Two lights are 1000 ns apart along a stretch of railway track. In the ground frame, the west light flashes $600 \mathrm{~ns}$ before the east light flashes. Could these flashes be simultaneous in the frame of a train moving along the track at a certain speed (that is less than the speed of light)?
A) Yes, if the train is moving east at the correct speed.
B) Yes, if the train is moving west at the correct speed.
C) Yes, if the train observer happens to be at the right distances from the lights when receiving their flashes.
D) No, the flashes cannot be simultaneous in any frame.

Question

Quizplus · Accepted Answer

According to the theory of relativity, simultaneity is relative and depends on the observer's frame of reference. If the train is moving east, towards the direction from the west light to the east light, the speed of the train can be adjusted such that in the train's frame, the light from both flashes arrives simultaneously. This is due to the relativistic effects of time dilation and length contraction.  See figure 3 below. If the train moves eastward and has a speed of $600 \mathrm{~ns} / 1000 \mathrm{~ns}$ or $3 / 5$, then the $x$ ' axis of the train frame will connect both events, meaning that they are simultaneous in the train frame.
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Two Lights Are 1000 Ns Apart Along a Stretch of Railway