# Basic special relativity question

1. Jan 15, 2009

### theneedtoknow

1. The problem statement, all variables and given/known data
Three rockets are lined up in a straight line an equal distance from each other and are moving at the same speed (in other words they are at rest wrt each other). The line of 3 rockets passes an observer, and, at the exact moment that the middle rocket passes the observer, the front and back rockets emit light pulses simultaneously (in the rockets' rest frame).
Do the pulses reach the middle rocket simultaneously? If not, which one arrives first?
According to the observer they passed, were the light pulses emitted simultaneously? If not,
which pulse was emitted first. Explain.

2. Relevant equations

3. The attempt at a solution
for the first part, i think they reach the rocket simultaneously since in their rest frame they are an equal distance from each other and at rest so both pulses will reach the middle rocket after a time of d/c where distance is the constant distance in betweenrockets.

Now he second part has me a bit confused
if the pulses reach the midde rocket simultaneously in one frame of reference, it means they reach it simultaneously in all frame, so the observer will see them reach the middle rocket simultaneously. Now, since th rockets are all moving in the same direction, it means that by the time the pulses reach the middle rocket, it would have moved closer to the spot where the front rocket emitted its pulse and away from the spot that the back rocket emitted its pulse, so to retain simultaniety, the observer would think that the back rocket emitted its pulse first, and the front rocket emited it second.
BUT I would also think that , since as the middle rocket passes the observer, the front and back rockets are equidistant to the observer at that point, wouldn't the pulses still be simultaneous and reach the observer at the same time BUT reach the middle rocket at different times? Obviously one of these 2 ways of thinking is wrong, so can someone point out whats the problem with one of them?

2. Jan 15, 2009

### Staff: Mentor

Good thinking. Everyone agrees that the pulses reach the middle rocket simultaneously.
That's right. According to the observer, the pulse from the back rocket has a greater distance to travel and thus must have been emitted first in order to arrive at the same time as the other pulse.
While it's true that the front and back rockets are equidistant from the observer at that moment, that doesn't mean the pulses are emitted simultaneously according to the observer. And if the pulses arrive at the middle rocket at the same time, everyone must agree on that fact.

3. Jan 15, 2009

### theneedtoknow

Oh I understand now :) Thank you very much! :)