Special Relativity and the Relativity of Simultaneity.

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alingy1
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The position of the rocket is not specific. We just know that it is at the left of the galaxy. We know that R will explode first in the rocket's frame.

Maybe the galaxy could be moving fast enough so that the time it takes for L to explode is enough for the rocket to see R's light first. In other words, in the time delay L explodes after R, maybe the galaxy could go past the rocket (end up to the left of the rocket). If the galaxy ends up to the left of the rocket and L explodes after that, then R is for sure the first light that the rocket sees.

http://imgur.com/1vzsRWW
 
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What did the problem statement say about the relationship between the rocket and the galaxy? Does it suggest to you any reason why your reasoning might be flawed?
 
Hi, the rocket "enters the galaxy from left". That does NOT mean that after R explodes, in the time it takes for L to now explode, the rocket could now be to the right of the galaxy.