Simultaneity Question

This question is from an IB exam in may, 2003 and i'm having a little trouble understanding how they got their answer.

The question is, Person A is in a carriage that is travelling in a straight line with uniform speed relative to person B who is standing on the platform. Person A is halfway between two people, X and Y, who are at either end of the carriage. At the moment person A is directly opposite person B as they pass each other at the station, X and Y both light a match, assume it's instantaneous. According to person A the events are simultaneous.
Discuss whether the two events will appear to be simultaneous to person B.

The answer is that they will not appear to be simultaneous. And the IB awards marks for thinking along these lines.
1) B sees A move away from the signal from X and since A receives them at the same time;
2) and since c is independent of the motion of the source;
3) B will see the light from X first / light from Y will reach B after light from X

The problem i've got is their first point, that A receives them at the same time. This is only his reference frame and they're using this 'fact' to prove a point in another reference frame. I wouldn't have thought it's possible to do that. Also wouldn't person B believe that person A doesn't seem them simultaneously? How would you answer the question without using the IB's first premise? or is there some other mistake?
 
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Doc Al

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theelusivecamel said:
The problem i've got is their first point, that A receives them at the same time. This is only his reference frame and they're using this 'fact' to prove a point in another reference frame. I wouldn't have thought it's possible to do that. Also wouldn't person B believe that person A doesn't seem them simultaneously? How would you answer the question without using the IB's first premise? or is there some other mistake?
Careful. While the two matches being lit at the same time is only true from A's reference frame, all frames will agree that the light from the two matches will reach A at the same time. (If the light didn't reach A at the same time, then A would conclude that they couldn't have been lit at the same time, according to his frame, since they are equally distant from A.)

Simultaneity of spatially separated events (like the lighting of the two matches) is frame dependent. But when things happen at the same time and at the same place (like the receipt of the light from match X and match Y at A), all frames will agree.
 
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Alright now for a more basic question. I've also seen examples where lightning strikes outside the carriage on either side and since A moves between the lightning strike and the light reaching him they don't seem simultaneous. how is that different from the match example if the motion of the source doesn't matter?
 

Doc Al

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It's not different at all. The only thing that matters is: What frame measures the lightning strikes (or match lightings) to be simultaneous? We know that if one frame measures the strikes as occuring simultaneously, the other frame will not.
 

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