"Two firecrackers A and B are placed at x' = 0 and x' = 100 ns, respectively, on a train moving in the +x direction relative to the ground frame. According to synchronized clocks on the train, both firecrackers explode simultaneously. Which firecracker explodes first according to synchronized clocks on the ground? Explain.
The Attempt at a Solution
Ok, so my logic is a person standing in the middle of the train will receive the light signal from A and B at the same time and hence will record the events as simultaneous. If you take that person and remove him from the train, A is moving towards him and B is moving away with him so thus it takes less "time" for light from A to hit that observer and thus A will be seen to explode first.
My question is, which would explode first would seem to depend on the position of the observer and from my understanding of relativity - the observation from the rest frame should be independent of the observer - is it something I'm missing from the definition of synchronized clocks?