This is sort of a long post but I have to explain the following situation in order to ask the question so bare with me. Lets say two people, person A and person B, are on opposite ends of a train moving at a constant velocity and another observer is at rest on the platform outside (most of you have heard this I'm sure). Person A is at the front of the train and person B at the back. They have agreed to set their wrist watches to 12:00 as soon as the light from a light bulb in the middle of the train reaches them. So, the light bulb is switched on and they both set their clocks to 12:00 simultaneously because from their perspective, the light had to travel an equal distance from the middle to reach both of them, and therefore they both set their clocks at the same time. However, person C on the platform outside who was standing still watching claims that person B set his clock before person A. This is because from his perspective, person B (in the back) is moving toward the light while person A (in the front) is moving away from it and therefore, the light had to travel less distance to reach person B. Since light is constant in all frames of reference, person C will indeed claim that it took the light longer to reach person A than it did to reach person B. Both claims are equally valid and both are justified in their reasoning, so both answers are equally correct. This all makes perfect sense to me and thats all great. But here's my question, finally. Since person C sees the light reach person B before it reaches person A, person C will conclude that person B set his clock BEFORE person A. So to person C, or anyone else on the platform, when it is say 12:05 on person B's clock, it will only be 12:03 on person A's clock (the precise number depends on the length and speed of the train but that's not relevant to the point being made). Again, this all makes sense to me. But now what if the train were to immediately stop and person A and B were to get out and confront person C. Now that all of their perspectives are equal, they should all agree upon the readings of both clocks (they have to if they're all standing there looking at them). But how is it that suddenly when the train stopped, it put the clocks back on equal footing from person C's perspective. If person C saw that the two clocks were different (12:05 and 12:03) when the train was moving, than even if the train slowed down and eventually stopped, wouldn't person C still claim that since person A and person B both slowed down and stopped at the same rate, their clocks also slowed down at the same rate and hence would still not be synchronized? What is it about the stopping of the train that puts person C's perspective on equal footing with person A and person B? Clearly I'm missing something, please help! Again I'm very sorry for the long post but this things been buggin me for a while. Thanks.