Relativity of Simultaneity & C Invariance Doubts

[printfede]

Hi all, I'm trying to understand relativity for the first time. First of all I'm sorry for my bad English, I'll try to be as clear as possible.
My doubt is the following: In my books and on many web sites I have red the thought experiment of the train and the two bolts of lightning to explain the relativity of the simultaneity ( like that in this video). In this thought experiment the observer on the train perceives the two events (the bolts of lightning at the end of the vehicle) as not simultaneous because, going to the right, he is reached first by the light beam coming from the right, though he is at the same distance from both events. But I think it implies that if the train has a speed of v in relation to the ground, the speed of the light beam coming from the right in relation to the train should be c+v, and that of the light beam coming from the left c-v, because if the speed of the two beams of light were c for both the beams the observer on the train would be reached simultaneusly by them, but it's in contrast to the SR imho.
If i wasn't clear please tell me. Thanks in advance.

 

[Doc Al]

because if the speed of the two beams of light were c for both the beams the observer on the train would be reached simultaneusly by them, but it's in contrast to the SR imho.

No. You could only conclude that if the two lightning flashes occurred simultaneously according to the train frame observers. But they don't.

The argument is this: Looking at things from the ground frame, we can prove that the light from each flash will reach the observer in the middle of the train at different times. (This is a fact true for everyone.) Then using this fact, and the fact that the speed of light is c for everyone, we can deduce that the lightning flashes could not have occurred simultaneously in the train frame.

 

[printfede]

Thanks for the answer. Brief and clear.