How can simultaneity and the constant speed of light stay coexist.

[fa7alerr0r]

Watch this video and tell me shouldn't the passenger in the train see both lightning strikes at the same time considering that light speed is perceived as the same speed no matter how fast you travel or where it comes from? Watch both these vids.
http://www.youtube.com/watch?v=8JKdqKtNPsU&feature=related

 

[Janus]

Because of the way the experiment is set up, the observer on the platform sees the strikes at the same time, and sees the flashes reach the train observer at different times. And both observers have to agree as whether the flashes reach either observer at the same time or not.

If the train observer saw both flashes at the same time then they would see the flashes arrive at the platform observer at different times and then you would have a contradiction as the platform observer sees just the opposite.

 

[JesseM]

Watch this video and tell me shouldn't the passenger in the train see both lightning strikes at the same time considering that light speed is perceived as the same speed no matter how fast you travel or where it comes from? Watch both these vids.
http://www.youtube.com/watch?v=8JKdqKtNPsU&feature=related

The point is that since the train-observer does think the light from each strike traveled towards him at the same speed, the only way he can square this with the fact that the light from each strike reached him at different times is to conclude the strikes actually occurred at different times in his frame. If there are two trees on either side of me and both are exactly 50 feet away from me, and at 3:00 I see lightning strike one tree and at 4:00 I see lightning strike the other tree, there's no reason this should conflict with the idea that the light from each strike took the same time to reach me, since I can just conclude one strike happened an hour later than the other one.