# Can anyone clarify this example of Relativity of Simultaneity [closed]

While doing this course: http://www.worldscienceu.com/ I couldn't understand this example http://www.youtube.com/watch?v=53oAxycVhhg. (full example here https://www.youtube.com/watch?v=Iiugtmt18W4)

As from what I understand, what makes a thing inside a moving environment behave as if they were at rest is the fact that the velocity of the environment will be "added" to whatever new velocity is generated in the environment (i.g. : throwing a ball, jumping etc..). However in that example since the speed of light is constant the people in the train and outside the train should see the exact same thing! Can anyone clarify why this reasoning is not correct ?

EDIT: To avoid watching the video, I will try to explain the example: In a moving wagon a light beam is fired in both directions (front & back)from the middle of the wagon. The people inside the wagon seen the light beam reach both ends of the wagon at the exact same time while an outside observer would see it rear end being hit first then the front end.

## closed as unclear what you're asking by ACuriousMind♦, Gert, Bill N, user36790, CuriousOneJul 13 '16 at 6:46

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• We shouldn't have to click on links and watch videos to understand the question... – lemon Jul 12 '16 at 15:31
• Could you summarize the example so we don't have to watch the videos unless we want to? – heather Jul 12 '16 at 15:32
• @heather I've just updated the post with a description of what happens in the videos – silkAdmin Jul 12 '16 at 15:37
• You are right in that the addition of relative speeds do not work for light, light has the same speed on all reference frames, and that actually causes that the light does reach both ends at the same time inside the train and reaches the back first if seen from outside the train. – Wolphram jonny Jul 12 '16 at 15:39
• the reason is that for somebody outside the train the back is moving towards the light, and the front away from the light, so the distances that the light has to move to reach the edges are different for an observer at rest outside the train. – Wolphram jonny Jul 12 '16 at 15:46

To cut the long story short 'It is an experimental fact.'! The principle of relativity suggests that the laws of Physics must be the same in all the frames. Experiments suggest Maxwell's equations to be the correct laws of Physics. So a theorist can argue that everything that is suggested by Maxwell's laws should be true in all the frames. One of such things is that the speed of light is $\dfrac{1}{\sqrt{\mu_0\epsilon_0}}$. This must be true in all the frames. But, of course, nature can always surprise us so the ultimate test of the validity of this claim is the experiment. And it has been verified (to great accuracies) that the speed of light doesn't depend on the frame.