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I'm trying to understand the famous train-platform thought experiment ( http://www.bartleby.com/173/9.html ). I understand part of the Theory of Relativity is that the speed of light is the same whether the observer is moving or not.

Does the train-platform thought experiment depend on the fact that the speed of light is the same for the observer in the train and the observer on the platform?

Suppose instead of two lightning bolts hitting the front and back of the train, we had two cannonballs hitting the front and back of the train, and the observers were listening for the sound of their impact.

In the above case we'll be using sound waves instead of light, and the velocity of sound waves can be added to the velocity of the train normally, would that change the results of the thought experiment?

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Yes. To see this, consider the velocity addition formula, $$v \oplus w = \frac{v+w}{1+vw/c^2}$$ where $\oplus$ means velocity addition in special relativity.

When $v$ and $w$ are small, the right-hand side is just $v+w$, so the normal rules of Galilean relativity apply. When you're dealing with light, the formula reduces to $c \oplus w = c$. So yes, the results of the experiment do change if you replace the light waves with sound waves.

If you dial up the speed of your sound waves, the result will gradually change between the intuitive, Galilean result and the special relativity result. In fact, if you could make your sound waves go near the speed of light, everybody in the thought experiment would die in a blazing inferno. But, you'd also get the same result as you would have for light waves. The thought experiment works for anything going at speed $c$, not just light.

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If there are 2 points of special relativity they are:

1) The speed of light (in a vacuum etc) is constant in all reference frames
2) Simultaneity is relative

So yes c is the same on the platform and on the train and everywhere else but may be experienced differently (through time) in different reference frames.

If the lady on the train went from the middle carriage to the locomotive carriage and turned on a torch/looked at the lights at the front of the train, that light would still be moving away from her at the speed of light, even if the train itself was travelling at relativistic speeds. A man on the platform would see the train moving away from him at relativistic speed and the light travelling away from him at c

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