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Can You Go the Speed of Light?

Einstein's classic thought experiment involves sitting on a train travelling at the speed of light. If you hold a mirror in front of your face, will you see your reflection in a mirror? How could light from your face reach the mirror if the mirror is travelling away from you? But it would be a pretty spooky train if you couldn't see your reflection so Einstein felt this solution wasn't realistic. On the other hand if you could see your reflection, it would mean light was travelling at the speed of light inside the train. But that meant the same light observed from outside the train would be going twice the speed of light. This again seems inconsistent. So Einstein resolved that you must see your reflection but that light must travel at the same speed inside and outside the train. The only way this is possible is if space and time are perceived differently by observers inside and outside the train.