Help with the theory of Relativity?

Question

In the train and mirror thought experiment conducted by Einstein both observers see light travelling at the same speed. However, the observer on the ground sees the light travel twice as far to reach the mirror. Since c = distance / time, this must mean that the observer outside the train saw the light take twice as long to reach the mirror. In other words, as seen from outside the train, time inside the train has slowed down.

I don't understand why the external observer sees the light travel twice as far to reach the mirror? Could someone perhaps rephrase this?

Answer 1

Hm...it's hard to explain exactly what it looks like.

I've studied this at school this year and I also couldn't understand it until one day we watched a video that showed exactly what both observers see.

It'd actually be alot easier if you were sitting right next to me now lol. I could draw it for you on a piece of paper quite easily.

Basically, I'll assume this is the scenario where you've got the beam of light that bounces up to the mirror, then down again. If you're sitting on the train, you're moving along with the light and you're in an inertial frame of reference so you're gonna see the light go up and down normally.

But a person standing outside the train (this is hypothetical - in reality you wouldn't see anything it'd go by so fast) sees the train going past them so the light is travelling from left to right AS well as up and down from the mirror. So, you see the bottom of these pictures http://static.howstuffworks.com/gif/rela... and the top of these pictures would be seen by the person ON the train (in the rest frame - it appears 'normal')

You'd think the light were travelling a greater distance, because the train is moving the light across your field of view at the same time.

Hope that explains it. It's alot easier if you see this sort of thing through an animation. Email me if you have any other question - I understand special relativity reasonably well for high school level this concept is just difficult to explain in words ;)

Answer 2

It has to travel a farther distance with regard to your persepctive. The page I included explains it fairly well.