# Equivalence principle - light beam through a rocket

1. May 8, 2015

### Bohr1227

An observer outside the rocket sees a light beam through a rocket that's accelerating. How will an observer inside the rocket see the light beam? (The problem is showed in the picture below)

My friends and I had this problem at school today, and we couldn't decide which is right. Here are our thoughts:

1) The rocket has a speed relative to the observer outside.

2) The person inside will experience a acceleration, which is equivalence to gravity. After reading the books and seen some pictures, I think the right answer is that the light beam will bend.

I hope someone can explain it in details. I don't understand why the observer outside don't see a bend light beam because the rocket has a speed and acceleration.

Thanks for the help!

2. May 9, 2015

### Brage

Yes you are right the light beam will bend, the trick is to think of the question relativistically, i.e. light always travels the same speed in any referance frame. Therefore, lets say it takes time t for light to go from one side of the rocket to the other if the rocket was standing still, the light then travels a distance $ct$. Then if the light went horizontal through the rocket with respect to the rockets floor, if the rocket moves distance $s$ in time $t$, the light will actually travel a distance $\sqrt{c^2t^2 +s^2}>ct$. Therefore the light seems to bend for the observer inside the rocket, as if the light enters the rocket at distance $H$ above the floor of the rocket, it needs to exit the other side of the rocket at a distance $H-s$ such that we have $\sqrt{c^2t^2 +[(H-s)+s]^2}=\sqrt{c^2t^2}=ct$