Today in my physics class, my teacher said that if one would point a laser into a falling elevator (acceleration because of a gravitational field), an observer inside the elevator would see the light form like a parabola, like i have tried to illustrate here:
He told us this is because the elevator accelerates downwards, and therefore the light would "bend" to an inside observer. But i'm wondering how that is, since the light also falls inside gravitational fields. If the light falls at the same rate as the elevator, an inside observer would just see a straight line. Like the image below:
My question is now: who is right? Will the light accelerate at the same rate as the elevator, or what will happen?
Thanks in advance.
By the way, this is my first question on the physics stackexchange, so please tell me if i could improve my question, thanks!
Best Answer
You are right; teacher was a bit misleading but not totally wrong.
Proof: motion under gravity satisfies a principle called the Strong Equivalence Principle. This says that in a reference frame in free-fall physics is locally just the same as if there were no gravity at all and you had a reference frame in constant velocity motion. In such a frame light travels in a straight line.
Your elevator falling under gravity is an example of a reference frame in free-fall. Therefore relative to the elevator light travels in a straight line.
Relative to the Earth the light beam bends down owing to gravity, and the bend is exactly enough to make it be a straight line relative to the elevator. You can use this to deduce the bend of a light beam owing to gravity! Congratulations: you will then have done an exact calculation in general relativity. (If you do the calculation you will find the bend is very small; the radius of curvature of the light beam track relative to Earth is something like a light-year).
All the above describes any particular light wave emitted by the laser. Now let's think about the fact that the laser source is being accelerated upwards relative to the elevator. This means that each successive moment it emits at a different height relative to the elevator, so you have a succession of light waves each of which travels straight (relative to elevator), but the later ones started out from a higher-up location relative to the elevator. I think the teacher was trying to convey this aspect of the situation but maybe was struggling to do so clearly.
Added remark on direction of the light
If you shine a light beam into something that is moving relative to you (e.g. shine a torch into the window of a passing train) then there is a slight change of direction, just as you would expect from Newtonian physics. e.g. If the light beam is at right angles to the moving window surface in your rest frame, then in the train frame the light beam is not at right angles to the window surface. This affects the elevator experiment too, only now the relative velocity between laser and elevator is increasing so this effect gets larger as the elevator falls. The light still propagates in a straight line relative to the elevator, but its direction of travel will be changing (assuming the laser is fixed relative to Earth). (Thanks to PM2Ring for pointing this out.)