My professor in his lectures has stated that a consequence of Einstein Equivalence Principle (EEP) alone is that light bends in a gravitational field.
The proof went as follow: Imagine to be a free falling observer (so an inertial observer in GR by definition) in a box, and imagine to shoot a beam of light through a hole in your box. Since you are a free falling observer locally laws of Special Relativity (SR) apply to you (as in fact stated by EEP) and so if the beam and the hole are aligned the light goes right through the hole in the box (because of course in SR light has straight trajectories).
Ok, now immagine to be an observer on the ground, you see the box (let's imagine a glass box so you can see through) falling and the light exiting the hole, but of course in the mean time that the light crossed the length of the box the same box has fallen a bit, so the light must take a curved trajectory to be able to exit the box through the hole.
Ok, the thought experiment seems to show that indeed light must take a curved trajectory for an observer on the ground. But: my problem lies in the initial statement: "a consequence of Einstein Equivalence Principle (EEP) alone"; in fact we are not only using the EEP, instead seems to me that we are assuming that both observer should agree on the outcome of the events. In other worlds: both observer must see the light passing through the hole, it cannot be that one sees light traversing the hole and the other sees light not traversing the hole.
This seems reasonable to postulate but is surely a principle not equivalent to the EEP; am I right?
If so, what is the name of the principle?