Image Source and Extract: Wikipedia Ladder and Barn Paradox
The simplest version of the problem involves a garage, with a front and back door which are open, and a ladder which, when at rest with respect to the garage, is too long to fit inside. We now move the ladder at a high horizontal velocity through the stationary garage. Because of its high velocity, the ladder undergoes the relativistic effect of length contraction, and becomes significantly shorter. As a result, as the ladder passes through the garage, it is, for a time, completely contained inside it. We could, if we liked, simultaneously close both doors for a brief time, to demonstrate that the ladder fits.
So far, this is consistent. The apparent paradox comes when we consider the symmetry of the situation. As an observer moving with the ladder is travelling at constant velocity in the inertial reference frame of the garage, this observer also occupies an inertial frame, where, by the principle of relativity, the same laws of physics apply. From this perspective, it is the ladder which is now stationary, and the garage which is moving with high velocity. It is therefore the garage which is length contracted, and we now conclude that it is far too small to have ever fully contained the ladder as it passed through: the ladder does not fit, and we can't close both doors on either side of the ladder without hitting it. This apparent contradiction is the paradox.
I just read about the ladder/barn paradox and was wondering about the following variation:
The barn is equipped with some electronics to measure whether the ladder is completely contained, and will switch on a light (on the barn's roof) if the ladder is inside.
Now would an observer on the ladder, looking back at the barn after he's gone through, see the light turn on? I assume he should be able to see the light, which moves quicker than the ladder, if it was turned on.
From what I've read in posts here, and on https://en.wikipedia.org/wiki/Ladder_paradox, I would guess that the barn electronics will find the ladder small enough and switch on the light. So the observer on the ladder will be surprised by this, which contradicts his own experience.
Is that simply the kind of surprises the observer has to live with (when using such transport :-) or is there some fault in my reasoning?