Every explanation video about special relativity comes with a constantly moving train and a vertical (according to the train's speed direction) mirror clock. So first of all, why in the classical experiment (perpendicular bouncing of light), we propose time dilation, but we do not propose that the distance between the roof and the floor of the train (where the mirrors are placed) has contracted ? (I have only see length contraction only in the direction of movement but not in the perpendicular direction).
Also, what happens to this thought experiment if we replace the perpendicular mirror clock with a horizontal one, meaning that the light between the mirrors travels in the same direction (back and forth) with that of the train ?
So let's suppose the train is moving from left to right with a constant speed. We have placed two mirrors, one on the back of the train (left) and one on the front (right). The light bounces between the two mirrors back and forth. BUT, when the light travels from the back of the train to the front, it needs to cover more distance than when it travels from the front to the back, because in the first case it travels along with the train, where in the second case it travels in the opposite direction.
So a stationary observer would have to say that from back to front the time passes slower but from front to back the time passes faster ? That doesn't make any sense. Any help to understand this ?
