Suppose that a fly flies into an elevator and hovers in mid-air. The doors close and the elevator goes up. In analogy with a similar example (link), I imagine that the fly will travel up, it won't fall to the elevator floor. And I guess this is because the 'air' in the elevator, which is what the fly pushes down with its wings to create an upward force counteracting its weight, is carried up as well. However, if I stand in the elevator, the force that is counteracting my weight is the reaction of the elevator floor, which is equal to my weight at the beginning, and temporarily increases as the elevator accelerates. This is felt as some additional pressure under my feet. If I am carrying a heavy sack of potatoes, for a moment it will 'feel' heavier. Is this correct so far? Now, if this is true, doesn't it imply that the air in the elevator will undergo some compression, i.e. for a brief moment there will be 'less' air near the roof of the elevator than near the floor? And if so, doesn't that affect the fly's ability to hover at a certain level, i.e. won't we see it go down for a brief moment as the elevator accelerates?