What happens to the air in the area, when things are transported or replicated?
A fundamental law of physics is, in short, that two things cannot exist in the same space at the same time. This is easily demonstrated by dropping a relatively large mass, such as pasta noodles, into a container of water, such as a pot. The water level will rise as it "makes room" for the pasta, and will overflow if you've put in too much of either. Conversely, if you were to scoop all of the noodles out (presuming you had a way to scoop just the noodles, without taking along any water at all) you would see the water sink down to its original level (or lower, if it had overflown earlier).
Taking this into consideration, I see a problem with transporter technology which I'm not sure I've ever seen addressed: What happens to the air surrounding a transport subject's origin point, or occupying the destination?
The transporter must have some means of compensating for the displacement, otherwise each transport should in theory be accompanied by a loud pop at each end - at the origin when the air collapses to fill a vacuum left behind, and at the destination when a relatively large volume of air is forced away to make room for the subject. 1018
This effect should be even more pronounced, and perhaps even hazardous, in closed environments such as spacecraft where the air has really no place to go.
One option would be to have the transporter exchange the air (or other matter, such as dust or raindrops) at the destination for the matter of the subject, as it is being transported. However, this is not seen as we would often notice small portions of dust storms or downpours getting dropped onto the transporter pad when people are transported into adverse weather conditions. Imagine having that cleanup as part of the Transporter Chief's job duties.
Another option would be to process the matter from the destination through the replicator, so that it is congruous with the same volume of air at the origin. This would be a fairly complex operation though, and could result in a lag too long to be acceptable by the laws of physics.
Come to think of it, this same (or a similar) issue should affect replicator and holodeck technology as well. Has any of this ever been addressed canonically, either in a Star Trek episode or in technical manuals? 513