How does the planet of Pandora and the floating mountains seen as one of the elements of science fiction in Avatar?
Obviously the forces holding up the mountains would have to be magnetic in nature, unless of course they are some kind of force that we aren't familiar with. One of the great things about science fiction is that it doesn't have to follow the rules of physics that we know about and suspending your disbelief is one of the things the movie expects you to do.
Otherwise, how do you explain arrows going through what would likely be incredibly impact-resistant windscreens? If we have cockpits that can withstand heavy machine gun and even light cannon rounds now, what would they be like then? Unless of course these arrows are propelled by bows that create forces beyond those which we currently understand...
So there are any number of things, but one of the biggest is the connection between all the living things, the trees and plants and the animals, etc.
The planet itself is a science fiction element because as of today, we have never discovered life at all on other planets. On Pandora, there is not only life, but intelligent life - life that has brains and emotions similar to humans - life that falls in love with robots controlled by humans.
As for the floating mountains - I think in order to have floating mountains there would have to be an extremely magnetic force field existing between the main planet and the mountain floating. In order to be strong enough to make a huge chunk of rock actually hover with such stability in the air - it seems it would be completely dangerous for humans to go near it.