About the floating mountains: From a Condensed Matter physicist.
The reason humans are on Pandora is to mine a mineral, Unobtainium. I speculate that this is a high-temperature superconductor. First, I will review a few facts about High Tc superconductors. In the second paragraph I will point out several pieces of evidence that support my conclusion.
Type 2 superconductors were discovered in the 1980s, by accident. After over 20 years of theoretical and experimental study, we still cannot explain exactly how they work. There is no theoretical limit to the temperature at which materials can superconduct. No one knows if there are more than 2 types of superconductors. A very peculiar behavior (of a substance we discovered by accident) is that when lowered from above the superconducting critical temperature in the presence of a magnetic field, they trap the magnetic flux inside the superconducting region. If the magnetic field has a gradient, the superconductor will remain locked in place and float. Here is a pic. If we were able to find a high temperature superconductor, it would be extremely valuable, possibly millions of dollars per pound.
I believe that unobtainium is a high temperature superconductor, and the floating mountains are made out of unobtainium in the presence of a strong magnetic field gradient. The first evidence of the nature of unobtainium is the piece in the boss' office. It floats, and there is no evidence that humans have developed artificial gravity (see pic, look familiar). Because the material conducts at high temperature it does not need to be cooled. Second piece of evidence is that there is a "flux vortex" right near the floating mountains. Only an extremely large magnetic field would cause the equipment on the ships to malfunction. In the presence of high magnetic field gradients the metallic ships would have to fly very slowly to avoid large eddy currents that might damage equipment. There are large geological structures that suggest magnetic field lines. These could plausibly be structures with ferromagnetic properties (like iron) that would focus the flux into those structures. (here is a pic.) Given that we have large deposits of a likely candidate for a high temperature superconductor and very likely extremely high magnetic field gradients (what else would be a "flux vortex"), I believe that it is very likely that the movie makers intended us to conclude. There were large deposits of unobtainium that cooled below their critical temperature in the presence of extremely high magnetic field gradients. While the rest of the mountain eroded, only the parts that were dense enough with superconductor floated.
This is by no means scientifically excluded from reality, it is just something we do not observe on Earth.
Edit: For those who still might not be convinced that something that large could be held aloft by magnetic fields, consider this picture of a solar prominence with Earth in the picture to scale. Pic
Any recommendations of what to fall asleep to next?
(Her real name is Susan)
