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In the movie Avatar, the moon Pandora had floating mountains. I believe it was in an area called the flux vortex that was said to have a electrical interference. Did they ever explain or give hints as to why those mountains floated?
Were they floating because they were at the balance point between the planet's and the moon's gravity? Did they float because of magnetism?
To quote from the Avatar Wiki:
On Pandora, huge outcroppings of unobtanium rip loose from the surface and float in the magnetic vortices due to the Meissner Effect.
(This was from the article on the Hallelujah Mountains)
In other words, the very minerals that the humans want to mine are essentially floating in the magnetic fields generated by Pandora and Polyphemus, the planet it orbits. The mountains are just the dirt and rock that's around those minerals that was also ripped out of Pandora along with the unobtanium by the magnetic fields.
I'm taking my information from my Activist Survival Guide (Not sure how to link this in! I can't find it under Google:books...must be censored by the RDA).
Pandora, like earth has a liquid iron core, producing a magnetic field in a similar way. Unobtanium deposits deep within the planet magnify this field a hundred fold. This intense magnetic field amplification is due to its five-fold crystal symmetry. And this in fact causes superconducting properties up to the materials melting point of 1789K. This intense amplification of the local magnetic field sets up high-gradient contours that act to stabilise the mountain.
When Pandora was formed, and still molten, large masses of unobtanium were repelled by similar masses still inside the planet. This is the main reason for the formation of the mountains. More details are available in the primary communication, A Confidential Report on the Biological And Social History of Pandora. (same book link as above)
A report on an event where James Cameron discussed the science of Avatar with some Caltech Physicists gives his own comments on the floating mountains:
Cameron admitted the film never explains exactly what unobtanium is for, but that it seems to act as a superconductor at room temperature whereas, in the known world, all known superconducting substances must be cooled way below the freezing point of water. This makes unobtanium extremely valuable back on Earth, hence the drive to expand mining operations on Pandora.
Some of the most spectacular visual effects -- like floating mountains -- were inspired by possibilities drawn from nature. Pandora possesses a large molten core, which generates a powerful magnetosphere. As Cameron explained, in a powerful magnetic field, the superconducting unobtanium levitates. So if you have mountains rich in unobtanium, you can have the floating Hallelujah Mountains of Pandora (visually based on the Huang Shan mountains of China.) Although, as Cameron admitted, to do that a magnetic field would have to be strong enough to rip the iron from the hemoglobin in your blood. But for the sake of the film, in this instance he was willing to compromise on the science.
In real life, superconductors exhibit the strongest possible form of diamagnetic levitation (where they are repelled by, rather than attracted to, an external magnetic field--see here for a good explanation), due to the fact that superconductors have zero eletrical resistance, which gives them what physicists call "perfect" diamagnetism (or superdiamagnetism), with the smallest possible magnetic susceptibility of -1. As explained on the superdiamegnetism wiki page, as well as on this page, this feature of zero electric resistance is considered distinct from the Meissner effect mentioned in Tango's answer, which causes the inside of the superconductor to have zero magnetic field.
