When Quaritch organizes a pre-emptive strike against the Tree of Souls, the mountains were floating on their own while the RDA vehicles needed engines to fly, why?
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The Hallelujah mountains float because they're essentially large chunks of unobtainium, which is a room temperature superconductor, thus subject to the Meissner Effect. This causes superconductors to "levitate" in the presence of certain strong magnetic fields:

Vehicles need engines to fly because gravity and the laws of thermodynamics still exist in the Avatar universe. So vehicles still need a power source for propulsion and can't defy gravity for no apparent reason.
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2although - looking at the size of the shuttle in the movie, it must surely use some unobtainium to help with lift... – HorusKol Oct 29 '13 at 01:17
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3@HorusKol Nah, just some futuristic power supply with unheard-of energy density & some futuristic engines with unheard of thrust-to-weight ratios. – Wingman4l7 Nov 21 '13 at 07:19