Unobtanium
The case of Hallelujah mountains
Unobtanium is a chemical element which is present an Pandora and has amazing features. But to understand it we have to define what is superconductivity.
Superconductivity is a property which can be found in many metals. It corresponds, when the temperature is low enough, to the expulsion of a magnetic field and zero electrical resistance (no loss of electrons and energy). In superconducting state, these materials are super-diamagnetic, that is to say that X (magnetic susceptibility) is negative and high. Thereby they are like diamagnetic materials, but the repulsion is more violent.
Superconductors which are known reach this state only with very low temperatures. In fact the hottest superconductor is HgBaCaCuO, wich has a critical temperature (temperature when it becomes a superconductor) of -189,4°F.
On the other hand, unobtanium is a superconductor at ambient temperature, that is to say about 80/110°F (temperature of Pandora). In other words, it creates a magnetic field and transmits energy without losing electrons.
Of course we've never discovered this kind of superconductor, but many physicians are looking for it.
Hallelujah mountains are really special mountains ; they appear to float in the air, defying the gravity of Newton. In fact it is a question of magnetism and superconduction.
Each magnet has a north pole and a south pole. It thus expels a magnetic field.
Iron fillings dusted on this magnet reveals its magnetic field.
Two identic poles repel and two different poles attract, that's how magnets work.
The two pictures below represent those interactions.
Reminders on magnets
We've seen that between a magnet and a magnetic material there is a repulsion. With a super-diamagnetic material, this repulsion pronounced enough to cause levitation of one of the two materials. That is called the Meissner effect. This effect can be seen in a laboratory, as we can see in the video below.
First of all, let's remember that material is made of atoms, which are made of an atomic nucleus and one or many electrons. These ones will interest us.
In fact, any electron has a spin, which is like a rotation on itself. What w'ere going to say here is to be taken lightly and not to be interpreted directly, because the field of quantum physics (at atoms level) is really against-intuitive, vertiginous and complex. Furthermore, the idea of spin has no equivalent in classical physics. Electron's spin can correspond to a little magnet which carry each electron. If, in a "normal-sized" object (in the field of classical physics) these magnets are aligned in parallel, the object in question becomes a magnet itself. If these little magnets are turned into different directions, there's no magnetic field to emerge, and the object isn't a magnet.
The capacity to magnetize is called magnetic susceptibility.
We distinguich four types of susceptibilities :
With H=intensity of the external magnetic field
X=proportionality coefficient, magnetic susceptibility
M=magnetic field of the atomic nucleus
These types of susceptibilities are thus distinguished by different values of X, so by the magnetic susceptibility of the material we put in front of the magnet. Without dwelling on each type, let's precise (that will be useful for the rest) that when a material answers a magnetic field by a magnetic field of same direction, the force between the material and the magnet is attractive. Ferromagnetic and paramagnetic materials are so attracted by the magnet. But let's take a look on the Magnet/diamagnetic interaction (fourth type). A diamagnetic material answers a magnetic field by a repulsion. In fact, the majority of the materials are diamagnetic but the effect is tiny and invisible for us, because the external magnetic field isn't strong enough.
So, the Hallelujah mountains take the role of the magnet which, in the video, levitates above the superconductor, or conversely they are the superconductor which float above the magnet. This inversion isn't a problem because unobtanium as a supraconductor at ambient temperature (while in the video the superconductor is below because it needs to be immersed into liquid nitrogen).
Theorically, the Hallelujah mountains are possible. However the magnetic field expelled by Pandora should be extremely high to allow mountains with a mass of several million tonnes to levitate at a hundred meters above the ground (estimation according to the movie pictures).
Anyway, if the magnetic field was high enough that would mean that the helicopter below cons should be violently attracted by Pandora, because it's made of metal (we hadn't planned to talk about technologies, but it was too tempting). Most of the metals used to make vehicles (steel, aluminium...) are in fact ferromagnetics. Without knowing the value of the magnetic field expelled by Pandora at the place of the Hallelujah mountains, we can surmise that it is high enough to deconstruct the atoms which interact with this field and directly pass the helicopter in the gaseous state...
We have retained two hypothesis to explain the presence of the Hallelujah mountains on Pandora.
The first one states that magnetic materials were already present on the surface of Pandora soon after its formation. Unobtanium was also present near the core of the moon. Thus, the distance between the magnetic materials and unobtanium was big enough to avoid having a repulsion that would move the mountains. However a magnetic field formed in the core of Pandora (similarly to the Earth's core, which we do not know yet how it was formed) and expelled unobtanium at the surface. Expelled unobtanium reduced the distance between it and the magnetic materials present on the surface, increasing the intensity of magnetic repulsion and expelling these magnetic materials above the ground.
The second hypothesis say that unobtanium and magnetic materials were already present at the surface of Pandora when it was forming (and very dense, so very massive). Thus the force of repulsion between the two materials was already strong but not more than the gravitational force exerted by the moon. Thereafter, Pandora lost density and mass. So the gravitational acceleration became low enough that the repulsion between unobtanium and magnetic materials allows the formation of the Hallelujah mountains.
The picture below show these two hypothesis :
