First: great movie, literally awesome visuals, stunning effects, good acting and execution, fun alien creatures, who cares if it’s a retelling of Pocahontas.
What I absolutely did not expect when I finally got to see James Cameron’s ‘Avatar’ yesterday afternoon was to see my own research appear in the movie. Granted, it doesn’t take a front-row seat and it doesn’t play any major plot roles. As I was driving home with my girlfriend (a fellow aerospace engineer), we got into a discussion about how this was a reasonably hard sci-fi movie. None of the technologies seem particularly farfetched: ducted-fan helicopters exist on Earth at a low technology readiness level (TRL), as do exoskeleton power suits. 3D glassy computer displays aren’t a stretch, nor are hovering VTOL aircraft on a low-gravity world. The flight to Alpha Centauri takes 6 years, meaning some reasonable sort of sublight propulsion. The ship Sully arrives on even has rotating segments, big radiators, and solar collectors. The avatars themselves don’t even seem too crazy, since we keep hearing about advanced prostheses that can be controlled by a user’s thoughts. (I’ll reserve judgment on mixing alien and human DNA until we have real alien DNA on hand.) Nor does a planetwide neural interface – though I have to wonder what selective pressures would cause such a thing to evolve – given that we have bacterial, fungal, and other life forms on Earth that can split and recombine, blurring the distinction between organisms.
But surely, I thought, those floating mountains are ridiculous. Visually stunning, yes, and great for those 3D flying scenes. But physically ludicrous.
We are led to believe, in the movie, that these mountains float against the force of (albeit reduced) gravity because there is an exceptionally strong magnetic field generated on Pandora. Cameron even gives us direct evidence of that field: you know how iron filings align themselves with a magnetic field, like that of a bar magnet?
Well, the magnetic field on Pandora is so strong that geologic formations align themselves with the magnetic field. The field is so outrageously strong that whatever iron content is in Pandoran minerals – most likely not 100%, even if those rocks are pure hematite or magnetite or something like that – is sufficient to make rocks suspend themselves against gravity in the shape of the magnetic field lines:
I know for experience that this might not necessarily be impossible, for a sufficiently strong magnetic field. After all, in my lab is a whopping-big NdFeB rare-Earth magnet about the size of a margarine tub, and even when it’s contained within its sarcophagal wooden box, I can get six-inch steel bolts to suspend themselves, against gravity, at a 45° angle in its field. So, for a sufficiently strong magnetic field, this flux-line rock formation is not at all out of the question, believe it or not!
How about the mountains themselves? Couldn’t the magnetic field strong enough to make these “flux arches” also levitate mountain-sized chunks of rock?
Well, I thought, surely not if it is solely the repulsion of like magnetic poles that is responsible. After all, Earnshaw’s theorem says that the familiar field sources that drop off with distance, like gravity, electrostatic attraction, and magnetostatic attraction, cannot be arranged in a passively stable configuration. If you don’t believe me, then I set for you a challenge: get some ordinary bar magnets, and lay them out on a table. Try to arrange them in such a way that they are within a few centimeters of each other, but the attraction of opposite poles and repulsion of similar poles cancel out so that the entire arrangement sits on the table without moving. (For safety’s sake, do not do this with the rare-earth magnets I mentioned above, because when you fail at the challenge, the magnets will jump towards each other with substantial force. Rare-earth magnets are brittle and will shatter if that happens, sending neodymium shrapnel flying around – if they didn’t pinch your fingers when they impacted.) You will find that no matter how hard you try, no matter how many friends you get to hold the magnets in position and simultaneously release them, no matter how you angle them and tweak them, you won’t ever be able to prevent at least one of the magnets from attracting or repelling some other magnet. The whole arrangement will either fly apart or collapse together. You might think that in 3D you’d be able to come up with some super-clever configuration that is stable, but, in fact, if you move beyond the two dimensions (and three degrees of freedom) of the table top the situation gets far worse, because all the bar magnets try to align themselves with one another in 3D. So, a combination of purely magnetic and gravitational forces cannot result in a stable configuration of those mountains.
“But, ha!” you say. “You must be wrong! You said that a combination of gravitational field sources can’t be in a stable arrangement, and clearly, the planets of our solar system have been stably orbiting each other for four billion years! And I’ve even seen those Levitron tops – magnetic tops that stably levitate against gravity, just like those mountains!“
The key difference between a Levitron or an orbit and the bar magnets on a table top are that they are dynamically stable. They require motion to preserve stability. Stop the planets from orbiting, and they will fall into each other and the Sun. Stop the Levitron from spinning, and it flops over – aligning itself with the magnet in the base – and drops to the ground. So, for Pandora’s mountains to levitate like that, they must be spinning or moving in some way. It might be the case that, if they were at Pandora’s equator, the repulsive magnetic force actually “cancels out” the low gravity of the moon enough that the mountains are actually in circular orbits about Pandora’s equator. But that situation is dynamically tricky, requiring exquisite balances of forces – and I would estimate from the different sizes of floating mountains that they have different magnetic mineral contents, so the balance between gravity and magnetism would be different for each mountain and each would have a different orbit. Doesn’t work.
So what’s the answer? Well, it’s all in those little gray crystals the imperialist human colonists of RDA are after. Unobtainium.
Above is a picture of an unobtainium crystal from the movie. It’s levitating above some crazy sci-fi antigravity contraption, that holds it stably up in the air where people can poke at it, spin it, pluck it out of midair and play with it before putting it back in exactly the same spot again. Now, wait a minute – where have I seen this behavior before? Oh, right. My research lab.
That is a picture I took of a NdFeB magnet, stably levitating over the high-temperature superconductor yttrium barium copper oxide, or YBCO. (For scale, the magnet is 3/4″ across.) You can do everything with that magnet that they do with the sample of unobtainium in ‘Avatar.’ Leave it alone, and it happily floats in midair. Poke it, and it rocks a little before going back to its equilibrium position. Give it a twirl, and it’ll spin over the YBCO – and if the magnet isn’t cylindrically symmetric, it’ll eventually stop spinning and settle down again. Pull it away from the YBCO, and you can put it back later and watch it float in exactly the same midair spot as when it started. You can even pin different sizes and shapes of magnets – all stable against gravity. This whole setup would work perfectly if the magnet was on the table and the YBCO was doing all the floating, too. It’s all because the magnet induces currents in the YBCO that are not opposed by any resistance – “supercurrents” – which generate their own magnetic fields that then interact with the magnet.
“Wait,” you ask, “that magnet is just a magnet. The supercurrents make magnetic fields. I thought you said that magnetic field sources couldn’t be arranged in a stable configuration! It’s Earnshaw’s Theorem again.”
That would be an astute question. The answer is that, in this case, the superconductor doesn’t have a fixed magnetic field. As the magnet moves around – let’s say it starts to fall from its equilibrium position, because gravity is pulling on it – then its motion causes the supercurrents in the YBCO to move around. The new distribution of supercurrents gets superimposed on top of the previous distribution of supercurrents, with the net result that the magnetic field from the YBCO tends to push back on the magnet, keeping it in its original position. It’s as if the field lines of the magnet get stuck, or trapped, in the volume of the superconductor. The effect is called “magnetic flux pinning” for that very reason, and it happens with Type II, or “high-temperature” superconductors. (If you know about Meissner repulsion, flux pinning is related but not the same.) So, that blue-glowing antigravity generator in the RDA command center, with the levitating sample of unobtainium, is very likely just a magnet. And the Hallelujah Mountains are just a scaled-up version of the magnet and YBCO in my lab.
But, you probably noticed from that photo, the YBCO has to be below liquid nitrogen temperature in order to superconduct and exhibit flux pinning. Clearly, Pandora is not at cryogenic temperatures, which pretty much pegs “unobtainium” as a room-temperature superconductor – a type of material that is highly sought-after in research labs today, and would indeed be extremely valuable. That means that the Hallelujah Mountains on Pandora likely consist of large deposits of unobtainium, which are flux-pinned to the stupendously powerful magnetic field lines coming from that field sources on the planet. This explains the value of unobtainium, how the mountains levitate the way they do, and why the floating mountains are so close to the flux arch structures.
There’s another interesting link between ‘Avatar’ and flux pinning. Remember how I said that the effect of flux pinning is as if a magnet’s field lines get stuck within the superconductor? Well, if you had a good electricity and magnetism course, that notion might sit uncomfortably with you, because you were probably taught that “field lines” or “flux lines” are not physically real, but are a good visualization tool for magnetic fields, which exist everywhere around a magnet and not just in neat little looping lines. Well, you’d be right, but things tend to get kind of weird inside superconductors. Magnetic fields are quantized just like everything else, and it is these magnetic flux quanta that get “stuck” inside the YBCO. In fact, they actually get trapped on impurities within the YBCO’s crystal structure. You might think that these quanta of magnetic flux would be called “fluxons,” but because they correspond pretty well to magnetic field lines, papers on superconductivity and flux pinning tend to throw around several names for them – like “flux lines,” “field lines,” and “flux vortices.” That last name likely comes from the fact that, in the superconductor, each of the magnetic field lines induces a little loop of electric current that races in a circle around the flux line, like a little vortex. The sum total of all these little currents adds up to the distribution of supercurrents that gives us flux pinning.
In ‘Avatar,’ every time they fly near the flux-arch structure, they talk about a “flux vortex.” It sounds like your classic sci-fi trope of combining sciency-sounding words. (“Invert the phase capacitors!”) But, hmm…maybe, just maybe, that’s not mere technobulshytt after all!
I’m pretty convinced that all this isn’t accidental. The filmmakers had every intention of unobtainium being a room-temperature supercondcutor and the floating mountains being flux-pinned to the field source within the planet. Because I know that this is not the first article on the web about it! But the fact that it’s my own research in this movie: now that is cool! (For the uninitiated, I’m working on using flux pinning to assemble and reconfigure modular spacecraft. More info on my web site and my research group web site. You can also check out Youtube videos of me demonstrating flux pinning and our microgravity experiments with flux-pinned spacecraft mockups from last summer.)
Of course, ‘Avatar’ doesn’t get it all right. And they shouldn’t be expected to. I know from my research that flux pinning is a very short-range effect; getting those mountains to levitate would require a (probably literally) mind-bogglingly powerful magnetic field. Not something I’d expect to see from a planetary dynamo. Nor would a dipolar magnetic field within Pandora explain the flux arches: those are clearly centered on a magnetic field source at the surface of the world. And if the field source is powerful enough to get the rocks to bend around and follow field lines – all the aircraft, armor suits, guns, mobile lab trailers, and equipment carried by the human scientists and soldiers probably has more than enough ferromagnetic metal content to be ripped towards the field source. And that doesn’t even account for this happening:
Oh, well. But, speaking as someone who hopes that our future space program will involve spacecraft build out of components that “levitate” near each other without touching, but still acting as if they are mechanically connected, I would sure love to see some room-temperature superconductors and floating mountains!