The Science of Avatar

by Stephen Baxter

  Now let’s suppose we stretch her up by twenty-five per cent, without making her any wider. She’ll still be shorter than the average Na’vi, at around three metres. Her mass has gone up twenty-five per cent, and so has her weight, but her cross-section hasn’t changed. So the pressure on her bones is up twenty-five per cent too.

  That could be a problem, if we kept stretching her. Grace’s bones can support only a certain maximum weight, because beyond that the pressure would overcome the binding energy of her bones’ molecules; the bones would splinter and Grace would fall. So, in a given gravity field, and with bones of a given strength, there is a limit on Grace’s height—and indeed her mass—unless you thicken up her bones like an elephant’s.

  But now let’s whisk Tall-Grace to Pandora. The gravity here is eighty per cent of Earth’s. And so, though her mass is unchanged, her weight (twenty-five per cent more mass times eighty per cent gravity) is the same as Short-Grace’s back on Earth, because the lower gravity has cancelled out the extra height. And thus the pressure on Tall-Grace’s bones is as low as it was for Small-Grace back on Earth, and she feels no discomfort.

  There are plenty of subtleties beyond this simple argument. Even given their height the Na’vi look remarkably slender—narrower bones mean higher pressure—but, as we’ll see in Chapter 25, their bones are strengthened by a naturally occurring carbon fibre.

  And we should remember that the Na’vi didn’t have to be as tall as they are. No animal has to grow as large as the laws of physics allow it to. The Na’vi’s apparent close relative, the prolemuris, is no more than a metre and a half tall, just as on Earth our hominid ancestors were all chimp-sized until the emergence of Homo erectus, about as tall as us, a couple of million years ago. The Na’vi are as tall as they are because something in their evolutionary history made it right for them to be so. However their height does illustrate that a human body form that would be impossibly tall and slender on Earth can work on Pandora.

  What are the limits? How big could a land animal grow on Pandora?

  Pandoran beasts are big. Even the direhorse is larger than any horse on Earth. The heaviest living land animal on Earth is the African elephant; a bull can stand some four metres tall at the shoulder. The heaviest animal of all was the brachiosaurus which died out some hundred and thirty million years ago, and stood around seven metres tall at the shoulder. The largest land animal we see on Pandora in Avatar is probably the hammer-head titanothere at maybe six metres tall—like an elephant scaled up in Pandora’s gravity field. Perhaps greater beasts roam in parts of Pandora yet unexplored.

  Pandora’s low gravity would help you fly, especially with the aid of that thick air. On Titan, the air is so thick and the gravity so low that a human could fly by the power of her own muscles, flapping artificial wings. So we could have predicted big flying animals on Pandora.

  Earth’s largest flying creature was the winged reptile Pteranodon ingens, which flew over Kansas some eighty million years ago, with a wingspan of around nine metres. On Pandora a mountain banshee exceeds that at around twelve metres wingspan, and a leonopteryx would dwarf it, with a wingspan of thirty metres. The size a flying creature could reach depends on other factors than gravity, such as the density of the air and the oxygen content—the more oxygen, the more energy you have available to keep you aloft.

  On Earth you have to look to the sea for the real monsters in size. The blue whale is thought to be the heaviest animal ever to have existed, weighing in at some hundred and ninety tonnes (compared to around five tonnes for an African elephant). If we visit Pandora’s oceans in the future, there will be monsters, I have no doubt.

  And what of the tremendous trees of Pandora?

  On Earth, the basic physical constraint on tree height is the need for the tree to be able to lift water to its uppermost leaves. The tallest known tree on Earth is a sequoia in northern California, at a hundred and sixteen metres tall. The theory says that a tree could possibly reach as much as a hundred and thirty metres—and there have been historical accounts of trees a hundred and twenty metres tall. By comparison Hometree on Pandora is some three hundred metres tall, nearly three times the size of that big old sequoia. This is more than the simple gravity scaling might suggest, but Hometree evidently has a different architecture from a sequoia, with pillar-like multiple trunks, themselves as sturdy as sequoias, enclosing a large internal hollow.

  Pandora’s low gravity would enable some wistful architectural designs: impossibly long arches, impossibly slender columns. We don’t see any native architecture on Pandora; with the hometrees available for habitation I suppose building is unnecessary. And the humans at Hell’s Gate show no imagination in their own functional building schemes. Maybe the Stone Arches are a glimpse of what would be possible.

  But in fact the Stone Arches seem to be a product of the single most remarkable physical phenomenon on Pandora: its unobtanium, and the magnetic fields with which it is associated. And if you followed Jake Sully to Pandora you would very quickly learn that unobtanium is the reason you, and RDA, are here.

  15

  OBTAINING THE UNOBTAINABLE

  What is it about unobtanium that makes it so valuable?

  Unobtanium is a room temperature superconductor—we’ll find out later what that means. On Parker Selfridge’s desk we see demonstrated one of its apparently magical properties, that a chunk of it can float in the air, defying gravity, over what looks like a magnet. Unobtanium has shaped Pandora’s geology. It is unobtanium’s gravity-defying properties that hold up the floating Hallelujah Mountains. When Jake climbs the “stairway to heaven” on his way to Iknimaya, his mountain-banshee challenge, you can see what look like lumps of rock embedded in the roots and tendrils, straining to rise like trapped balloons, boulders presumably laced with unobtanium.

  But the real value of unobtanium lies in its superconducting properties, which have led to a new industrial revolution on Earth, including the building of Venture Star-class starships—and generating vast profits in the process.

  Is all this fanciful?

  The very name “unobtanium” suggests that we’re dealing with impossible physics. According to science-fiction archivist David Langford, the word is an engineer’s in-joke dating from the middle of the twentieth century, applied to any ideal substance you need to achieve the impossible—frictionless bearings, for example. The word “unobtanium” was actually formally defined in the U.S. Air Force University’s Interim Glossary of 1958 as “a substance having the exact high test properties required for a piece of hardware or other item of use, but not obtainable whether because it theoretically cannot exist or because technology is insufficiently advanced to produce it.” The word has been used in science fiction before, for instance in David Brin’s 1983 novel Startide Rising. Cameron has suggested that maybe the discoverers of unobtanium on Pandora adapted the old tongue-in-cheek name as a joke for this magical stuff, and it stuck.

  But in fact there may be nothing unobtainable about unobtanium. Superconductivity is a real property. And a superconductor really can defy gravity, at least in the presence of a magnetic field.

  As the name suggests, a superconductor is a material that is a “super” conductor of electricity—so super, in fact, that unlike common conductors like copper wire, it conducts with virtually no resistance at all. This means that no electrical energy is wasted in heating up the conductor, and the current could apparently run for ever, without losses.

  This seemingly impossible property was first discovered by accident, as a consequence of research into low temperature physics.

  In 1908 the Dutch scientist Kamerlingh Onnes was the first experimenter to turn the gas helium into a liquid. Whereas water liquefies from steam at a hundred degrees centigrade, to liquefy helium you need to reach the astoundingly low temperature of just four degrees above absolute zero—around two hundred and seventy degrees below zero centigrade. Having achieved his liquid helium Onnes tried dunking familiar materials in it, ju
st to see what happened. (Well, you would, wouldn’t you?) And he discovered that in certain pure metals, as they cooled down, electrical resistivity suddenly switched off—or at least, it dropped to values too low to measure.

  The industrial applications of such a substance are startling. You could run extremely high currents, for instance to power the very strong electromagnets needed by fusion reactors and starship antimatter traps, without the fear of heat damaging your apparatus. Low-loss power transmission lines are another possibility. Heat produced by electrical resistance is a problem in computers, forcing a limit to how much connectivity you can jam into a finite space—the smaller your computer is physically, the faster it can operate. With superconductivity there would be no heat limitations, in principle.

  And superconductors can be used to generate lift: to defy gravity.

  A superconductor in a magnetic field has a remarkable property called “perfect diamagnetism”; it expels the magnetic field from its interior by creating an electrical current running on its surface. The magnetic field reacts by pushing back at the superconductor. This is called the Meissner effect, and was first discovered in 1933—and it is presumably the effect we see holding up the lump on Selfridge’s desk, as the magnetic pressure balances gravity.

  This effect, “magnetic levitation”—“maglev”—can be harnessed as a friction-free load-bearing mechanism. You could imagine using it for frictionless bearings and flywheels. Larger-scale industrial applications could include lifting heavy weights, and running trains on frictionless tracks. Maglev trains are mentioned in a deleted scene in the 2007 script for Avatar. In fact maglev trains have already been trialled, though using only conventional electrical conductors. In Japan in 2003 such a train reached a speed of nearly six hundred kilometres per hour, faster than the record set by conventional trains. With no friction from the track, the main resistance to the train’s motion comes from the air; if it were run in an evacuated tunnel it’s thought that such a train could reach speeds of thousands of kilometres an hour. This might be very useful on the airless moon, where you could build a “mass driver,” an idea of Arthur C. Clarke’s, basically a train so fast it could take off into orbit…

  So superconductivity is a real phenomenon, and superconductors do indeed have enormous industrial potential. The trouble with the first superconductors, however, was that it took extreme cold to trigger the superconductivity in the first place. You couldn’t realistically run a maglev train track through a hundred-kilometre-long tunnel filled with liquid helium.

  But unobtanium is self-evidently at room temperature, as we see when Parker Selfridge casually picks up the trophy lump from his desk without having his hand freeze solid. Is this possible?

  After Onnes’ accidental discovery, the mechanism of super-conductivity took decades to unravel. In fact it had to wait for a whole new branch of physics to emerge. Once again we must approach the eerie science of the quantum.

  Electrical current in a conductor is a flow of electrons. It turns out that at sufficiently low temperatures the electrons in a conductor bond into pairs, called “Cooper pairs.” (Leon Cooper was one of a team that won the 1972 Nobel Prize for figuring this out.) Like entanglement (Chapter 11) these couplings are a typically spooky quantum-physics effect; the electrons don’t have to be physically close to each other, but they are still attached. Physicist and science-fiction author Charles Sheffield compared them to a husband and wife at a crowded party, separated yet always joined.

  Crucially, each pair stops behaving like the electrons from which it is composed, and more like another class of particle entirely—called “bosons,” which includes photons, the particles that make up light. And bosons have very different properties from “fermions,” the class that includes electrons. The electron pairs become “correlated,” lined up, as if the whole of the interior of the conductor is a single quantum object. All the photons in a laser beam are correlated in the same way. The way I think of it is that in a conventional conductor the electrons, all loners, are like a jostling crowd, cramming their way through a corridor. Cooper pairs are like a Soviet march-past, synchronised, smooth and slick, and getting by with far fewer collisions with the furniture.

  The trouble is, the coupling of electrons into Cooper pairs is a fragile effect that is easily destroyed by heat. For decades it was believed that no such thing as unobtanium, a room-temperature superconductor, could ever be found because of this.

  So everybody was surprised when, in the 1980s, certain ceramics were discovered which can remain superconducting at the balmy temperature of ninety degrees above absolute zero—above the temperature at which nitrogen boils, let alone helium. Later, copper-oxide-based superconductors pushed the limit up to over a hundred and thirty degrees above absolute zero. The latest developments include the discovery in 2008 of iron-oxide-based superconductors working at around the same temperatures. The scientific jury is out on how this works, presumably through a high-temperature analogue of the electron-pair correlation effect seen at low temperatures. For now, the grail of a true room-temperature superconductor is still out of reach—but it’s coming closer.

  For the sake of the Avatar storyline, unobtanium has some other key properties. It can exclude magnetic fields much stronger than other superconductors can cope with—in a strong enough field most superconductors eventually break down. And it doesn’t just exclude magnetic fields, it also has the ability to anchor strong magnetic fields in parts of its structure, perhaps using non-superconducting components embedded in a superconducting matrix. This is what enables Pandora itself to support very strong magnetic fields, as we’ll see in the next chapter. None of this is entirely implausible, and unobtanium’s superconducting properties at least don’t look unobtainable, in principle, and it certainly would be highly valuable in industry.

  Where did Pandora’s unobtanium come from? The answer comes from the peculiar (fictional) history of Alpha Centauri’s formation. As the system’s young stars coalesced they were perturbed by an intruder, a runaway neutron star, the surviving core of a supernova explosion, a lump composed purely of jammed-together neutrons with the mass of a star but the diameter of a city block. The neutron star, itself a source of powerful magnetic fields, ripped into the young Centauri stars, and some bizarre nuclear reactions followed. The result was a system laced with unobtanium. And that’s why unobtanium is not present in our solar system, whose origin was unperturbed by neutron stars.

  But even if we could find it, could a superconducting mineral like unobtanium really lift a mountain?

  16

  MOUNTAINS IN THE SKY

  The Hallelujah Mountains, ranging in size from boulders to many kilometres across, float thousands of metres above the ground. The Hallelujahs are a lovely visual concept, inspired in part by the Huang Shan Mountains of China, spectacular karst limestone formations that themselves look too delicately vertical to exist.

  The Hallelujahs are lifted by the push of Pandora’s magnetic field on the superconducting unobtanium in the mountains’ rocks. The magnetic field itself is a complex product of the presence of the unobtanium in the ground. Indeed it was an early sighting of the Hallelujahs that led human scientists to suspect the presence of superconducting unobtanium in the first place.

  In fiction, flying islands go back at least as far as the eccentric aerial kingdom of Laputa, in Jonathan Swift’s Gulliver’s Travels (1726). And as it happens Laputa is held up by magnetism too. It contains a magnetic rock, “a Lodestone of a prodigious Size… The stone is endued at one of its Sides with an attractive Power, and at the other with a repulsive… When the repelling Extremity points downwards, the Island mounts directly upwards” (Part Three, Chapter 3).

  But just how strong would a magnetic field have to be to lift a mountain?

  Consider Selfridge’s trophy unobtanium lump on his desk.

  If this is equivalent to a ten-centimetre cube, say, and if the density is about that of rock on Earth (a couple of tonnes per cub
ic metre), then the mass is a couple of kilograms. It is held in the air by a push from a magnet in the base unit. The “push” comes from “magnetic pressure,” which is an energy density associated with the magnetic field. It really is a pressure, a force per unit area, measured in pascals (newtons per square metre) just like air pressure (which on Earth is about a hundred thousand pascals at sea level).

  So with a cross-section of ten centimetres squared, and if Pandora’s gravity is eighty per cent of Earth’s, the pressure required to hold up the lump is (weight divided by area) about sixteen hundred pascals.

  The standard formula for magnetic pressure (easy to find in any physics text) tells us that the pressure exerted by a magnetic field is proportional to the square of the field strength. And the standard unit of magnetic field strength, or “flux density,” is the tesla (T)—named after Nikola Tesla, a Serbian-American inventor once played by David Bowie, in the 2006 movie The Prestige. (A tesla is equivalent to ten thousand gauss, in other units.)

  It turns out that to get a pressure of thirteen hundred pascals you need a magnetic field strength of around sixty mT (milli-teslas—each a thousandth of a tesla). How strong is this? Well, it’s several hundred times the strength of Earth’s magnetic field at ground level (which is only about a ten-thousandth of a tesla; a tesla is actually a pretty large amount). It’s stronger than a toy fridge magnet, at a few milli-teslas, but weaker than the coil gap in a loudspeaker, which might be about a tesla. So it’s certainly plausible that a lump like Selfridge’s desk ornament could be lifted by a magnet of everyday household use.