This was inspired by the discussion on earthbending going on next door - I started getting sidetracked into talking about all four elements, so decided to write a standalone article. Critique/complement/discuss to your heart's content.

There's a lot of different opinions on how bending works. Personally, I put it down to chakra - no, that's not a way of weaseling out of an explanation, I'm saying that in the avatar universe, there exists a physical force of nature/physics that could be approximated to our notion of chakra - a force generated by living things (not exactly the same, as I'll explain later, but I'll use the word anyway - it gives the right idea). I'm not just pulling that out of the air either - as I remember, when Aang was getting training from that monk to attain control over the avatar state, they were doing it by unblocking various chakra reserves. Bending, of any type, is essentially the ability to use the inherent chakra of a certain element to your advantage.

Now, since water and air aren't "alive" in the conventional sense, I'm going to modify the basic idea and propose this idea: each form of bending is in fact utilising a different form of chakra. Firebending is utilising the inherent chakra of living things - thus, firebenders create fire from their own breath, converting their own energy into a physical form. This also explains why certain highly skilled firebenders (Iroh, Azulah and Ozai) can create and bend lightning. After all, lightning technically isn't fire - it's a more 'pure' form of energy. Firebending emphasises raw power - the energy of life. Being the energy of life, firebending is also the energy of change and progress - the fire nation is the most industrial nation in the world of the avatar, and is currently concerned with bringing about a new world order (going about it the wrong way, but that's by the by...). It is also ready to accept and apply new ideas - just two seasons after capturing the hot air ballon that Aang and Co used to keep the fire nation clear of the western air temple, the fire nation have adopted the technology and created an armada of war zeppelins - less than a year of real time. However, whether it is due to the loss of the knowledge that fire is more life than destruction, or just that living energy is by nature chaotic and unpredictable, firebenders lack the degree of control and finesse that other benders have - they rely on the sheer destructive force of fire to batter their opponents into the ground rather than any particular technique (not to say that techinique is unimportant to firebending, merely that fire develops a great deal of power without being refined much).

Water on its own is not alive (although it is the source of much life) and so it must use a different form of energy to firebending. The clue to what kind exactly, is in water's nature: fluid, malleable, amorphous. Even in the calmest body of water, there is movement (except in the case of ice - more on that later). I would go so far as to say that the motion energy within the water itself is enough to move it in any way - the problem is that in it's natural state, the movement is disorganised, incapable of any meaningful work. Waterbenders utilise this disorganised chakra, aligning it to work in concert.

A better understanding of how this works can be gained from looking at magnets. A piece of iron (or any other magnetisable material) has the potential to be a powerful magnet. Each individual grain of iron has its own polarity, and thus generates its own magnetic field. However, in normal iron, the grains are disorganised, with no particular arrangment: the indivudual magnetic fields cancel each other out and the net effect is that the iron has no magnetic properties. However, if the individual grains are all aligned in the same direction, the iron becoms a magnet.

Waterbending functions on the same principle: by organising the inherent energy already present, waterbenders can cause a piece of water to move with seemingly no external force being applied - or, they can quell the motion within the water, forcing it to slow down, and thus freeze. The ease with which this can be done is dependent on size (a larger body of water means more energy that needs to be reined in at once) and the complexity of the movement (a technique like the water whip requires a high degree of control in order for the water to keep its shape).

Healing using waterbending uses this approach, but in a more subtle manner. Borrowing a leaf from the pages of eastern philosophy, I will say that in the world of the avatar, the body of a living being flows with chakra in certain patterns. Damage, whether caused by injury or disease, disrupts this flow, resulting in a less-than-functional individual. Waterbending healers use their skill to mold the water into the correct shape, bridging the gaps in the body's natural chakra flow or redirecting the flow so as to accelerate the natural healing process. The more drastic and dire the damage, the harder it is to fix.

Earthbending works in a similar fashion to firebending: except instead of using their own energy, earthbenders use the energy inherent in geological rock. Now, this energy is similar to firebending in that it is based on living things (hence why water is opposed to fire, but earth isn't). But instead of using the free-flowing, libreated energy of a living person, earthbending uses the 'crystallised' energy of rocks.

Bear in mind that rocks fall into one of three categories: sedimentary, igneous, and metamorphic. Sedimentary rock is the compressed remains of organic material - the residual life energy in those organisms gets 'trapped' in the rock, and is there ready to be tapped into. Even being worn down into sand doesn't release this energy, although it does make it harder to control, as Toph discovered while trying to prevent the sand bandits from stealing Appa. Igneous rock is formed by molten lava reaching the surface and cooling into solid rock. Again, energy is trapped within - only instead of organic energy, it is pure heat energy. I'd say that this makes little or no difference to the earthbenders ability to use it - heat energy and life energy are essentially the same, as evidenced by firebenders. The confirmation of this can be seen when Aang organises the earthbenders of the fortune-tellers village to dig a trench to divert the lava flow. Being at the base of a volcano, it is almost certain that the soil in the area is volcanic. Finally, metamorphic rock is sedimentary rock that has been subjected to great heat and pressure, and converted to a different type of rock as a result - essentially the same as igneous rock in terms of earthbending.

As for why contact is needed or preferable for earthbenders: I'd say that by being in contact with the ground, earthbenders are using their own energy to control the earth more directly, similar to how a landline connection is stronger than a wireless one. It's still completely possible to bend earth without physical contact, it's just that transmitting the instructions through earth is easier than through air. Although that raises the question of how it does get transmitted. Dust particles in the air, perhaps?

Metal creates a problem for earthbenders, since it has been extracted out of the soil - being an element, rather than an organic compound, iron has no inherent chakra. No chakra, means nothing to use for bending. Toph can sense the miniscule particles of earth left within the metal during the smelting process (iron is never completely pure, and in fact the inclusion of some organic compounds composed of carbon and nitrogen can strengthen the metal). Although the metal itself is unaffected by Toph's bending ability, she can use the earth particles inside to force the metal to move, much as bloodbending forces people to move by controlling the water inside them. Nevertheless, the scarcity of earth in metal makes it quite difficult - if you watch the series, Toph never bends metal from a distance - she is always in direct contact. Also, she doesn't have the same precise control as she does with earth - she can force the seams of a metal barrier apart, but she can't make neat pedestals of metal rise up as she can with earth.

With regards to Toph's vibration sensing ability, I think it's essentially just that - a form of echolocation which she's attained through training. Thus, even though sand is essentially the same as earth, vibrations can't travel well in it, and so Toph is blinded. However, vibrations travel well in metal - the fact that the metal isn't part of the earth beyond makes sensing through it unfeasible, but the vibrations travel through the actual metal quite well - enough for Toph to feel the returning vibrations from the organic impurities.

Like waterbending, airbending is based on the energy of motion. However, it works in a different manner to water. Consider the difficulty Toph had when teaching Aang to earthbend - as an airbender, Aang's natural tendency was to sidestep an attack, rather than face it head on as an earthbender would. Likewise, when using his glider, Aang bends the air around him and rides the resultant air currents, rather than using the air to forcefully push the glider up into the air. Also, when fighting, Aang is more likely to sidestep his opponent's initial attack and then strike while their defences are open, than to attack head-on and try to break through their defences. This indirect way of attacking mirrors the nature of wind itself. Any wind, even a powerful gale, is not the result of a physical force pushing against a body of air - rather, all winds are the result of pressure differences. Air moves from areas of high pressure to low pressure, and theirin lies its strength. Rather than fighting against the natural inertia of matter, as earthbending does, air relies on that inertia: the tendency of nature to stablise and even out. Just as an aircraft wing produces a powerful lifting force by doing nothing more than creating a pressure difference, so Aang uses those pressure differences to create powerful winds.

Now, you may argue that a mere pressure difference could not produce the sheer force required to smash a flaming boulder to smithereens, as Aang does on one occasion, but consider this: one of the most powerful forces in nature (if not the most powerful) is the vacuum. An experiment in the 17th century involved taking two hemispherical cups and joining them with an airtight seal. A (newly invented) vacuum pump was then used to remove the air from inside the hollow ball. A team of ten horses was unable to pull the two halves apart. While Aang's airbending probably doesn't use quite so drastic a level of pressure, he is still very capable of feats involving incredible amounts of force, using nothing more than the pressure differences that are responsible for creating wind.

This might also explain why air is not diametrically opposed to fire, while water is. Even with the indirect use of pressure, the motion of air is more linear and direct than water, and is thus in less conflict with fire's raw nature: however, earthbending is at odds with airbending due to the fact that it is imparting motion to a static medium through sheer brute force, however refined it may be. This is almost diametrically opposite to airbending's strategy of using inertia and stability to it's advantage.

Finally, in closing, a brief overview of how this theory explains the inability of the average bender to learn more than one type of bending: namely, the fact that each bending art uses a fundamentally different basis. Firebending uses the living energy of the individual. Earthbending uses living energy as well, but it uses the energy in the soil itself - external rather than internal. Waterbending and airbending both use energy of motion, but waterbending redirects the motion within the water itself, while airbending creates external pressure differences and lets the air do the moving for it. With such wildly divergent methods of bending, it is small wonder that only the Avatar can master all four arts in one lifetime.