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According to another question on this site it appears that lightsabers are controlled plasma streams. These streams are seen deflecting laser bolts and of course dueling with other lightsabers.
But plasma isn't solid, in physics it behaves as a gas - so how can it deflects blaster bolts and other lightsaber blades? Lasers pass through plasma, and a plasma stream wouldn't stop another plasma stream in a duel.
My best guess is that the blaster bolt is ALSO energy, so it's the magnetic bottle that holds (and shapes) the plasma stream that is doing the actual deflection.
edit Ok; I take it back.. No guess; take a look at the lightsaber article on the Wookieepedia:
When cutting through dense material, the immense electromagnetic field generated by the arc caused resistance rather than letting solid matter enter and interrupt the arc. This gave the blade a feeling of being solid when immersed in dense material. Rarely, some solid materials could actually pass through the electromagnetic field and short out the arc. Other electromagnetic energy fields and coherent energy were also repelled by lightsabers' arcs. These include most force fields, blaster bolts, and other lightsaber blades.
(Emphasis added)
Remember; Blaster bolts aren't lasers, exactly. They are charged particles.
Though it's decidedly not canonical in the Star Wars universe, Darths and Droids strip 9 gives a good explanation. Quoting.
A laser sword has to be a magnetically contained tube of plasma. Anything else is clearly ludicrous. The containment field would obviously work in both directions. A blaster shot is also plasma. Q.E.D.
That's why a lightsaber can deflect blaster bolts.
I have a pretty good basis in physics so I will try an explain using that instead of canonical sources. The physics of the lightsaber itself which is espoused by b_jonas is that magnetic field controls or contains a length of plasma which some consider to be a fourth state of matter (the other three being liquid, gas, solid).
Magnetic fields generally are governed similar to the laws of electricity (as discovered by Maxwell) and the two modify each other. a moving magnetic field creates an electric field, and I think the inverse applies although the exchange is not identical (I am talking about the direction and shape of the magnetic field). Plasma carries a charge:
Wikipedia: "Heating a gas may ionize its molecules or atoms (reducing or increasing the number of electrons in them), thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions"
Therefore, if the blaster is firing an electrical blast (I think plasma is a super high conductor) then when the lightsaber is swung around it will create an opposite directional field like the two poles of a magnet where the rule "like rejects like" will deflect the plasma bolt!
I would point out that Lightsabers seem to have a physical presence rather than just being a bunch of plasma contained by a magnetic field. For example, when Jinn and Kenobi are slicing up droids during the opening scene of Phantom Menace, the pieces do not simply fall apart, they are sent spinning by the contact with the blade. Later, when Jinn thrusts his blade into the blast doors of the bridge, melted metal is displaced by the blade, forming a rim of molten metal around the blade as he cuts through the door, much like pushing a heated metal rod into a block of wax. So perhaps Lightsabers are more like a multi-layered, tubular force field. There is an impenetrable inner core, covered in a layer of energized plasma, which is then contained by another more permeable force field, which prevents excessive radiation of heat but still allows physical objects to come into contact with the plasma. So anything that isn't vaporized as it penetrates the permeable outer 'skin' will still be stopped/deflected by the solid inner core.
