Alright, the physics of lightsabers are up for debate since nothing like them exists. However, we can draw a lot of conclusions based on what we see in the movies.
Those of you thinking about them as "flashlights that cut" are dead wrong. Period, end of sentence, whatever you need to hear to make you understand. They are explicitly not photon beams like a laser, and function nothing like that.
Lightsabers clearly have mass. Heck, for all physicists know photons may have mass. We think they don't,but no one knows for sure. The hilt of a lightsaber (going by how the actors have handled them) are quite dense and have a fair amount of mass. This makes sense given that there is a high output power generator in there.
If you're going by the movies, then you have to consider what the actors are really swinging when the filiming is being done -- they're pretty thick metal rods that are attached to the "lightsaber" handles that we can see. The heavy metal rods get replaced during the Rotoscoping process by the lightsaber blades.
So, what the actors are really swinging really does have mass and length and really does act a fair amount like a real sword, because it is a certain length of metal rod. Ewan McGregor had several identical lightsabers made for him, because he found that he could get quite animated and kept bending the metal rods. So, they had to keep fixing them, and had to have a number of them in stock because it took them a lot longer to fix them than it took him to bend them.
How all that works out in game physics, is not something that is clear to me. You can't just put all that mass into the handle -- you've got to somehow keep the majority of the mass in the blade. Otherwise, it just doesn't swing the same way.
You really don't want to try to talk about the mass of photons, because even if you were to take a particle that does have real measured mass (like an electron), to get enough electrons together to make up enough mass to make the balance work right, well that would be a heck of a lot of energy -- check out Einstein's E=mc^2 equation. That would be enough energy to make a small tactical nuclear device.
Sure, lightsabers have a lot of energy and they can cut through just about any type of matter, but putting a Thermal Detonator in their hands is bad enough -- you don't want them walking around Mos Eisley with a TacNuke strapped to their waist.
The more I think about it, the more I think we should just treat lightsabers as a "hand wavy" type of weapon, and not try to delve too deep into the physics behind them. They do what they do because that's what we say they do, and that's what makes sense from a narrative perspective. And whether that's us as individual players or GMs saying that, or FFG as the "official" game designers saying that, I think that's the way they should work.
But I would definitely keep the skill separate from standard melee weapons and many melee-based talents probably wouldn't be applicable to them, although both Strength and Agility could be quite useful when applied correctly by someone who is properly trained. I also think that anyone not explicitly trained in how to use them should suffer massive difficulties in trying to actually use them in combat -- like maybe have to throw two or three extra purple dice, or maybe have all their purple dice upgraded to red dice. Or maybe both.
It's one thing to turn on a lightsaber and carve a slot in the stomach of a dead Taunton in a non-combat situation, it's another thing entirely to try to fight someone with a weapon you've never trained in and doesn't work like any other weapon you've ever known.