It is his hand. I was curious to know for sure myself now so I took a screen shot into Photoshop and zoomed in. It's 100% a hand with a lightsaber. Though it's not gripping it. The hand is open falling in beside the hilt of the saber. Afterwards I stumbled on this-
My screenshot actually turned out clearer than this one, though I don't know if it's different because mine is from the special ed. It also really looks like his left hand which is curious.
I don't think it is his hand. Luke was sucked into one of those many red circular vent things which you can see all over the place in that huge funnel.
when Luke falls, he gets pulled sideways into one of those vents, he then travels down a silver corrugated tube where he comes to rest, theres no sign of the severed hand or lightsaber
that tube opens & Luke falls again down another similar tube to a hatch which is already open to the weather vane
Luke lands on the weather vane with a jolt, the weather vane moves with Lukes weight, then we see the piece of debris falling
If this was Lukes hand, the chances of the hand & lightsaber being sucked into the same vent, and falling out of the city after Luke falls out are pretty slim
I think its just debris added to make you more aware how perilous Lukes situation is
Having subsequently goggled this, it appears that this debate has been rumbling on for many years.
This excerpt from the script would seem to confirm that it was indeed intended to be debris:
EXT. BOTTOM OF CLOUD CITY - WEATHER VANE - DUSK
Unable to hang onto the pipe, Luke tumbles out, emerging at the
undermost part of Cloud City. Reaching out desperately, he manages to
grab onto on electronic weather vane.
Ben... Ben, please!
Luke tries to pull himself up on the weather vane but slips back down.
He hooks one of his legs around the fragile instruments. All the
while, a powerful current of air rushes out at him from the exhaust
There is an ominous cracking sound from the base of the
weather vane and a piece breaks off, falling into the clouds far below.
Hear me! Leia!
Ronsters observations are always interesting to read, even if the visuals are now locked down :-)