At the end of Star Wars: The Empire Strikes Back, Darth Vader was trying hard to capture Luke. Even with the hard way... The Carbonite Freezing!
After cutting off Luke's hand, capturing Luke would have been easy. Luke lost his lightsaber too. But still, he used speech to seduce him and failed. And, just after that, when Luke let himself fall, he didn't use the force to stop him from falling. Why?
He could even apply carbonite freezing on Luke after dragging using force.
Earlier in the film
VADER: "He will join us or die."
later
VADER: "Join me."
LUKE: "NEVER!"
[Vader's thoughts]: "So...let my son be tortured to the breaking point by Sidious, or kill him...oh look, he's falling. Decision made."
Vader: "Eat pit, Jedi."
The "Jedi Pit Theory" states that Jedi are nearly unassailable warriors except in the presence of pits. It points out how, in the OT, every time a Jedi is in trouble, they are near a pit (Ben dies on the Death Star, near a shaft; Palpatine dies when he falls into a pit, Luke is in trouble near the Sarlaac pit, etc)
Luke was at his darkest hour. He had just learned his father was a Sith Lord, that Obi-Wan, his mentor, had (from Luke and Vader/Anakin's perspective) lied to him, and had just had a thorough trouncing -- as well as realizing his friends were now captives of the Empire. Oh, and there's that whole thing about losing his hand.
From Vader's point of view, if all this was not enough to make Luke angry enough to give in and to come over to the Dark Side, what would? But Luke wasn't feeling full of rage. He was hurt, he was wounded, and more to be pitied than feared. Vader would see him, at that point, as unwilling to join him and probably even weak. So he likely saw no reason to save him. He was either too weak to be Sith or strong enough in his refusal to turn that he'd be an enemy.
Luke was much more powerful than Vader expected, likely due to Yoda's training, which hadn't figured into his plan. When the point comes that Vader had planned for Luke to be frozen, he remarks, "All too easy...". Then, when he realizes that Luke has escaped the trap, he says "Impressive...most impressive." At that point, he's realized that Luke is too powerful to defeat in the simple way he'd planned.
My take on the events following Luke's decision to fall is that Vader did use the Force to guide Luke's fall into one of the exhaust pipes. There was no obvious reason why Luke's body suddenly veered into the exhaust pipe. I didn't see a large exhaust fan or tractor beam pulling Luke in. It's reasonable to presume Vader was acting from a distance as he watched Luke plummet.
But why Vader didn't immediately levitate Luke when he stepped off the gantry? There are three possible reasons:
1) Vader was caught off guard by Luke's sudden decision to commit suicide.
2) Given Vader was likely exhausted from the duel, and in addition seriously injured by one of Luke's blows, he may have been unable to levitate Luke with Force powers in his weakened state (although we might surmise he had just enough strength for a gentle Force "push" into the exhaust pipe). Certainly Luke was too weak and scared (and unskilled with using the Force) to levitate himself off the gantry to safety, so some degree of concentration is required to lift heavy objects.
3) Vader wanted Luke to willingly join the Dark Side - or die:
VADER There is no escape. You must join me or die. Don't make me destroy you here... The Emperor is strong with The Force. But if you join me, together we could overthrow Him. Do not resist. It is our destiny!
Although this answer would contradict Vader's actions in saving Luke from falling to his death if Vader Force pushed Luke into the exhaust tube. Unless Vader was bluffing with the ultimatum "Join me or die."
At first, he just wanted to freeze Luke to bring him to the Emperor.
But when he saw that the Force was strong with Luke, he changed his plan, thinking he could bring Luke to join him so they could rule the galaxy. Maybe he also understood that Luke could defeat him and take his place, if he was trained by the Emperor.
That's why he tried to talk him into joining the Dark Side at his side and he didn't use the Force to bring Luke to the Emperor.
No one has mentioned that Vader had a Plan B. He had his men deactivate the hyperdrive in order to capture Luke and his friends. Then use the tractor beam to bring them all in.
Seems he coaxed Luke into the exhaust pipe, though I don't know how he knew that it would lead to the outside of the city and that the Falcon would find him? But they did find him.
vader decided to wait it out, knowing that he had luke's friends and luke would not abandon them. Vader knew that Luke would return to save them.
Well, maybe this is naive but to me, he did not stop him because he couldn’t. At least that’s what the writers intended.
The force is neither immediate nor all powerful and it doesn’t allow to read thoughts as demonstrated by Darth Maul fate and so many others during the series. It does allow you to read feelings and to instinctively react but that’s it.
So why did Vader let Luke escape? He didn’t. He simply didn’t expect Luke to jump. The movie depicts this very clearly. Vader still has his arm stretched in the offering to Luke. The truth is, it took him by surprise (and I think that is pretty well reflected on the movie) and by the time Vader reacted it was too late already for him to use the force or any other means to prevent it.
In a comic book I feel there would have been a bubble on top of Vader’s head when Luke jumps with the text: “WTF?”
Not applicable.
One more thing, more practical; the G-canon doesn't ever show "Force Pull" IIRC. People are pushed directly away, choked with their feet on the ground, etc, but never lifted off their feet (possibly excepting Padme; I can't remember if she's lifted off the ground) or pulled toward the Force user. In G-canon, levitation by the Force only happens on inanimate objects or the Force user themselves to augment leaps. Even in Extended Universe, levitation of a living thing is almost always through the Dark power, Force Choke. – KeithS
The accepted post, answers the question of if Lord Vader could have saved him, why didn't he? Your question is moot, before asking if he could. Which he could not. N/A.
I doubt he wanted to bring Luke to the Emperor as he was. When Lando told him the carbon freezing could kill Luke he said something like "I do not want the emperor's prize damaged". But then he went and cut off his hand. There was also the bit where he encouraged Luke to overthrow the Emperor. Wouldn't want that getting back to Palpatine. Better to wait. There would be other opportunities to bring him in.
This is simple.
Usage of the Force needs concentration. The Force is equal to midichlorians in a being's body. Now, Vader is only 60% man. Cybernetics get in the way of using the Force, and because Luke's drop was very sudden, he had no time to concentrate -- with his concentration already a bit more useless than it originally was.
