A rising Star Wars theory casts Darth Vader’s actions in a new light, while giving some much needed props to his daughter, Princess Leia. The idea — presented recently by Reddit user u/khdutton — is that in The Empire Strikes Back, Vader was trying to track down the Millennium Falcon because he could sense a powerful Force user onboard, long believed to be Luke Skywalker. In reality, Vader was sensing Leia, whose latent powers were just beginning to emerge, leading to her climactic rescue of Luke. This adds more buildup to Leia’s training in the Force, and explains away an oversight on Vader’s part.
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Star Wars: Episode V — The Empire Strikes Back picks up three years after the events of A New Hope, with Darth Vader leading a galaxy-wide hunt for the Rebel Alliance, and in particular, the pilot who used the Force to make a near-impossible shot that destroyed the Death Star. In the film, Vader does not know Luke is his son, but he was right behind Luke at that climactic moment, and he would have killed Luke if the Millennium Falcon hadn’t intervened. The canonical novels make it clear that Vader knew already that Luke was a Force-user.

The Empire launches an all-out attack on the Rebel base on Hoth, leading the Rebel forces to scatter. Leia leaves with Han Solo and Chewbacca on the Millennium Falcon, while Luke takes his X-wing to Dagobah in search of Yoda. Vader seems to have no inkling of where Luke went, yet he continually works hard to track down the Falcon. On one level, this may be a grudge over the ship’s well-time shot in the Battle of Yavin 4, but it’s also clear that he wants to find this young Force-user — especially once the Emperor reveals that this is Anakin Skywalker’s son.
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Vader holds Leia hostage, believing that Luke will come to rescue her. There’s no indication that he has figured out the princess is his daughter, which is a bit odd since the Force grants him so many other insights. His judgement is clouded by the Dark Side at this point in the story, but perhaps there’s something else going on as well.
Leia Scrambles Vader’s Senses

Darth Vader knew he had killed Padme and believed their unborn child had died with her, not know that they had twins who survived. If he was reaching out with the Force searching for his child, it would make sense that he would mistake Leia for Luke. Furthermore, he would begin this search on the Millennium Falcon, creating an easy false trail for him to follow.
This has the convenient side effect of distracting Vader from searching more widely for Luke, which might have led him to Dagobah and Yoda. Once Leia was in his grasp, her presence in the Force may have continued scrambling Vader’s efforts to search for Luke.
This all fits nicely in the same movie where Yoda first hints at Leia’s true identity, saying: “No. There is another.” It pays off in the end when Luke is able to reach Leia through the Force her guide her to his rescue in the Falcon. Finally, it really pays off in the climactic duel at the end of Return of the Jedi, when Vader finally realizes who Leia is by sensing Luke’s thoughts. He threatens to kill Luke and work on corrupting Leia instead, insinuating that she is also a powerful Force-user and an acceptable replacement as his Sith apprentice.
Leia’s Arc

This could also be helpful context for those who felt Leia’s arc in the sequel trilogy and other later stories came out of nowhere. The princess undertook true Jedi training after the war was over, and developed some incredible power and finesse off-screen. To many fans, it strains credulity when she pulls herself from the vacuum of space in The Last Jedi, or when she completes Rey’s training at the beginning of The Rise of Skywalker. For what it’s worth, her potential was clearly set up early.
Meanwhile, this interpretation humanizes Vader in some ways, and emphasizes how much the Dark Side clouded his judgement and his sense. It helps to explain some of his actions and why he trusted his own faulty intuition, making this era of his life all the more tragic.
Star Wars fans are unparalleled at finding hid layers of nuance in their favorite stories, and they have plenty of material to work with. You can revisit the movies now on Disney+, and find more insight in novels, comics, and other mediums.