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Empathic? That walking leather kink suit? Oh please.
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Star Trek memes and shitposts
Come on'n get your jamaharon on! There are no real rules—just don't break the weather control network.
Leia also has powers with the Force.
Star Wars is basically a more accessible version of Dune. In Dune people had precognitive abilities that would allow them to predict the future. Problem is if someone else can foresee the future one person is reacting to what they predict the other will do, but then the other changes what they'll do based on what they predict the first person would do. So it results in kind of a stalemate. Two people with precognitive abilities can't predict each other's actions. Or the actions of those under the other's influence.
So the Sith's abilities are weakened by the presence of a Jedi and vice-versa. Leia's ability with the force (whether she knew she had them or not) prevents Darth Vader from sensing much about her other. Also the Sith's abilities wouldn't be effective in predicting the actions of any rebel following Leia's leadership.
This... Isn't the answer.
More to the point, every answer to this question is talking about something completely different. Vader was distracted. Vader was only clued into Leia's existence after Luke thought about her. Vader had too much on his plate...!
But this answer, even among all the above, is reaching at things that just make no sense. By your logic, every force user would be crippled at the battle of Geonosis, with hundreds of jedi and sith present.
Qui-Gon and a young Obi-Wan took on Darth Maul, where the latter was able to use his ability without seemingly any hindrance at all. Similarly with Obi-Wan and Anakin against Count Dooku. When Yoda steps in, it's 3 jedi against Dooku. There's no evidence of Dooku bring weakened, as he matches Yoda in force abilities without much effort. By your logic, the sith in both encounters should have been weakened. That is clearly not the case.
The simple and obvious truth is this: at the time of writing, Lucas never intended for Leia to be Luke's sister (hence their kiss) and so, there simply wasn't anything for Darth Vader to sense. Retconning that and then adding in some wishy-washy explanation just trashes the credibility of the franchise.
By my logic the Jedi wouldn't be able to sense that Palpatine was a Sith even while sitting in a room with him where there was no dangers or distractions. I'm no prequel fan, but I recall that it's mentioned the Jedi's ability with the force was being weakened.
And it wouldn't affect the ability to swing a lightsaber around. Though it would affect the ability to use precognition to predict where the opponent was going to swing their lightsaber. I mean they can deflect blaster shots all day but can't deflect a lightsaber that's moving much slower? Why is this? Makes sense if you consider the guys shooting the blasters don't have much force abilities so they can use the force to predict where the shot will be and deflect it. But another force user's actions can't as easily be predicted so it comes down to good old fashioned martial arts abilities.