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The Heisenberg Compensator in Star Trek: The Next Generation
The idea of a transporter is that it breaks down essentially all of your particles down to like the subatomic level, right? And it maps that and then it carries those and then it rebuilds you somewhere else. But in order to do that, you have to know where every single particle is. The physics limit that we have for that is Heisenberg's Uncertainty Principle. So essentially, I don't think transporters will ever be a thing that we can do.