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Kim Stanley Robinson and other skeptics aside, some version of "FTL" is not necessarily impossible. We already know of a couple of potential theoretical loopholes, even though we lack the means (as of yet) to exploit them.
Many things that were considered impossible 200 years ago, or had not even been imagined as yet in fiction, are today commonplace. That we sit in our homes (or in a park far from any outlet) and access much of the collected knowledge of humanity, and hold discourse with persons around the entire globe in text, or voice, or video, and do so cheaply and easily, was not even a fantasy in 1816. Yet here we are...
Yeah but the problems with these theoretical loopholes are things like "requires more mass-energy equivalent than exists in the observable universe." Or "requires arranging matter on a level that is orders of magnitude smaller than electrons." Or, my personal favorite, "you have to have a warp drive to build your warp drive."
This is decidedly different from just not having a concept of how to send a radio signal.