It seems to me that most of the "impossible" things in Star Trek - all the shows, movies, etc - are solvable with adequate energy, technology, etc.

The things I think are likely unsolvable even with advanced technology - and a whole lot of energy, are:

Remote sensors, such as being able detect life forms from beyond a solar system, etc. Or even from orbit really, at least in terms of detecting life forms directly. Detecting gases that might SUGGEST advanced life forms with technology etc, we can do now with gas chromatography etc.

Humans producing children with alien species, such as Vulcans, Klingons, Romulans... Of course, much of this "theorizing" in Star Trek simply comes from the reality that most "aliens" depicted in sci-fi are simply humans wearing makeup. Actual alien life likely to be far more different. But even if bipedal-type life is discovered on other planets, the chances seem vanishingly small that humans could successfully... "interact"... with them, in that way. Humans are genetically far more similar to other forms of life on Earth, than they are likely to be with any extraterrestrial life; and yet, humans cannot reproduce with any other life form on Earth.

I omit the transporter because I suspect that it might actually be possible to do something like that, although probably always with a receiving mechanism as well, but it would be a case of destroying the original and creating a copy. And if people are stupid enough to do that, fine. I'm not. But I don't think that makes it necessarily impossible.

Thoughts?