Dilithium is the magic unobtanium that makes the warp engine work - and of course, provides a plot device like imaginary elements essential to advanced tech often do in science fiction.
As far as FTL travel itself, just like time travel, we have no idea whether those things are actually possible. Most of the mass and energy in the universe are in forms we don't really understand though - so there's a certainly a lot of physics left to be discovered. Transporters as they're described on the show are unlikely. But could we someday build devices that achieve the same effect, say by folding space? Who knows. Not anytime soon that's for sure! Magical telepathy is of course impossible. If we all had wireless implants that allowed us to interface directly with technology and communicate mind-to-mind with others over the network, that would give us artificial telepathy. Wetware and radio waves.
Star Trek has always been full of technobabble. Pressure inversions in the plasma manifolds, phase variances in the chronoton field, and so on. If I was Captain Picard there were plenty of times I would've asked Geordi "Are you making this shit up?". "Yes Captain, our systems are so reliable Starfleet hasn't actually needed engineers for the last century. We have to invent reasons to keep us around so we don't lose our jobs." 😎
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