The Banach-Tarsky theorem applies to life force, not to mass.
(The ending of ST2 and beginning of ST3 already imply some kind of life force.)
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I was kicking around a story idea called āGhost Fleetā, in which Captain Sulu uncovers an operation within Star Fleet; where copies of all the ships and all their crews are stored in pattern buffers for when they might be needed. If it is a question of ālife forceā, then how come the Riker transporter twins were so virile?
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Hey - itās Riker weāre talking about.
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The Banach-Tarsky theorem shows that, given certain interpretations of set theory, if you can divide a space finely enough, you can take any object, divide it into 5 or more pieces, and assemble multiple complete copies of itself, or a larger copy, or a smaller one; if it is true, then there is no conservation of volume.
So itās mathobabble saying there is no conservation of whatever-it-is.
Except in Futurama, of course, where they need an external source of matter.
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Arenāt we always talking about Riker? 
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Ive been rewatching Voyager and got to the episodes where the Hirogen take over Voyager and turn the whole ship into a holodeck.
It made me think, surely Stsrfleet could place holo-emitters throughout their ship, then if they were ever forcefully boarded they could create as many holographic soldiers and weapons as needed to repel the invaders.
Anyway, just a thought.
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And what about transportes? They could just make the invaders materialize in Space.
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But youād have to turn off the safety protocols to make that effective, and that always causes troubleā¦ just look what happened with Moriarty! That way lays madness, my friend!
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Nahā¦ travelers just donāt have time to be clean-shaven!
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Ha! I am no match for your superior Trek-Fu ! 
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Checks out 
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I agree
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And they could use transporter jammers, transporter as a weapon, replicators as weapons, holoweapons against Starshipsā¦ They use direct energy weapons and torpedos because We are familiar with the concepts of throwing things to damage enemies. Imagining different things can cause too much strangeness in the audience.
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I totally forgot about the other Riker, thatās another good example. Even assuming the life force thing is valid, it seems like the transporter would be a medical panacea for people not yet dead. I can understand why they donāt want to use it from a drama and storytelling standpoint- nobody wants to see Spock at the end of Wrath of Khan just get casually beamed out before death and reverted to an earlier Spock to fix his horrible radiation burns (who then has to ask for a recap of what happened with that whole Khan/Genesis situation), but has it ever been really explained in-universe?
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But they manipulate the time itself.
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Well, Seven of Nine brought back Neelix from the death ( I presume for Tuvokās chagrin) once and It was never mentioned again. They use some miracle stuff in some Episodes, but It would make a lot of cool dramĆ”tic situations useless in the rest of the series.
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Have you seen the series āDark Matterā (The 2015 TV series)? I really liked their āteleportationā method, and it is cleverly abused in several episodes.
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I have not.
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