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TobyBartels comments on Harry Potter and the Methods of Rationality discussion thread, part 11 - Less Wrong
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They wouldn't disappear. They would, after a period, go back in time in order to become one of the other people in the battle.
Using a time turner to make clones in battle is a very, very dangerous idea. Harry has been warned, strenuously, by Professor McGonnagal that he should not directly interact with himself, and we have an anecdote about an auror/criminal pair that went insane because they abused time turners. I imagine that one of the more stable time loops would involve the original Dumbledore/Harry getting disabled before going back in time for the first time.
But yeah, the cloning objects thing is a reasonable use of a Time Turner.
Edit to add: If by collaborating on tricky problems, you are referring to e.g. academic problems, rather than problems of strength, this amounts to a rather absurd charade. If you use a Time Turner to put 6 copies of yourself in a room, and in an hour they succeed in answering the problem, that means that at the beginning of the hour, 5 of them already knew the answer.
I forget if we're discussing MoR or canon, but either way I object. In canon, my objection is pedantic: it's Hermione who was warned, and she only later passed on that warning to Harry. In MoR, Harry has interacted with himself, a few times, and while they didn't all go well, there were no disasters.
Not that strenuously:
You're right, I misremembered. Still, I think there is a lot to suggest that interacting directly with one's time-clones (as opposed to waiting with one's eyes closed while a clone drops off a message, for example), particularly in battle, is a bad idea. You would never observe a future-you doing something ineffective in combat---failing to dodge or block, or casting an ineffective spell, for example---since, after observing that mistake, you would be prepared for it in the future. So the only consistent possibilities involve losing or running away before you can go back in time, or winning right away.
But, since you know these are the only consistent possibilities, if you showed up to a battle intending to use a Time Turner and didn't see your time clones appear at the very beginning, you would deduce that you would not win, and therefore (if you could) you would run away. So, I expect that from Time's perspective, the most stable solution for people who intend to use Time Turners in battle is for them to not do battle at all.
He has never interacted directly with himself in a way that involves seeing a copy of himself, or coordinating actions in real-time, as would be the case in a battle. Harry has so far always heeded Professor McGonnagal's advice, and looked the other way when his time clones are around. Though, as pedanterrific points out, I have overstated the severity of McGonnagal's warning.