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solipsist comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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So, you could put a 6-hour stretched pebble in someone's pocket, and they wouldn't be able to use a Time-Turner?
I'd say yes (until the 24 hours run out and the pebble stops being time-stretched).
Similarly, if you go back 6 hours in time and, say, cast a spell that creates fireworks visible from a large distance, you've just prevented everyone within that radius from using a Time-Turner.
Finally, I'm mostly sure that the incredibly-small-scale changes caused by simply going back in time 6 hours propagate quickly enough that only one person on Earth can use a Time-Turner on any given day.
So yeah, there's a bit of a problem here. Presumably this is one of those "it works how Merlin would have expected it to work" things.