Synchronized random bit generator

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Dragonfall
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Is it possible to construct 2 devices which simultaneously generate (the same) random bits indefinitely? No matter how far apart spatially they are. And I don't mean a pseudorandom number generator with the same seed. I mean something like sharing entangled particles, but without the need to exchange stuff continuously.

It wouldn't violate FTL, so what's keeping us from doing it?
 
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Well, by definition, any such devices would be pseudorandom number generators. If the two devices were separated by enough space to no longer be causally connected, for example, then they might as well be operated at different times, too. If they're operated at different times, yet produce the same sequence of numbers, then by definition those numbers are not random.

- Warren
 
That's true. Good point.