Copyright in a vast vast Universe.

You may have heard of the theory that goes something like this, that if you had an infinite amount of monkeys randomly pounding on an infinite amount of keyboards, most the content they come up with would be junk, but somewhere in there you might have Shakespeare.
So that rises the question, the Universe is vast, possibly infinite. If the Universe is in fact infinite, doesn't that mean it's possible that something copyrighten here could exist somewhere else? Possibly even old enough to be public domain?
If this is in fact true, and somehow these worlds managed to cross, perhaps a world exactly like ours but 95 years ahead of us exactly, what would happen then, because everything we make, the copyright would immediately be invalidated, because on their planet, it just hit public domain, and here in America, we accept the 95 year expiration, regardless of where it's from. Perhaps our planet is exactly 95 years behind them because the Universe itself has observed their copyright law, it is written into the stars themselves, by the time we even think of it, it's already in Universal public domain, so the Universe is finally saying to us, "fine, you can have a turn now," but in reality, Disney hasn't owned the copyrighta to Mickey for over 95 years, and they've just been exploiting our lack of knowledge of Universal copyright law to keep us from using him 95 years longer than the Universe has declared our right!