Does information paradox in the Many Worlds interpretation cause a problem? I'm taking a philosophy of time travel class. In one of the lectures, the teacher was discussing problems with the Many Worlds interpretation. He talked about how since anything that can possibly happen happens in some timeline, in one timeline there is a person that comes out of what appears to be a timemachine with the complete works of Shakespeare. This person didn't actually come from the future, but he and the works of Shakespeare were created due to random quantum fluctuations. He gives the book to Shakespeare, who publishes it as his own. Later in the same timeline, someone reads his work and creates what he thinks is a timemachine to go back and give Shakespeare his complete works. He gets into this machine and disappears. My teacher says this is a problem because it is indistinguishable from a genuine information paradox. My questions are:


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*Is this really a problem? Even though it looks like an information paradox, it doesn't seems to be one. Instead of the book coming from nowhere, it came from random fluctuations.

*This question's more weird: Even if it were a paradox, would it matter to people in the other universes or would it not be a problem for them? Since people in one timeline can't observe another timeline, would the paradox be isolated and not actually affect any other universe or am I confused about what a paradox would mean?
This isn't super important, I'm just curious. I originally posted this in philosophy.SE, but physics.SE might be a better place to ask these questions.
 A: This alleged problem falls apart as soon as you do a rigorous analysis. It should be clear that with such random accidents there is no causation. If event A really causes event B, then that's reflected in the state of the system. You'll have a state of the form 1/sqrt(1+|u|^2)[|A B> + u |not(A) not(B)>], so an entangled state containing information about the sequence of events and also about the counterfactual events.
A: Many-world interpretation can be consistent with the second law of thermodynamics. It is not a problem. Now, about this hypothetical time travel:
If you went back in time to tell Shakespeare about his work and he published it after, it looks consistent but it is ultimately a paradox because where does that knowledge come from? Information, or strictly knowledge of this level of sophistication, requires order. If you want to create that knowledge, some other parts of that toy universe would be affected because on the whole, entropy does not decrease. You just cannot create knowledge without cost.
