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comment Does natural unit of information and entropy, nat, play special role in the freebit picture?
I don't understand why you're calculating the entropy S by averaging over all x in the interval [0,1]. If you really take seriously that this is Knightian uncertainty, then you ONLY know that x is in [a,b]: you don't even have probabilistic information beyond that, and you certainly don't know that x is uniform. So, not knowing where your formula came from, it's hard to say whether it's "just a neat mathematical coincidence" or whether it has some operational meaning.
Nov
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comment Quantum version of the Galton Board
Well, I think you can at least get a pretty good approximation in closed form, if you're willing to count special functions as "closed form."
Nov
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revised Quantum version of the Galton Board
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revised Quantum version of the Galton Board
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answered Quantum version of the Galton Board
Sep
28
comment Is the firewall paradox really a paradox?
By "actual" I meant "referring to the real world, not to a particular approximate method of calculation." You seemed to be suggesting that one can resolve the information-loss problem by saying that information IS lost in a semiclassical approximation, but isn't lost when you sum over all topologies. I was explaining why I don't think that answers the question: because one can state what's "hard to swallow" here or an apparent challenge to locality, without ever needing to make assumptions that come from the semiclassical approximation.
Sep
28
comment Is the firewall paradox really a paradox?
Well, suppose the external observer applies a unitary transformation to the early Hawking radiation, that lets the infalling observer easily see that the early radiation is entangled with the radiation just coming out. Then by monogamy of entanglement, the radiation just coming out can't ALSO be entangled with the modes just inside the horizon. But if they're not entangled, then the infalling observer won't experience a smooth QFT vacuum. That's pretty much the content of AMPS.
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answered Is the firewall paradox really a paradox?
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