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I just burnt a piece of paper containing a 5 digit number I made up randomly and as far as I am concerned no one else will ever be able to retrieve the information contained on that piece of paper. So to me this information is lost irretrievably. From my reading of the literature (more pop science than technical papers) the consensus is information is never lost in a black hole, but is my simple experiment an example of the fact that information can be lost? How can any time reversal process ever possibly recover that five digit number?

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Information can be lost and it is even difficult to transmit. Imagine somebody who does not understand your joke. –  Vladimir Kalitvianski Nov 24 '12 at 18:40
    
It wasn't meant as a joke, I guess I was too vague and wanted to know how information is not lost in a black hole, thanks for replying –  jimmymc Nov 24 '12 at 18:42
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In principle, someone could reconstruct your 5-digit number, given all the information available at some time after the paper has been burned: all the photons, heated air molecules and ash and their positions and velocities.

In practice, of course this would be virtually impossible since it would require vast amounts of time and computational resources.

There is a difference between information being difficult to recover, and irretrievably lost. If the sheet of paper falls into a black hole, then classically the information is irretrievably lost i.e. it would be impossible to recover even in principle.

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Thanks Jason. My understanding is Hawking conceded information is not lost in a black hole, so I guess though not lost its in practice impossible to recover said information –  jimmymc Nov 24 '12 at 18:45
    
Yes, his theory was that quantum perturbations of the event horizon could allow information to escape from a black hole, thus it is not irretrievably lost. Rather than say "impossible", I would say "impractical" or "virtually impossible", to be more precise. :) Either way, I think this is still a subject of debate, e.g. see en.wikipedia.org/wiki/Black_hole_information_paradox –  Jason Davies Nov 24 '12 at 18:55
    
Cheers for the link Jason I thought the whole issue had been settled –  jimmymc Nov 24 '12 at 19:20
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