Why the black hole information paradox still hasn’t been solved
No matter what you do in the Universe or how you do it, the overall entropy within our cosmic horizon always increases. Even when we go through the effort to put things in order — assembling a puzzle, cleaning our houses, even (yes, it’s possible) unboiling egg whites — it will still only be the local entropy of that one isolated component of the total physical system that decreases. In order to accomplish these feats, we have to expend energy, and that expenditure of energy will actually increase the total entropy of the entire cumulative system by a greater amount than the “ordering” process decreases it. As a result, the total entropy always goes up.
From another, equivalent perspective, the total amount of information in a physical system can only stay the same or increase; it can never go down.
But for black holes, there’s a paradox which arises, as this “information preservation, or increase” doesn’t appear to necessarily be the case. If you throw a book into a black hole, that book contains all sorts of information: the order of the pages, the text contained on them, the quantum properties (like baryon number and lepton number) of the particles making up the pages and the cover, etc. That information goes into the black hole, adding to its mass/energy and increasing the size and surface area of the black hole’s event horizon. Much later, when the black hole decays via Hawking radiation, that energy comes back out, but the information encoded in that radiation is predicted to be totally random: it’s as though the book’s information has been erased. Despite ongoing claims that this paradox, the information paradox, has come to an end, it still remains very much unsolved. Here’s the science of what’s really going on.
