3 ms·

> This behavior is exceedingly non-intuitive, at least to me. I've been thinking about the notion of the Bekenstein Bound lately, and I'm not really sure how a

> This behavior is exceedingly non-intuitive, at least to me. I've been thinking about the notion of the Bekenstein Bound lately, and I'm not really sure how accurate the whole idea is. There seems to be a few problems with it, and I don't get the sense that it is a particurly heavily studied problem in the physics community (compared to something like general relativity or QFT). For one thing, nobody is certain that "actual" black holes exist. What I mean by this is a black hole where matter has actually fallen into it. Instead, the matter approaches the event horizon at an increasingly slower pace for an observer until at some point in time it is effectively frozen an infinitesimal distance from the event horizon (but still not in the black hole). In this sense, of course the information content is proportional to the surface area of the black hole. (I should note that mathematically, "effective" black holes and "real" black holes end up having the same properties and behavior; they'd be indistinguishable to an observer). Another problem with the Bekenstein Bound is that quantum states aren't localized to a volume of space. You can't just hold up a beach ball and say "What's the maximum information content of this beach ball?". Why? Because you can't just have a wavefunction of just "the beachball". It's a pretty good approximation, but what about the electron-electron correlations at the edge of the beach ball? And what if the spin of an electron within the beach ball is entangled with an electron outside of it? The information describing that particular quantum state is then delocalized.

Steuard 13y ago
Don't count on finding big misconceptions here: in fact, questions about black hole entropy and the Beckenstein bound are some of the most intensely studied topics in theoretical physics today. Not that we understand the answers! But these issues are very near the heart of questions about quantum gravity. As for your question about "actual" black holes, I think you may be missing some pieces of the puzzle, and I don't have the time to chat about them at length here. But one important point is that while outside observers may see infalling matter appear to stall out an infinitessimal distance from the black hole horizon, the standard classical or semiclassical result is that an actual infalling observer would pass through the event horizon without noticing anything special about it at all. (For a stellar-sized black hole, they would probably have already been ripped apart by tidal forces at that point ("spaghettification"), but that's unrelated to the horizon. For a truly massive galaxy-sized black hole where tidal forces are small at the horizon, the observer wouldn't notice anything special at all as she crossed the point of no return.) There is at this moment a massive debate raging in the particle physics community about whether quantum gravity effects might lead to a "firewall" at the horizon of a black hole that would change this story, but I don't think the question is settled yet. As for localization of quantum states and information, again, all I can tell you is that people have been studying those issues a lot, too. The details of entanglement of states inside and outside a black hole are closely tied in with the current "black hole firewalls" debate that I mentioned earlier, for instance. So don't make the mistake of thinking that the physics community has neglected this sort of issue!

Steuard 13y ago

Don't count on finding big misconceptions here: in fact, questions about black hole entropy and the Beckenstein bound are some of the most intensely studied topics in theoretical physics today. Not that we understand the answers! But these issues are very near the heart of questions about quantum gravity. As for your question about "actual" black holes, I think you may be missing some pieces of the puzzle, and I don't have the time to chat about them at length here. But one important point is that while outside observers may see infalling matter appear to stall out an infinitessimal distance from the black hole horizon, the standard classical or semiclassical result is that an actual infalling observer would pass through the event horizon without noticing anything special about it at all. (For a stellar-sized black hole, they would probably have already been ripped apart by tidal forces at that point ("spaghettification"), but that's unrelated to the horizon. For a truly massive galaxy-sized black hole where tidal forces are small at the horizon, the observer wouldn't notice anything special at all as she crossed the point of no return.) There is at this moment a massive debate raging in the particle physics community about whether quantum gravity effects might lead to a "firewall" at the horizon of a black hole that would change this story, but I don't think the question is settled yet. As for localization of quantum states and information, again, all I can tell you is that people have been studying those issues a lot, too. The details of entanglement of states inside and outside a black hole are closely tied in with the current "black hole firewalls" debate that I mentioned earlier, for instance. So don't make the mistake of thinking that the physics community has neglected this sort of issue!