In this thread, Lib suggests that if information can escape from a black hole (a la Hawking’s conceded bet), then the logical consequence of this is that spacetime cannot be infinitely curved at the centre of a black hole, ie. that information escape logically precludes the existence of singularities. I suggested that this was a non sequitur, and that Hawking’s bet pertained to the information content of the entire volume within the event horizon, not just the very central point, and so whether information is ‘destroyed’ at the very central point is irrelevant. I referenced p.114-116 of The Universe In A Nutshell in which Hawking discusses the destruction (or not) of information whilst still referring to singularities throughout, even in the case of information re-emerging.
So, for those amongst us versed in such matters, would escape of information from black holes logically preclude the existence of singularities?
According to Roger Penrose in chapter 30.8 (p840) of Roads to Reality the jury is still out on this and there are 3 options.
Information is lost when the BH evaporates
Information is stored in a remnant after the BH evaporates (although he does not actually state it I suspect that this option implies some kind of naked singularity)
All information contained in the BH is returned in the evaporation.
Penrose himself prefers option 1.
To a large extent the arguments is purely theoretical and unlikely to ever be determined fully as even a 1 solar mass black hole will take approx 10[sup]16[/sup] years to evaporate and the majority of BH’s are postulated to have amuch greater mass than this.
So by the time BH’s do start to evaporate there may be nothing for them to evaporate into, especially if we do experience a “big rip” or similar.
Personally I suspect that Penrose is correct, any information that enters a black hole would be lost. Even when the mass of the black hole returns to the outside universe as radiation the information it contains would not be the same as the information that went in to the BH.
I agree with you that Hawking radiation is an effect that occurs just outside the event horizon and that it would not preclude the existence of singularities.
For the record, there are actually two premises that compel the conclusion: (1) that the amount of information going into the black hole and coming out is exactly the same, and (2) that black holes are thermodynamically stable; i.e., that entropy continues to increase inside them.
The reasoning goes like this:
The singularity is one point of infinite spacetime curvature. The singularity is in the center of the black hole. One point of infinite spacetime curvature is therefore contained within the black hole. (From the definition of singularity.)
The mass/energy within the singularity cannot be infinite. If it were, it would consume the rest of the universe. But it must be infinitely dense, because its volume is zero. (From General Relativity.)
As such, the singularity cannot be a part of our universe, since physical law is everywhere the same. It must therefore be a gateway to some other universe. (A premise of both Special and General Relativity, and our second premise.)
Hawking has conceded that, “[If] information is preserved, there is no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will be returned to our universe, but in a mangled form. [It will] contain the information about what you were like, but in an unrecognizable state”. (Our first premise.)
If there is no gateway to other universes, and a singularity is a gateway to other universes, then there is no singularity. (By modus tollens.)
QED
There might be a point that is really really dense, but no point that is infinitely dense.
No gateway for a macroscopic object, Lib - he is still not saying that there can’t be an infinitessimal point of infinite curvature (whose “information content” does or does not affect that of the entire volume or that of the body you’re trying to shove through a ‘gateway’).
If I may suggest, let us two sit back and see what factual answers come in to this General Question.
Yes, but I don’t want my statements to be misrepresented, however unintentionally.
I have never said that Hawking drew the same inference. In fact, I have specifically said that he did not — on account of the fact that he is not a logician or philosopher. What I am saying is that the conclusion is inescapable no matter who says what, given the two premises. What is required now to debunk the conclusion is to find a flaw in the tableau, not to cite Hawking. Hawking was cited in the premises.
Perhaps it is best if this is moved to Great Debates since, for whatever bizarre reason, predicate logic is not considered something “factual”.
Again, I suggest that we two simply stay out of this thread for a couple of days and see what happens here. If it becomes inappropriate I’ll ask for it to be locked.
So that people have a better idea of what some of the various arguments are, I suggest the following article from New Scientist.
What this suggests to me is that Lib and SM are asking the wrong question. Information may survive a singularity or the singularity may not exist in the first place. Either way it seems likely now that the Hawking-style singularity will not be the final interpretation.
A true relativist like Chronos will speak on the issue properly (I hope), but, unless I’m very wrong, you simply can’t have infinite curvature of space and a mathematically-consistent description of what happens in such a situation. A singularity, by definition, is not a mathematically-definable object, and hence it’s not possible to calculate anything about what happens to matter once it is “swallowed” by a gravitational singularity.
So, any attempt to resolve the “information paradox” with the hope of some answer other than a question mark is, by necessity, predicated on the notion that infinite space-time curvature is not a physically realistic phenomenon, and that matter within a black hole exists in some state that is finite in spatial extent (though whatever’s in there could be very, very, very tiny, and hence stupendously dense).
That some “nugget” of superdense matter exists at the center of a black hole is, in the absense of a complete theory of quantum gravity, conjecture. I don’t think there are many physicists out there who doubt the basic premise of the conjecture, but it cannot be said that the issue is presently resolved in any satisfactory way.
I guess I should follow up (in my completely non-expert way) by saying that if physicists are actually trying to calculate something about information coming out of a black hole, and still talking about “singularities”, they are using the term out of habit or convention, and in this case, it is a misnomer. Whatever lies beyond the event horizon, if it is calcuable in any other way than to render some physically meaningless variety of infinity as the answer, it is not a singularity, by definition. Maybe some of the physicists are just calling it a singularity because they imagine whatever it is is a pretty tough thing to deal with computationally, anyway. I’ve read that Hawking’s initial work on black hole evaporation, which, if I understand things correctly to the extent that I can, involves using QFT in curved (albeit still a fixed metric) rather than flat space, was a terribly daunting exercise. Perhaps increasing curvature more and more makes things progressively more daunting, I don’t know. Anyway, whatever this non-singularity thingy is, it’s not described by any tested theory, and hence people can only make educated guesses about what’s going on.
I think, regardless of what you say about the existence or non-existence of “real” singularities in nature, this is still not an entirely correct statement. There’s nothing especially strange or intractable about physics on one side of an event horizon or the other, especially as the mass of the black hole in question gets bigger. Information (meaning, in this case, what you can know in principle about all the states of the quanta that make up the system, which amount to the answers to all the yes/no questions you can ask about the system) is not destroyed beyond the envent horizon, in Hawking’s semi-classical description of black-hole evaporation; it’s potentially destroyed at the singularity, because singularities destroy everything, even your ability to say anything meaningful about them. In the centers of some galaxies are black holes so massive you wouldn’t know it if you passed the event horizon or not, except if you tried to get away; but all that defines that transition is the breach of a 2d surface deliniating all the orbits requiring a velocity of c to maintain. Otherwise, it’s business as usual until, in your inevitable future, you get close the singularity, in which case, if it is a singularity, what happens to you is ultimately unknowable. If it isn’t unknowable, then it’s possible, in principle, to say what might have become of all that information.
The maximum entropy (S) of the system, by the way, is defined as some constant K multiplied by the natural log of “omega”, a term which itself is just a tally of all the possible states of the system. All the laws of thermodynamics say the entropy of the system should increase; but as a classical gravitational singularity lasts forever, that can’t happen. Bekenstein and Hawking showed that the entropy of the black hole must increase (unless GR and QFT are very wrong, and those are so well-tested there’s no good reason to doubt the consequence of the semi-classical marriage of the two to describe quantum phenomena in curved spaces). That means “information” is leaking out of the black hole. But has that information been so randomized by the “singularity” that nothing about the original state of quanta that encountered it can be recovered? In principle, if you can calculate what happens at the point of highest curvature in a black hole, you may be able to recover at least some of that information. It’s still an open question (though I guess not open enough, in the mind of Hawking, to prevent him from conceding the bet).
I’ve dreampt up a thought experiment. I don’t know how physically meaningful it is, so I’m hoping one of our experts shows up to either endorse it or smack it down.
Anyhoo, imagine a particle in the vicinity of an evaporating black hole (which they all are, I guess).
Let’s think about information, as it pertains to this particle: Does it have mass? Does it have integer or fractional spin? Is it a lepton or a quark? Is it charged? Is the charge positive or negative? Is it a whole unit of fundamental charge, or a fraction of one? And so on.
Now that I’ve answered all the requisite questions, I can say it’s an electron.
Now, the electon is on a shallow trajectory that takes it just inside of the event horizon; but as the EH is receding due to the evaporation of the black hole, the region of space the electron finds itself is now suddenly on the outside of the EH, and it becomes observable again. In principle, if the electron didn’t interact in any truly strange way with something inside the EH, all the information (which is the collection of everything you can possibly say about the electron in terms of those yes/no questions) is preserved quite intact.
Now, what if we’re talking about another electron, which encounters the region of highest curvature beyond the EH? Eventually the BH might evaporate, leaving not a trace but escapees in a similar situation to the electron in scenerio above, and Hawking Radiation. Is the information about the unlucky electron recoverable? Is it perhaps somehow encoded in the Hawking Radiation? I’m pretty sure those are the big unanwered questions.