"Work gives you meaning and purpose and life is empty without it." -Stephen Hawking
Throw a book into a black hole, and the information must somehow wind up inside. Same goes for a star, a planet, or even a single proton: that information must be maintained. But allow enough time to pass, and quantum theory and general relativity, combined, predict something troubling: that black hole will decay, and none of the information will come out in the decay products.
In physics, that’s what we call a paradox. Every individual quantum process affecting a particle and its interactions should be time-reversible, but if we run the clock backwards on black hole evaporation, that’s an impossibility. The worst part of the information paradox is that every proposed solution has problems that may be even greater than the paradox itself.
Hmmm, gets one thinking about the disappearing sock in the washing machine - sock in, no trace at end of spin cycle.
The Eater of Socks,.
Heh, heh, heh ....
Susskind's hypothesis is that the sock turns to lint that is smeared across the event horizon of the lint filter. The sock is still there, but there's no practical way to put it back together.
Now that's an interesting hypothesis; must tell my wife!
No, the lint is transported to everyone's belly button.
And, occasionally, to the corners of your sports bag.
sorry to stray from socks :D but one question..
it is sort of a variation on Sabine's no. 2 option... but here goes. What if there is no singularity but rather a supper dense state of matter... like a super-neutron star at the center of BH. And Hawking radiation doesn't evaporate BH into nothingness.. but at most can reveal a super dense core.. which will probably last as long as the universe, just like neutron star cores.
It would mean that there's either a force much stronger than strong nuclear or something can go faster than light. And possibly both.
@Sinisa #7: I think that could solve the information paradox, provided that superdense core can contain sufficient entities (particles or whatever) to encode the information content (i.e., entropy as ln(Nstates)) of whatever produced and felll into the BH in the first place.
Such a core would have a surface, which is inconsistent with the observable properties of a black hole (see, for example, the study of Sgr A* emissions from a couple of years ago). However, that core is presumably hidden behind the event horizon, and is therefore not visible. The EH is what behaves as the observed not-surface.
That won't work. I know I'm going counter what Michael Kelsey just wrote and he should mop the floor with me on all things physics related, but it doesn't solve the problem as far as I understand it.
The diameter of the EH is determined by the mass of the BH. It doesn't matter if the core is an infinitely dense point or an ultra-super-mega dense ball. Hawking Radiation shrinks the EH because BH (either singularity or superball) is also losing mass. At no point can the singularity or superball ever become naked. The superball would shrink in tandem and remain shrouded until it simply wasn't there.
The problem is in classical versus quantum models of gravity. In the classical version space-time is warped. Once you get inside a black hole space-time is so warped that all directions point toward the singularity. Information in the singularity CANNOT get back to the universe because there is no pathway for it to get back to the universe.
With a quantum theory of gravity, space-time is flat but movement is probabilistic with bias in the direction of mass. Once you get to the EH, the probability of moving toward the singularity is 100%.
The big difference there is that with things not effected by gravity, there *IS* a potential path back to the universe with quantum gravity where there is not with classical gravity.
Just blue-skying here...is the many worlds interpretation of QM relevant? Perhaps what we observe as the information-poor Hawking radiation coming from a BH is just a part of the BH's overall wavefunction, with the unobservable rest containing the information???
A more down-to-earth question: have we actually measured Hawking radiation from a BH? With all due respect to the theorists, we should probably measure it and see if they have it right before we get too worried about a paradox. We may have another 'ultraviolet catastrophe' on our hands here.
Not really, eric, MWI doesn't give us any out.
And BH hawking radiation is so miniscule for any BH that came from a full sized star that we wouldn't be able to find it if we were orbiting it.
yes, that scenario assumes some new force that would withstand infinite compression beyond strong force.
Like you mentioned in the end. This would still appear to be a point like object because the surface would be inside the EH. Small.. but not zero.
I feel there is a big difference between singularity and some small but still finite object.
You can't work with infinity. The reason BH go "puff" through Hawking is because inside mass radius (very unprofessional term) is 0. So once all mass radiates away... you're still left with 0. But if you have a finite object within the EH.. then the EH can't go smaller then it. If that object continues to loose mass it will just revert back to a star... or more likely explode.. But is an interesting mental image... as the gravity of BH get less and less.... as EH approached inner mass radius... light slowly is able to overcome gravity.. and that object starts to glow again.
All of it, of course, under the guess that it's not all doom once the strong force gives way....
SL, and that means it exists outside the black hole. And the superdense stuff would always be hidden (see denier's point), so we need to see that force and/or things moving faster than light before we can accept the idea that there's some ubersolid stuff uncompressed in a black hole's interior.
Until that point, it's not even a guess.
"it" being the greater than "strong nuclear force" force.
Denier's argument is (correctly) based on the Schwartzschild solution to GR field equations. But that solution assumes point like mass. An object i.e. half the size of a neutron star but 3 times the mass IMO wouldn't be correctly described by schwatrzschild metric. Thus the geodesics and light cones would behave differently.
If that object continues to loose mass it will just revert back to a star
^^^This is exactly why it doesn't solve the information paradox. If the BH lost enough mass to revert it back into a star, all the information about the lost mass has been lost. You're still losing information.
Information Paradox aside, classically speaking it can't work the way you propose. Ignore the ball versus singularity. I also believe there is a ball, but that ball cannot revert to a less dense state unless the "superball" (quark/preon/planck) degenerecy pressure is variable and evaporation somehow increases that pressure. There is absolutely nothing to support that idea. Theoretically the Earth could be a stable black hole if it were compressed down to the size of a pea. It is not raw mass that makes a black hole. It is density enough to overcome the neutron degeneracy pressure that does it.
"Denier’s argument is (correctly) based on the Schwartzschild solution to GR field equations. But that solution assumes point like mass."
But because of the square law of gravity and our three dimensions of space, any mass can be considered equal to a point mass at the centre of gravity, and similarly for GR, at least in gross. E.g.spinning or charged BHs unaccounted.
So they should still hold for most of the space inside the black hole and the matter inside would be well hidden.
If, indeed, in this universe, it could be considered to have actually fallen past the event horizon at all, yet.
re: information loss
As long as you have enough "something" left to encode the information in it's degrees of freedom within that super-ball i.e. quarks and gluons... then it doesn't matter if some of the initial BH mass has been shed... through Hawking or anything else.
"Theoretically the Earth could be a stable black hole if it were compressed down to the size of a pea"
" It is not raw mass that makes a black hole. It is density enough to overcome the neutron degeneracy pressure that does it."
It's the raw mass vs. the radius it occupies that makes it a BH. It is true that at those energies, the strong force also gives way. But BH is about curvature due to gravity.. not the colapse of nuclear force.
It’s the raw mass vs. the radius it occupies
There is a word to describe that: density
BH is about curvature due to gravity
Yes, but a BH comprises everything out to the EH. The superball/singularity *IS* about what happens to matter once the nuclear force has collapsed. You seem to be interchanging terms incorrectly.
it doesn’t matter if some of the initial BH mass has been shed
Not buying it. I'm sticking with Hawking, Susskind, and Sabine on this one.
after some digging (or research .. :D) .. did find this: Black Holes and Massive Remnants (page 9)
basically sums up what I was thinking.. and have to check and learn more about cut-offs. But is interesting to ponder...am not that happy it requires strings... sort of. In any case.. a nice dreaming.
this one is also interesting as a though experiment
"...we suggest that this is because the classical Einstein
theory of gravity is really an effective macroscopic description of a fluid. In other words, we propose that the classical Einstein equation only describes the "fluid phase" of some unknown fundamental degrees of freedom. If so, then the "crystal phase" cannot be described by quantization of the Einstein-Hilbert action, implying that the
Einstein-Hilbert action is not fundamental. Roughly, this is analogous to the fact that ice cannot be described by quantization of a non-fundamental macroscopic fluid
equation, such as the Euler equation or the Navier-Stokes equation. The transition from the fluid phase (described by general relativity) to the crystal phase (described
by as yet unknown theory) occurs via a phase transition..."
tough this sounds to me that if it's case... then we can really say space-time is real.. as real as any solid :)
The notion that information is not lost seems inconsistent with black holes. To use the example in the blog, when a book burns it emits particles that disburse. If a photon, for example, enters a black hole, then that information represented by the photon is not available, such that the book cannot, even theoretically, be reconstructed.
This assumes that Hawking radiation actually is random information, and that the black hole remnant does not retain the information.
@t marvell: Yeah, that's the crux of the controversy. On the one hand, quantum theory says that information can't be lost. On the other hand, relativity says that nothing can be seen again once it goes behind an event horizon. There's an inconsistency between theories that needs to be reconciled.
But General Relativity says that from this universe's point of view, nothing gets past the event horizon in anything less than infinite time.
I wonder if the entropy of the bit of the star inside the event horizon when it reached black hole density also just happened to be the same as the entropy from the surface of the black hole to create a gap for Hawking radiation to appear.
I also whether I've just restated the idea of Hawking radiation's derivation....
information can be turned into energy, but can the information later be deduced from the energy? What happens when a particle carrying information collides with its anti-particle? I'm just a no-nothing layman, but this notion of conservation of information seems wrong.
When you whip eggs, can you find the original egg in the resulting batter?
I think BHs must be preserving information somehow. Conservation of energy is the most fundamental law of physics. There is no single experiment nor observation in the history of physics breaks it. And if you think about it, conservation of energy is really conservation of information. Can we really expect BHs would break it?